Multi-product firms, markup adjustment and import competition
By Boris Georgiev*
This paper studies the pro-competitive effects of increased import competition
on product-level markups, using highly disaggregated data on Danish manufacturing firms in the period 1999-2012. In the past 20 years, import shares have
gradually increased across time, sectors and trading partners of Denmark, especially after China’s the accession in the WTO in 2001 and deeper integration of
the member states in the EU. Denmark has also experienced increasing imports
from other European countries as well further contributing to a more competitive
landscape for Danish manufacturing firms on the domestic market. Previously,
the literature has studied firm-level outcomes of import competition without taking into account the potential heterogeneity in markup responses and product
level adjustments across multi-product firms. More than half of all Danish manufacturing firms produce more than one product and these are responsible for
the majority of industrial output. Thus, studying the within firm markup effects
stemming from intensified import competition has important policy implications
as firms adopt different strategies along the product ladder. The results suggest
that import competition has a differential impact across products within a firm
and is negatively correlated with product level markups, lending strong support
for pro-competitive effects even at the product level. On average, an increase
by 10% points in the Danish manufacturing sector during the sample period,
leads to a reduction of markups by 3-6% on average and after instrumenting
- by up to 16-20%. Following an increase in import competition, firms adjust
the markups of their core products more relative to their peripheral products.
These observations are consistent with theoretical models of multi-product firms
with variable markups where core products have the highest markup and thus
have greater room for adjustment relative to peripheral products. These findings
uncover a previously unexplored layer of within firm heterogeneity and informs
about have crucial policy implications as they suggest that import competition
has heterogeneous effects not only across firms but also within firms.
JEL: L10, L15
* Aarhus University, School of Business and Social Sciences. E-mail: [email protected]. I am grateful to Philipp Schröder,
Frédèric Warznyski, Kerem Cosar, Ariell Reshef, David Jinkins, Esther Ann Bøler, Marcel Smolka, Florian Mayneris,
Kaleb Girma Abreha, Martin Alfaro and the participants at the Danish International Economics Workshop 2016 in
Aarhus for the useful discussions and comments. Many of their suggestions have been incorporated in the current draft
of the paper. The financial support of the Tuborg Research Centre for Globalisation and Firms is greatly acknowledged.
1
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I. Introduction
The ongoing process of globalization has allowed countries to integrate deeper in terms
of trade. This has led to gains but also loses for consumers and businesses. On one hand,
consumers benefit from greater access to more varieties of goods and lower prices. Firms, on the
other hand, get the opportunity to serve more markets by exporting part of their production,
increase the residual demand for their products and additionally source inputs from the global
market. With the rise of many developing countries and the emergence of various trade
agreements, many policymakers and academics have questioned the different margins through
which these welfare gains occur and especially how the developed world has responded to the
increased competition due to globalization and trade. Imports across countries, firms and even
products have been on a positive trend across most developed countries and Denmark is not an
exception in that respect. Much of the production in high wage countries has been offshored
to labour-abundant countries, which offer significant cost savings and domestic employment in
manufacturing has been steadily declining as documented by Ashournia, Munch and Nguyen
(2014) and Bernard, Smeets and Warzynski (2016). An important question in this regard is
how firms producing domestically react when faced by intensified import competition and how
firms cope with such changes in the operating environment.1
This paper is concerned with the competitive effects of import competition on productlevel markups and the important role that multi-product firms play in the economy. Stylized
facts across many countries, including Denmark, suggest that around 50% of firms are multiproduct and these firms are responsible for the a very large fraction of aggregate production
and employment in the manufacturing industry. Naturally, when a firm has several product
lines it needs to optimize to optimize its pricing, markup and quality decisions for each product
individually in their portfolio as most firms produce different products that compete in separate
markets and face different competitive pressures. On the other hand, multi-product firms
manufacture diverse products with different capability and quality, which suggests that there
are important heterogeneous effects within the firm and across products, which have important
implications when quantifying the gains from trade. These microscopic adjustments along the
intensive and extensive margins are an important area of research, because portfolio changes
within affect aggregate outcomes, such as firm survival, product churning, employment growth,
innovation and firm profitability. Product-level effects and within firm heterogeneous effects
so far have not been investigated in depth, which motivates the research agenda of this paper.
Unless researchers get a deeper understanding of the dynamics “below the surface” of firm,
this leaves the implicit assumption that competitive effects dissipate homogeneously across
workers and products within firms. the impact of import competition may be heterogeneous
1 Throughout the paper the terms “import competition” and “import penetration share” are used interchangeably and
are meant to capture the role of imports relative to domestic manufacturing output.
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MARKUPS AND IMPORT COMPETITION
3
along the firm’s portfolio. Recent theoretical models have put forward the idea that multiproduct firms possess superior expertise in manufacturing their core product - usually the most
important product in terms of sales for the firm (Eckel and Neary, 2010; Bernard, Redding
and Schott, 2010; Mayer, Melitz and Ottaviano, 2014). The further away the product from
the top performing product, the less productive the firm is in manufacturing it. In frameworks
with variable markups (Melitz and Ottaviano, 2008; Mayer, Melitz and Ottaviano, 2014),
the markup depends on the elasticity of demand, which is precisely the channel from which
import competition can affect products. Eckel and Neary (2010) and Mayer, Melitz and
Ottaviano (2014) offer extended frameworks where multi-product firms are incorporated and
that feature variable markups due to internal specialization. In this class of models, firms have
heterogeneous productivity along their portfolios featuring a product ladder. The core product
is also the one with the highest markup e.g. the most profitable for the firm as it can produce it
at the lowest marginal cost relative to all other goods in the portfolio. The theoretical models
on multi-product firms offer a wide range of testable hypotheses regarding the behavior of
firms and their products. In particular, since core products have bigger markups, this offers
more scope for downward adjustment when firms face import competition relative to peripheral
products at which they are not as productive. Hence, firms should be more sensitive to import
competition in their core competency products. Along this line of reasoning, core products are
also the most important ones for firms as they generate most of the revenue. This suggests that
the role of these top-ranked products is more important than peripheral goods. Taking into
account the empirical facts regarding the pervasiveness of multiproduct firms both in domestic
and international markets, suggests that the effects of import competition may not be identical
across products within firms. Studying the product-level responses of markups would not be
relevant in a world where there is no vertical differentiation but only horizontal and where
firms charge the same markups across each individual product. However, the ample evidence
on the link between product quality and multi-product firms suggests that firms sell products
of different qualities and produce them with a varying degree of productivity, using different
inputs and ship them to markets with different tastes for quality differentiation (Manova and
Zhang, 2012a,b). By not taking into account the product-level margin of adjustment important
heterogeneous effects may be missed out. This paper aims to fill this gap and shed light
on how firms adjust markups across their product portfolio in response to tightened import
competition using the highly disaggregated data from the Danish manufacturing industry.
This research article speaks to several rapidly developing strands of the literature. On one
hand, it is concerned with the pro-competitive effects of international trade. In recent years,
numerous studies have focused on different firm performance measures and margins along
which import intensity affects firm-level outcomes. Recent empirical work has emphasized
that firms adjust across several margins when faced with tougher competition. For example,
firms may increase innovation activity in order to differentiate themselves and bring better
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products to the market (Aghion et al., 2005), invest in technology upgrading Bloom, Draca and
Van Reenen (2016), change the nature of investments along the product portfolio (Dhingra,
2013), productivity (De Loecker, 2011; Dhyne et al., 2015; De Loecker and Van Biesebroeck,
2016), upgrade the quality of its products (Amiti and Khandelwal, 2013), reduce employment,
shut down operations (Mion and Zhu, 2013; Utar and Ruiz, 2013; Ashournia, Munch and
Nguyen, 2014; Utar, 2014; Dauth, Findeisen and Suedekum, 2014), alter the financial terms of
trade (Demir and Javorcik, 2014) or finally adjust markups (De Loecker et al., 2016; Meinen,
2016). The latter study focuses on the import competition effects from the rise of China
on firm-level markups for Danish firms. He finds that markups are negative correlated with
import competition. Other papers studying the relationship between firm-level markups and
trade liberalization are Liu and Rosell (2013), Liu and Ma (2015) and Lu and Yu (2015), where
they find that trade liberalization disciplines market participants by reducing the dispersion
in markups and provide evidence for pro-competitive effects. One the other hand, the paper is
also related to the growing empirical literature on multi-product firms, which aims to explore
the within firm margins of adjustment in response to trade liberalization. Manova and Zhang
(2012b) study the link between multi-product firms and quality choices. They find that companies’ most important products are also of superiour quality and emphasize the import role
that quality differentiation play in multi-product firms. The current paper is closely related
to the work of De Loecker et al. (2016), who offer a structural framework for the estimation of
product-firm level markups and relate them to the tariff liberalization period in India. They
find that the drop of input tariffs had a positive effect on markups by lowering marginal costs
and a pro-competitive effect coming from the output tariffs channel.
The current paper extends the state of the literature in several ways. First, it contributes
to the literature on markup responses to import competition by undertaking an empirical
investigation of how markups react to the increasing import competition both from developing
countries but also from the developed world where greater trade integration has allowed further
increases in trade among countries. The core focus lies on multi-product firms and the markup
adjustment strategies that they undertake facing a tougher competitive environment. So far
most empirical studies have addressed the margins of adjustment to import competition at
the industry, firm or worker-firm level at most. However, it is important to recognize that
these investigations may not be telling the full story. One reason is that import competition,
per se, affects the sales, availability of goods and naturally markups are set at the product
level and not at the firm. This is where the current paper departs and offers novel findings
about the inner margins of markup adjustments of firms. With the ongoing improvements in
data availability at highly disaggregated levels and the advancements in empirical methods,
a wealth of new questions can be addressed in the context of multi-product firms and the
strategies that firms adopt to counteract the increased competitive forces. The distinction
between single and multi-product firms is important as firms that have more than one product
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5
in their portfolio may adjust their markups differently depending on their core competency and
degree of product differentiation. Second, multi-product firms are bigger, earn higher revenues
and serve more markets. These facts suggest that firms with many products in their portfolio
represent the lion’s share of total domestic output in terms of value calls for special treatment
of this type of firms. Hence, understanding what adjustment strategies firms undertake is
highly important for understanding the welfare effects from import competition.
To preview the results, I find that intensified import competition is negatively related to
product-firm level markups as inferred by economic theory. The estimated parameters predict
that a 10% percentage point increase in import competition within a product category, leads to
a markup reduction of around 3-6% on average. Adopting the instrumental variable strategy
to account for the potential endogeneity of import competition does not shift the sign of the
effect, but increases the magnitude of the effect - a 10% points increase in import competition
causes firms to reduce markups on average by 15-20% depending on the specification. Most
importantly, the results reveal substantial response heterogeneity along the product ladder
within firms. Heterogeneity in markup responses at the product level suggests that firms’ core
products are way more sensitive in terms of markup adjustment relative to peripheral products
in the portfolio and core products suffer a greater decline in markups than peripheral ones.
These are novel findings, which have not been explored so far in the literature. These results
remain robust to alternative specifications of import competition in terms of product scope
(CN8 vs. CN6), timing assumptions regarding the potential effect, product differentiation and
different time-varying controls. I run several specifications of the main econometric model,
where I exploit variation within firms across products; within narrowly defined products across
manufacturing firms and finally a highly demanding specification where only variation within
a given product-firm pair is used to identify the coefficients of interest.
The remainder of the paper is structured as follows. The next section introduces the data
used in the empirical analysis. Section III introduces the methodology for markup estimation
at the product-firm level. Section IV presents the results of the empirical analysis and provides
evidence for within-firm markup adjustments at the product level. Section V conducts a
battery of robustness checks that support the main results and do not alter the main findings.
Finally, section VI concludes the paper.
II.
Data
This section presents the data used to build the sample of manufacturing firms in Denmark
and conduct the empirical analysis for the period 1999-2012.2 According to the official industry classification of the EU - NACE, the manufacturing sector encompasses all firms belonging
to the codes 10-33 in the 2-digit NACE Rev. 2 classification. These separate industries can
2 Appendix
A provides detailed information on the applied data cleaning procedures to obtain the final sample.
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then be further aggregated to a 2-letter NACE classification, which is the preferred industry
definition used in the analysis as it encompasses more firm observations and still makes a clear
distinction about firms operating industry.3 Focusing on import competition and markups at
the finest level of disaggregation requires the use of product-firm level information linked together with firm-level variables. To this end, four separate data sources are combined together.
Three of the datasets comes from register-based databases provided by Statistics Denmark and
one by the UN and the French Research institute CEPII.
A.
Data description and sources
Information on product manufacturing and sales (both domestic and to export markets) are
obtained from the VARS database, which is equivalent to PRODCOM. The database covers
around 60% of the manufacturing firms in Denmark, which generate more than 90% of the
manufacturing output in the country. The reason behind this partial coverage is that not all
firms are required to report sales if they are below a sales and/or employment threshold. The
included variables are the product name, sales value in thousands of DKK and quantity in
various measurement units, all reported at the 10-digit Combined Nomenclature (CN) product
level.4 I concord the products to the 8-digit level in order to be able to match the product
information with the trade dataset. The availability of sales value and quantity for a given
product allows to compute product unit values, which are used as proxies for product prices.
An important caveat in the panel dataset is that the CN is subject to annual revisions, where
certain products change classification code from one year to another. To properly account for
these changes across time, I follow the procedure by Beveren, Bernard and Vandenbussche
(2012), which ensures that a specific good is reported with the same unique product identifier
across the different revisions, accounting for temporal changes. This procedure ensures that
a change in the CN code of a good is not erroneously interpreted as product dropping or
introduction of a new good. If a firm produced a good that has been revised in the following
year, then it would appear as if that firm dropped the product from its portfolio where in
reality it has simply been a change in the classification code. This feature is crucial for
the identification of single product firms across time because in the estimation of production
functions I rely on single product firms that manufacture the same product for at least 2-3
years. Ignoring these crucial aspects of the data introduce a severe bias and would erroneously
discard many single product firms from the sample due to year-to-year changes in the CN
codes. After implementing the concordance from 1999-2012, more than 56% of the product
codes in the sample have switched codes. In the VARS database all manufacturing firms are
3 The
mapping between the two classifications is shown in Eurostat (2008), pp. 44.
fact that the total production data is reported following the CN classification is a rare feature. For example,
Amiti, Itskhoki and Konings (2016) and Dhyne et al. (2015) use the Belgian PRODCOM where products are reported at
a more aggregated classification (PC) compared to CN. This feature leads to issues in the mapping between production
data and exports as not all CN8 codes have equivalent PC8 entries. In this paper, the trade data from UHDI is reported
under the CN system, which facilitates the cross-sectional match between the two databases.
4 The
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MARKUPS AND IMPORT COMPETITION
7
identified by a unique ID code, allowing me to link this dataset to the firm-level variables
necessary to estimate markups.
The balance sheet and accounting data are reported at the firm-level and come from FIRE.
This dataset covers the universe of Danish firms and provides information on firms’ industry
affiliation according to several NACE classifications, total revenue, value-added, wage bill,
number of employees, material purchases and capital. All the variables are reported in DKK
except for the number of employees, which are given in physical units. The NACE Rev. 2
industry codes are only available from 2000 to 2012. The sample coverage is extended to 1999
by tracking backwards manufacturing firms in 2000 that existed as well in 1999. The same
unique ID from VARS allows me to link the two databases and only keep those firms that are
present in both datasets.
The third data source is the UHDI database, which covers the universe of all import/export
product transactions undertaken by Danish firms. The researcher can observe the source/destination
country, the import/export value in DKK, quantity in various supplementary measurement
units and weight in kilograms by each firm at the 8-digit CN product level. This database
allows me to compute the share of total imports by product that each country has. It is important to note that firms face competition in a given product not only from other manufacturing
firms but from all firms in the economy, such as retailers that import and sell similar goods.
Thus, one needs to take into account the entire universe of imports flowing into the domestic
economy and not only those undertaken by manufacturing firms. Similar to the approach
in VARS, the product codes are concorded across time to ensure the consistent treatment of
goods that undergo changes in their product codes. The importing and exporting activity of
Danish manufacturing firms can be identified using the same unique firm-level ID.
Finally, to implement the instrumenting strategy, I make use of the BACI trade dataset
provided by CEPII. It builds on the UN COMTRADE database and reports all imports and
exports among all country pairs at the 6-digit HS product level. In essence the HS and the
CN product classifications are equivalent up to the sixth digit. The trade flows from 1999
to 2012 are available at the 6-digit code, HS Rev. 1996. I map the HS codes to their CN8
counterparts and ensure that all the flows at the product level can be matched.5 To combine
this data with the information from UHDI requires matching the CN8 to HS codes. The
product codes have not changed at the 3- and 4-digit level. Given the equivalence of HS and
CN, the BACI dataset can be used to construct instruments to mitigate potential endogeneity
concerns related to import competition measure at the product level. Therefore, the product
information according to the HS and CN classification can be linked together to construct the
instrument - World Export Supply (WES) of all countries excluding Denmark as importer and
5 All the world imports and exports from 1999 to 2012 in BACI are reported in according to the 6-digit HS classification
following the revision in 1996. Hence, the product codes are consistent across years even without concording them to the
HS+ classification, proposed by Beveren, Bernard and Vandenbussche (2012). Appendix A describes in further detail the
concordance strategy across all datasets.
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exporter country.
After cleaning and matching the first three datasets, Table 1 reports the industrial composition of the sample and offers several key statistics. First, the “Food products, beverages
and tobacco products” industries represent the highest share in terms of total value in the
sample as a Denmark is a leading producer in Europe in those fields. For the average year
in the sample, around 2,200 firms are present in a cross section, manufacturing close to 3,400
unique 8-digit CN products. Slightly more than 50% of all firms in a given year of the sample are single product firms and remainder manufacture multiple products. The distribution
is heavily skewed as the top 25% of the distribution comprises of very large firms with big
portfolios, which are responsible for a big share of output in their respective industries. The
“Basic metals and fabricated metal products” industry features the greatest number of firms,
but in terms of value this sector is only the third largest in the sample. In terms of product
diversity, the first two industries in Table 1, unsurprisingly manufacture the greatest number
of unique product varieties. One potential issue is the low number of single-product firms in
CB and CE, as this makes it difficult to estimate the parameters of the production function,
which are also obtained by NACE 2-letter industry aggregation.
Table 1—Sample descriptive statistics by NACE 2-letter product industry grouping for the average year
NACE 2-letter manufacturing product industry
Output share
# of
# of single-
# of unique
out of total
firms
product firms
CN products
CA - Food products, beverages and tobacco products
33.3%
263
76
1,055
CB - Textiles, apparel, leather and related products
3.1%
97
30
590
CC - Wood and paper products, and printing
4.8%
201
110
91
CE - Chemicals and chemical products
5.9%
88
26
406
CG - Rubber and plastics products, and other non-metallic mineral products
8.2%
232
118
201
CH - Basic metals and fabricated metal products, ex. machinery and equipment
8.6%
500
298
357
CI - Computer, electronic and optical products
4.8%
90
62
127
CJ - Electrical equipment
4.5%
131
91
134
CK - Machinery and equipment n.e.c.
14.8%
291
196
269
CL - Transport equipment
2.3%
55
43
65
CM - Other, repair and installation of machinery and equipment
9.8%
302
192
122
100%
2,249
1,241
3,417
Note: This table shows how the different 2-digit NACE Rev. 2 industry code map into the Danske Branche (DB07) classification. The NACE Rev. 2
and DB07 are equivalent but the 36 industry grouping is developed for the Danish manufacturing sector. The estimation of the production function
for single product firms is performed by 2-letter industry code, which ensures that enough observations are present throughout the entire sample
period from 1997-2007. From the list above 2 sectors - 19 and 21 (CD and CF) are dropped due to insufficient number of firm observations. The
excluded sectors cover “Oil refinery” and “Manufacture of pharmaceuticals”, respectively.
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B.
9
The manufacturing sector in Denmark and the rise of import competition
Denmark has enjoyed the benefits of its strong focus on innovation and quality, which helped
the country maintain its leading position in many manufacturing industries e.g. industrial
equipment, textiles, furniture, chemicals and consumer goods. Overall, the products of Danish
manufacturing firms can be described as high quality and heavily branded with Denmark as
the country of origin. To a large part this has kept much of the manufacturing activity
within domestic boundaries. However, since the 1980’s a gradual shift towards offshoring to
countries with cheaper manufacturing costs has taken place, leading to a gradual decline in
employment and number of manufacturing firms in favour of increased economic activity within
services. Recent evidence of these dynamics are studied by Bernard, Smeets and Warzynski
(2016) who provide evidence that many firms switch their industry affiliation towards services.
The increasing competitiveness and market access of many developing countries and new EU
member states have also helped accelerate these industrial shifts. First, lower trade costs
have contributed to an increase in both importing and exporting. Second, countries have
become more interconnected through different economic arrangements such as FTAs, RTAs
and Customs unions, which naturally boost trade among members states. Third, nowadays a
big part of trade is in intermediate inputs where wider access to inputs has allowed firms to
lower their costs of production but has also exposed domestic intermediate input manufacturers
to more intense competition. The same has been the trend for the imports of final goods, where
they have increased substantially, leading to a greater choice for consumers but also tougher
competitive environment for Danish producers.
To understand the changes in import patterns that have occurred in the past 15 years,
Table 2 reports the 20 most important import partners for Denmark, their respective rank
and import share in value terms from the start of the sample period in 1999. In line with
the vast literature on trade, exploring the factors affecting trade intensity among countries,
Denmark imports more from neighbour and culturally similar countries such as Germany,
Sweden and the Netherlands. A vast majority of the countries are also EU member states
and part of the Single market. Germany stands out as the most important trading partner
and has kept its dominant rank throughout the sample period. It is clear that the rankings
and import shares of many developed European economies and Japan have declined or at best
remained unchanged relative to 1999. For example, until 2003 Poland had a constant import
share but after joining the EU in 2004, its trade intensity has sharply risen leading to almost a
doubling in its import share. Among the countries in Table 2, China clearly stands out. After
its accession to the WTO in late 2001, the country obtained its most-favoured-nation status
and ever since has seen an explosive export growth to the rest of the world and Denmark
has not been an exception in that regard. China has almost tripled its import share and has
established itself as one of the most important sourcing countries for Denmark.
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Table 2—Top import partners for Denmark
Country
Germany
Sweden
The Netherlands
Great Britain
France
Italy
USA
Norway
Belgium
Finland
China
Japan
Poland
Spain
Switzerland
Ireland
Austria
Taiwan
Portugal
Russia
1999
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2000
1
2
4
3
5
7
8
6
9
11
10
13
12
14
16
15
18
19
22
20
Rank
2003 2006
1
1
2
2
4
3
3
5
5
7
7
8
10
10
6
6
9
9
11
12
8
4
21
20
12
11
13
13
17
17
15
15
14
16
22
22
23
29
18
14
2009
1
2
3
5
7
9
10
6
8
13
4
28
11
14
15
16
18
30
31
21
2012
1
2
3
5
10
7
11
6
9
12
4
33
8
13
18
15
17
26
31
19
Cumulative:
1999
21.7
12.3
8.0
7.9
6.0
4.7
4.6
4.4
3.5
2.8
2.7
2.0
1.8
1.4
1.3
1.3
1.1
0.9
0.8
0.7
89.9
Import share in
2000 2003 2006
21.3 23.2 21.9
12.5 13.0 14.5
7.5
7.0
6.3
8.6
7.0
5.3
5.1
4.9
4.5
4.2
4.2
4.0
3.9
3.0
3.2
5.1
4.5
4.6
3.3
3.5
3.4
2.8
2.3
2.3
3.0
3.8
5.4
1.5
0.8
0.9
1.8
1.8
2.3
1.4
1.7
1.9
1.2
1.1
1.1
1.3
1.2
1.2
1.1
1.3
1.1
1.1
0.8
0.8
0.7
0.6
0.4
0.9
1.1
1.5
88.3 86.8 86.6
%
2009
21.3
13.3
7.2
5.9
3.5
3.4
3.2
5.4
3.5
1.7
6.8
0.5
2.7
1.4
1.1
1.1
1.0
0.5
0.5
0.8
84.8
2012
21.4
13.3
7.5
5.7
3.1
3.7
2.5
5.4
3.1
1.7
7.2
0.4
3.3
1.5
0.9
1.2
1.0
0.5
0.4
0.9
84.7
Note: The country rank and import share evolution is based on the universe of trade transactions reported in the UHDI database across 3-year
intervals. The countries are sorted in a descending order according to the country’s trade rank in 1999. The cumulative import share of all 20
countries do not sum exactly to the percentages in the last row due to rounding.
Finally, this subsection takes a look at the composition of the Danish manufacturinf sector,
paying special attention to multi-product firms. Table 3 presents descriptive statistics, characterizing single and multi-product firms in terms of their count share and product sales share
in the economy. The sample used for the empirical analysis and markup estimation reveals
that slightly less than 50% of the firms are multi-product. However, looking at these firms’
contribution to aggregate sales in the economy, their crucial role becomes apparent. Firms
manufacturing with more several products in their portfolios are responsible for the around
65% of the total value of manufactured goods in Denmark, which emphasizes the big role that
multi-product firms play in the economy. In the final sample many multi-product firms have
been dropped due to missing product quantity or measurement units. This explains why the
product sales share and count share is around 5-6% points less than in the population statistics. The cleaning algorithm requires that for at least 20% of the product portfolio there is
available quantity information. In case quantity is missing for more than 20% of the portfolio
in a given year, the entire firm series are dropped from the sample (see the description of
VARS in section A.A1).
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11
Table 3—Single vs. Multi-product firms in the Danish economy
Year
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
Count share in %
Single
Multi
51.5
48.5
52.9
47.1
54.4
45.6
54.8
45.2
55.1
44.9
54.8
45.2
54.8
45.2
55.0
45.0
55.0
45.0
55.6
44.4
58.0
42.0
58.2
41.8
56.1
43.9
55.8
44.2
Sample
Total product sales share in %
Single
Multi
34.2
65.8
30.7
69.3
33.5
66.5
34.3
65.7
32.1
67.9
33.6
66.4
36.2
63.8
34.2
65.8
37.9
62.1
39.3
60.7
38.6
61.4
39.0
61.0
35.8
64.2
36.9
63.1
Count share in %
Single
Multi
45.7
54.3
45.5
54.5
46.0
54.0
46.5
53.5
46.7
53.3
46.7
53.3
46.6
53.4
46.5
53.5
45.9
54.1
47.3
52.7
48.3
51.7
48.8
51.2
48.0
52.0
47.8
52.2
Population
Total product sales share in %
Single
Multi
28.7
71.3
24.3
75.7
27.0
73.0
27.3
72.7
24.8
75.2
25.1
74.9
24.9
75.1
24.6
75.4
25.0
75.0
27.0
73.0
27.2
72.8
25.4
74.6
23.3
76.7
24.2
75.8
Note: This table shows the share of single and multi-product firms across several dimensions: count share, total revenue share and total production
value share. The columns “Total product sales share in %” contain information from VARS and report the value share of all goods, produced by
Danish manufacturing firms.
C. Measuring import competition
Typically, the literature has investigated the effects of import competition at the industry
level (CN or NACE) or at the level of the firm.6 Import competition at the industry level
can be observed by looking at the total industry imports relative to the sum of imports and
domestic production in that same industry. The higher the ratio, the greater the importance
of imports in that industry. At the firm level, the penetration ratio can be assessed by looking
at the product sales share weighted average of the import penetration ratio for each product.
In this paper the main focus is on the product dimension. First, this requires a different
approach as the previously mentioned variables vary at a higher level of aggregation than
what is required in the current setting. Second, there is substantial heterogeneity in the
exposure to import competition across narrowly defined products, which requires a much
more refined measure in order to relate this to product level markups. It is important to note
that the analysis at the product level allows us to investigate the import competition effects on
markups of both domestically produced final and intermediate goods. For example, observing
an increase in the import penetration ratio for electronic circuit boards, would enable us to see
the markup response of Danish manufacturers of electronic circuit boards, which are themselves
used as intermediate inputs in many electronic final goods. Hence, for some producers of
6 For papers adopting these approaches and studying the effects of import competition on firm-level markups, wages
outcomes, firm death and employment growth, see Mion and Zhu (2013), Autor, Dorn and Hanson (2013), Ashournia,
Munch and Nguyen (2014), Dauth, Findeisen and Suedekum (2014), Hummels et al. (2014), Hummels, Munch and Xiang
(2016) and Meinen (2016).
12
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
electronic final goods, higher import competition in the market for electronic intermediates
could lower markups and consequently lower marginal costs for final good producers. The
current approach and methodology cannot capture the effects of offshoring on markups and
how these cost savings affect markups, but can only inform us how manufacturing firms in
Denmark producing a given good domestically adjust their markups in response to changes in
the import penetration ratio for that same product on the market. Even though globalization
has allowed firms to source from more locations at cheaper prices and in some cases move
production almost entirely abroad, the current analysis is meant to capture only the domestic
market competition effects. By virtue of the data disaggregation, after obtaining the markup
estimates and product unit values, it is possible to compute marginal costs at the CN8 product
level and investigate whether import competition has triggered marginal cost savings for firms
in the form of productivity improvements or on the contrary, an increase in marginal costs
due to quality upgrading and product differentiation. These alternative hypotheses can tested
using the established empirical framework and detailed product level information.
To measure import competition I introduce several measures, which are then employed
separately in the empirical and robustness analyses. First, the markup estimates vary at the
product-firm-time level implying that manufacturers of the same CN8 product can charge
different markups. Preferably, the main regressor of interest should vary at the same level,
which suggests that to take into account this firm-specific variation, the import competition
measure should be defined at the same level. Hence, the preferred specification for import
competition is product-firm-time specific and captures the notion that the competitive pressure
on a given product can vary across firms based on their own importing activity of that good.
The import competition measure takes the following form:
(1)
ICijt =
Mjt − Mijt
,
Mjt − Mijt + YjtDK
where ICijt denotes the import competition for product j ∈ {CN 8, CN 6}, produced by
firm i in year t. The variables Mjt and Mijt represent total imports of product j in the
economy and total imports of the same product by firm i, respectively. The total domestic
production of product j in Denmark is denoted by YjtDK . The reader should be informed
∑
that Mjt =
i∈importers Mijt , which is calculated from the universe of trade transactions
and includes the imports of a given product j by all importing firms from all sectors in
the economy and not only manufacturing firms. This measure allows for different import
penetration ratios across firms within the same product. This distinction is important because
some manufacturing firms import products that they also manufacture domestically. The
impact of neglecting own imports of manufacturing firms is that the IC measure would always
be inflated upwards, appearing as if the firm experiences more intense competitive pressure
JULY 2016
MARKUPS AND IMPORT COMPETITION
13
from imports. By correcting for the imports that firm i undertakes in a product that it also
produces, I ensure that the measure captures only the exposure from other importers of the
same product on the market. The IC measure in (1) is calculated at two different product
aggregations - CN8 and CN6. This is driven by the data limitation from the BACI database,
which is used to construct one of the instrumental variables. The product codes are reported at
the 6-digit level, which is why an IC measure is computed at the same level of disaggregation.
An alternative measure for the import competition is specified at the product-year level,
where the import behavior of individual firms is not taken into account:
(2)
ICjt =
Mjt
,
Mjt + YjtDK
where as before ICjt captures the import penetration ratio for product j ∈ {CN 8, CN 6}
in time period t. Both ICijt and ICjt exhibit substantial variation cross products, which
necessitates a closer look at the evolution of import competition across industries. Figure 1
provides evidence for the dispersion in the import competition measure for narrowly defined
product categories in the sample. The bottom right panel of the figure shows that more
than 34% of the CN8 products face a different import competition intensity relative to goods
defined at the 6-digit level. Most multi-product firms produce goods that belong to the same
CN4 product industry but that differ at the CN6 level. This suggests that the portfolios of
multi-product firms are subjected to heterogeneous competitive pressure, which can lead to
differential markup adjustments within firms. Hence, keeping the analysis and treatment at
the firm or aggregated product industry level, e.g. CN2, masks substantial heterogeneity in
import competition exposure.
To shed light on the forces affecting domestic manufacturers, Figure 2 plots the evolution
of the median import competition across CN8/CN6 products within their respective broad
product industries and the import competition computed directly at the 2-letter product industry level (2-letter NACE-CN). Each product-industry category encompasses hundreds of
unique CN8 products, which implies substantial heterogeneity within these industries across
individual products. Table A1 in the appendix shows how the different product and industry
classifications are mapped into an aggregate grouping. Overall, the direction and movement of
these measures are highly correlated, but the levels differ, which indicates substantial heterogeneity in import intensity across narrowly defined products.7 The plots reveal that import
competition has intensified across all industries with the exception of manufacture of machinery and equipment (CK), where in 2012 the industry level import competition was close
to its 1999 levels. Looking at Figure 2 and 3, reveal that industries such as manufacture
7 Table A2 in the Appendix shows that IC measures at several levels of product aggregation are positively correlated
with each other.
JULY 2016
25
80
AARHUS UNIVERSITY WORKING PAPER
10
4
40
15
4
−1.0
−0.5
0.0
0.5
CN8 Import competition demeaned by CN2
1.0
−1.0
−0.5
0.0
0.5
CN8 Import competition demeaned by CN3
1.0
0
0
0
0
5
2
20
2
Percent of observations
6
60
20
6
8
14
−1.0
−0.5
0.0
0.5
CN8 Import competition demeaned by CN4
1.0
−1.0
−0.5
0.0
0.5
1.0
CN8 Import competition demeaned by CN6
Source: Statistics Denmark, UHDI and VARS
Figure 1. Import competition dispersion across different CN product aggregations
Note: The plots contain the histograms of the demeaned import penetration ratio calculated at the CN8 product level. The CN8 import penetration
ratio is demeaned by CN2, CN3, CN4 and CN6 product level import competition measures, respectively.
of “Food products, beverages and tobacco products” (CA), “Electrical equipment” (CJ) and
“Computer, electronic and optical products” (CI) have experienced an increase in their import
penetration ratios of around 15%-23% based on the average and median changes, respectively.
Even though for 9 out of 10 industries the value of imports in real terms declined during the
financial crisis, Figure 2 reveals that the IC measures have not followed the sample path. The
continued increase in this measure even during the financial crisis can be linked to an even
greater decline in domestic output produced by Danish firms. For example, real imports in
“Basic metals and fabricated metal products” (CH) declined by around 40% from 2008 to 2009,
while the import penetration ratio for the same industry in Figure 2 fell in the same period
by only 9%-13%. Since the import penetration ratios relate imports to domestic output, the
patterns show that even if imports in real terms decline, import competition can intensify if
domestic output declines by even more.
The change in import intensity across manufacturing sectors can shed light on the evolution
of import competition across time. Table 4 shows that there is substantial heterogeneity across
narrowly defined industries and very high dispersion at the product-level import competition
measures. It is important to note that Denmark does not import the entire spectrum of CN
8-digit products that are also manufactured domestically. However, for only 78 domestically
produced CN8 products there are no imports to Denmark. For reasons discussed in subsection
II.C, it will be beneficial to analyze the markup responses using both CN6 and CN8 productlevel measures. Total import value in all industrial products fell sharply with the greatest drop
in imports occurring in CC, CM, CK and CL. The post-crisis recovery path has followed the
initial positive trend with the only exception being the CL where imports have continued to
decline even after 2009. Macroeconomic and financial shocks common to the economy affected
MARKUPS AND IMPORT COMPETITION
Industry CC
0.70
Industry CH
0.60
0.50
0.60
0.50
Industry CG
0.40
2012
0.70
Industry CJ
2003
2006
2009
2012
0.30
0.30
0.20
2003
2006
2009
2012
Industry CK
2000
2003
2006
2009
2012
2003
2006
2009
2012
2003
2006
2009
2012
Industry CM
0.40
0.60
0.20
0.30
0.40
0.25
0.20
2000
2000
Industry CL
0.30
0.60
0.40
0.30
0.40
0.30
2000
2000
0.60
2009
0.50
2006
0.80
2003
0.50
0.60
0.70
Industry CI
2000
0.20
2012
0.40
0.50
2009
0.40
2006
0.35
2003
0.30
0.60
0.40
0.70
0.30
0.20
2000
0.50
Import competition measure
0.40
0.80
0.50
Industry CB
0.90
0.60
Industry CA
15
0.60
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2000
2003
2006
2009
2012
2000
2003
2006
2009
2012
2000
2003
2006
2009
2012
Source: Statistics Denmark, UHDI and VARS
Figure 2. Aggregate and median import competition by NACE 2-letter product industry
Note: The solid red line and the dashed blue line indicate the median import competition at the CN8 and CN6 product levels, respectively, by
k = med(IC k , ..., IC k ) and j ∈ A indexes a unique CN8/CN6 product that is produced by
industry during the sample period, where ICgt
g
1t
Jt
industry g and k = {CN 8, CN 6} denotes whether the measure is computed using the(product-level IC at the
) CN8 or CN6 level.; The dash-dotted
∑
∑
DK , where the set A contains all CN8
green line shows the import competition measure computed as ICgt =
g
j∈Ag Mjt /
j∈Ag Mjt + Yjt
DK total domestic production of good j.
products j that belong to industry g, Mjt denotes total imports of product j and Yjt
the import behavior of Danish firms. However, even if imports decline, competitive pressure
exerted on domestic producers does not necessarily have to decline. Since import competition
is measured as an import penetration ratio (see subsection II.C), this implies that if domestic
output falls by more than imports, then import competition can increase even though the
value of imports declines.
Specifications (1) and (2) are computed at two different levels of aggregation for each product
j. Even though product markups are always computed at the 8-digit CN level, having the
import competition measure vary at a higher level of aggregation has economic justification.
First, it captures a wider range of products, which can be potential substitutes and that
compete in the same product market. Second, going to a higher level of aggregation safeguards
the analysis from being too narrow by assuming that a given product only competes with the
same 8-digit CN product imported from abroad or manufactured by other producers. Consider
the example of Isoprene rubber (CN 40026000). Looking at how this product’s markup is
affected by foreign import competition of exactly the same good, would imply that consumers
can choose among more varieties (brands) of the same CN product. However, in reality
the increase in importing of substitute or complimentary goods, which fall under different
16
AARHUS UNIVERSITY WORKING PAPER
CK
CK
CB
CB
CC
CC
CG
CM
CL
CG
CH
CL
CM
CH
CI
CJ
CJ
CI
CA
CA
0
5
10
15
Average IC change in %
20
0
5
10
15
20
Median IC change in %
JULY 2016
25
Source: Statistics Denmark, UHDI
Figure 3. Change in import competition by NACE 2-letter product industry, 1999-2012
Note: The Average IC change is obtained by subtracting the mean import competition measure in 1999 from 2012 across all CN 8 products within
each 2-letter NACE product industry. The median IC is computed similarly where again the difference between the terminal and initial periods of
the sample is taken. Both panels are sorted by the change in import competition in an ascending order by industry.
Table 4—Import competition descriptive statistics by NACE 2-letter product industry
NACE 2-letter manufacturing industry
Mean Standard
deviation
CA - Food products, beverages and tobacco products
0.457 0.353
CB - Textiles, apparel, leather and related products
0.765 0.271
CC - Wood and paper products, and printing
0.541 0.312
CG - Rubber and plastics products, and other non-metallic mineral products
0.495 0.311
CH - Basic metals and fabricated metal products, ex. machinery and equipment 0.513 0.329
CI - Computer, electronic and optical products
0.514 0.280
CJ - Electrical equipment
0.544 0.287
CK - Machinery and equipment n.e.c.
0.391 0.301
CL - Transport equipment
0.469 0.320
CM - Other, repair and installation of machinery and equipment
0.482 0.302
P25 Median P75 Product-year
observations
0.111 0.397 0.816
7,197
0.653 0.879 0.972
4,223
0.252 0.541 0.847
751
0.210 0.490 0.767
1,647
0.216 0.490 0.826
2,219
0.302 0.461 0.762
614
0.316 0.542 0.789
886
0.131 0.317 0.611
1,956
0.191 0.445 0.739
445
0.212 0.469 0.725
854
Note: The mean, standard deviations, median, 25th and 75th percentiles are computed across individual 8-digit CN product codes by their
affiliation to 2-letter NACE manufacturing industry. The last column reports the number of product-year observations that belong to a given
manufacturing industry and where each product has a distinct import competition measure. Only products that are included in the final sample of
manufacturing goods are used in the construction of the correlation table.
CN codes, may affect the elasticity of demand of Isoprene rubber. Such is the example of
Chloroprene (chlorobutadiene) rubber (CN 40023900). These products belong to the same
group at the 4-digit level (4002) but to different 6- and 8-digit codes. The two goods are
rather different in terms of material and quality. The idea that import competition at a higher
level of aggregation can have an indirect effect on the demand and markups of close substitute
goods, justifies the construction of IC at the 6-digit product level. This measure is used in
JULY 2016
MARKUPS AND IMPORT COMPETITION
17
the robustness analysis in Section V and Table A1 in the Appendix provides an excerpt of the
mapping between product codes and 2-letter NACE industries.
D. Instrumental variables
One econometric challenge in isolating the causal impact of import competition on the
product-level markups is the potential endogeneity of ICjt in equation (19). The main concern is that shocks to markups may be correlated with globalization and increases in import
competition, which would confound the true effect of the variable of interest. In particular,
the omitted variable problem can arise due to the presence of unobserved supply and demand
shocks that simultaneously affect the markups charged by firms and the exposure of Danish
firms to greater imports. To combat this issue I construct several instrumental variables,
which vary the product level. I employ two sets of instrumenting strategies. First, I follow the
insights by Hummels et al. (2014) and Ashournia, Munch and Nguyen (2014), by using the
World Export Supply (W ES) and adjust the instrument to vary at a level as close as possible
to the level of markup observations. The data for this instrument comes from the global trade
database, BACI, which is based on UN COMTRADE and contains the universe of global trade
flows by product, time, value, quantity and country of origin and destination.
The above-mentioned studies focus on wages, employee- and firm-level outcomes in response
to import competition. Furthermore, their main focus is on China as this country has gained
a significant import share in many developed countries since the beginning of the century. The
identification strategy hinges on the assumption that the increase in the world export supply of
countries across various categories of products is due to supply side factors, such as increasing
competitiveness, comparative advantage in manufacturing certain goods, deregulation, decline
in trade barriers and ability of foreign firms to penetrate international markets.
To have a sound identification strategy, both the validity and exogeneity assumptions for
the chosen instruments have to be satisfied. What is required is that the W ES measure is
correlated with import shares in Denmark but uncorrelated with the markup setting by Danish
firms. The idea behind this measure is that the rise in imports of goods from other countries
in the world is a reflection of their productivity and comparative advantage in manufacturing
these goods. Hence, observing a higher share in imports of a certain goods relative to domestic
Danish production, implies that other countries induce a supply shock and increase imports
for other trading partners as well and not just for Denmark in a given product category.
Hence, relying on the total export supply of all other countries producing a given 8-digit CN
product as an instrument for Danish import exposure captures the exogenous component of
the improved competitiveness of those other countries and isolates the effect from possible
confounding shocks that could affect simultaneously product markups and supply/demand
conditions. In contrast to previous studies that rely on the same instrumenting strategy
(Ashournia, Munch and Nguyen, 2014), the focus in this paper is not only import competition
18
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
from China or Eastern Europe but from all sourcing countries for a given good. The data
shows that a big majority of products are imported by many firms and from many sourcing
countries. On average, a given 8-digit product is imported to Denmark from six countries
(the median is three trading partners) and by seven firms (median is four firms) with large
standard deviations, suggesting a lot of heterogeneity across products.
I specify the instrument as:

(3)
IV _W ESjt = log 
∑
c∈E

W ESjct  ,
′
where W ESjct is the export of product j at time t by country c to the world excluding
′
Denmark. Note that the set E excludes Denmark both as exporter and importer. The
intuition behind this approach is that the Single Market and the similar economic development
of most Western European countries implies that the competitive landscape and shocks may be
correlated across countries, which would violate the exogeneity assumption of the instrument.
The BACI dataset offers information both on value in US dollars and quantity at the CN6
product level, which allows to construct two instruments - one defining W ES in terms of
nominal values and one in quantity units. Both of these measures are supposed to be correlated
with the import shares at the product level.
The second instrumenting strategy is similar in spirit to the one adopted in Mion and Zhu
(2013), where nominal exchange rates and product level import shares are used to build an
instrument that varies at the product level and is uncorrelated with markups. The instrument
reads as follows:
(4)
IV _EXjt =
c
∑ IMj,1998
log (EXct ) ,
IMj,1998
′′
c∈E
where EXct is the nominal exchange rate of country c with respect to the Danish Kroner,
E is the set of all trading partners that do not have a fixed exchange rate with the Danish
c
currency, IMj,1998 and IMj,1998
are global and country-specific imports to Denmark of product
j in the pre-sample year 1998, respectively.8 Note that the shares are fixed as contemporaneous
import shares are highly likely endogenous. Not all countries export every product in 1998.
Furthermore, there are instances where a given good is imported for the first time to Denmark
later in the sample period but not in 1998. I proceed by fixing the import shares to the
′′
8 Denmark is not formally part of the Eurozone but has its currency pegged to the Euro at an exchange rate of
7.46038 DKK/EUR, which does not exhibit sufficient variation as it is kept in +/-2.25% bands to the peg. In reality the
fluctuations are less than 1% of the exchange rate target.
JULY 2016
MARKUPS AND IMPORT COMPETITION
19
year when a good is imported for the first time to Denmark. The import share-weighted
exchange rates are necessary in order to make the measure vary at the product level. One may
worry that excluding all trading partners from the Eurozone fails to account for the fact that
exactly these countries are the top trading partners for Denmark (see Table 2). On the other
hand, including the Eurozone countries would remove a considerable share of the variation
in IV _EXjt . Importantly, we do not miss any products in the instrument as basically the
majority of goods that are imported from the EU are imported from other countries as well.
III.
Methodology
In this section, the key methodologies for the markup analysis are described. Since the key
objective of the study is to understand how firms adjust the markups of their products at the
finest available level, I present the estimation methodology and the construction of the import
competition measures next. On the markup side, I closely follow the novel structural approach
by De Loecker et al. (2016) to obtain product-firm level markups taking into account various
biases, which are known in the productivity estimation literature.
A. Markup derivation
The estimation of the product-level markups is obtained from an underlying structural
model, based on the product-firm specific production function. First, consider a general production function for a given product j, manufactured by firm i at time t:
(5)
Qijt = Fit (Vijt , Kijt ) exp (ωit + ϵijt ) ,
where Qijt is the product output in physical units, Fit (Vijt , Kijt ) is a general production
function, which can vary across firms and time. Each product is produced by using static(Vijt )
and dynamic (Kijt ) inputs. The elements in the exponential function captures a firm-specific
productivity shock ωit and ϵit is an idiosyncratic disturbance or measurement error, stemming
from the fact that output in physical units may be measured with an error. Several key
assumptions are necessary for the estimation methodology to yield markups at the productfirm level.9
First, equation (5) assumes that a given product j of a multi-product or single product is
manufactured using the same production technology, defined by Fit (·). Second, it is assumed
that the production function is continuous and twice differentiable w.r.t. to at least one freely
adjustable or variable input from the vector Vijt . This implies that manufacturing firms can
adjust their output instantaneously by changing the amount of variable input used in the
9 For
a detailed overview of the assumptions behind the markup estimation, see pp. 9-10 in De Loecker et al. (2016).
20
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
production. Third, the productivity term, ωit is firm-specific and Hicks-neutral. This suggests
that a multi-product firm is equally productive across all the products it manufactures.10
Fourth, the approach assumes that input expenditures can be traced to the product level.
This means that if the econometrician knows the allocation share for inputs across products,
then it is possible to map total input expenditures at the firm level into product-specific input
expenditure.11 Finally, firms are always assumed to cost minimize taking input and output
prices as given. More importantly, the assumption implies that input prices should not depend
on input quantities. Even though this may be a simplification of reality, it is a substantial
improvement relative to the previous state of the literature, where input price heterogeneity
across firms has been largely neglected.
Assume that a firm uses both dynamic and static inputs in the production of a given product
j. The cost minimization problem for a given product can be written as:
min
v ,K k
w.r.t. Vijt
ijt
T Cijt =
K
∑
k=1
k
k
Wijt
Kijt
+
V
∑
v
v
Wijt
Vijt
v=1
s.t.
Qijt = Qijt (Vijt , Kijt , eωit ) ,
k
where T Cijt denotes the total manufacturing costs of product j incurred by firm i, Wijt
v are the product-input-firm-specific prices for the dynamic (k) and static (v) inputs,
and Wijt
respectively. This formulation implies that the input prices that a firm pays vary across
products. The Lagrangian function looks as:
L (Vijt , Kijt , λijt ) =
K
∑
k=1
k
k
Wijt
Kijt
+
V
∑
v
v
Wijt
Vijt
+ λijt [Qijt − Qijt (Vijt , Kijt , eωit )] ,
v=1
v yields the
and taking the FOC with respect to a variable and freely adjustable input, Vijt
following result:
(6)
∂Qijt (Vijt , Kijt , eωit )
∂L (·)
v
=
W
−
λ
= 0.
ijt
ijt
v
v
∂Vijt
∂Vijt
Standard optimization theory postulates that λijt is the marginal cost (shadow price) of
10 For a relaxation of this assumption in the context of productivity estimation, see Dhyne et al. (2015), who estimate
product-firm-specific productivity measures using an alternative framework.
11 Equation (B2) in Appendix B illustrates this assumption. This is necessary as most datasets do not report productspecific inputs, but only total expenditures at the firm level.
JULY 2016
MARKUPS AND IMPORT COMPETITION
increasing output by one unit, λijt =
sides of the equation by
v as:
variable input Vijt
(7)
v
Vijt
Qijt
L(·)
∂Qijt .
21
Re-arranging terms in (6) and multiplying both
allows to construct the output elasticity with respect to the
v
ζijt
=
v Vv
1 Wijt
ijt
,
λijt Qijt
where the nominator in the second fraction is the total spending on input v for product j by
v
v = ∂Qijt (·) Vijt . Using the definition
firm i at time t and the output elasticity is defined as: ζijt
∂V v Qijt
ijt
P
ijt
of marginal cost, λijt , the markup is given by µijt ≡ λijt
, where Pijt is the output price.
Re-arranging and pre-multiplying both sides of (7) by Pijt , yields the markup for product j:12
(
(8)
µijt
)
P
Q
ijt ijt
v
,
= ζijt
v Vv
Wijt
ijt
{z
}
|
−1
(αvijt )
(
)−1
v
where αijt
is the share of expenditure on input v of total product sales. The markup
expression is very similar to the result in De Loecker and Warzynski (2012). The major
difference is that now the output elasticity and elements in the brackets vary at the firmproduct level. The complication in the current setup is that the input expenditure for a given
product is not observed in the data in contrast to the setup where markups are estimated at
the firm level (De Loecker and Warzynski, 2012). In the latter case the input expenditure
share of total revenue can be directly calculated from the data which traditionally reports
information on total material expenditures at the firm level.
From the discussion above it is evident that the two necessary components for the derivation
v and αv , which are not directly observable and have to be estimated.
of markups are ζijt
ijt
First, the output elasticity has to be estimated for each manufactured product by a given
firm. This is a major complication as the literature has so far estimated production functions
at the firm level without distinguishing explicitly between single- and multi-product firms. As
shown in Table 3 close to 50% of the firms are multi-product, suggesting that this elasticity
may not be constant across products within a firm. Second, the big majority of datasets
report total expenditure on inputs such as capital, labour and intermediate inputs but do not
provide product-specific allocation shares. In the data, the econometrician can observe the
∑
v V v . To allocate the total
total expenditures on input v at the firm level: T Eitv = j Wijt
ijt
expenditures on a given input across all products, one needs the allocation shares, ρ̃ijt , which
12 For
further details on the intermediate steps in obtaining equations (7) and (8), see De Loecker et al. (2016).
22
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
∑
13 This relationship between the total
all together should satisfy the condition:
j ρ̃ijt = 1.
v V v = ρ̃ T E v . Since T E v is observed in
expenditure on input v, T Eitv and ρ̃ijt , yields: Wijt
ijt
it
it
ijt
the data, the only element that needs to be estimated in order to obtain the denominator in
(8) is the input allocation share.
B. Estimation of markups
The previous subsection indicated several methodological challenges, which are important
for the estimation of markups. First, firms do not report input quantities and input prices.
Second, the input allocation shares across products are not known. A reasonable assumption is
that different firms pay different prices for inputs, depending on quality, number of suppliers,
location, etc. I rely on the insights by De Loecker et al. (2016) to overcome these issues and
obtain unbiased coefficient estimates of the production function by accounting for input price
heterogeneity.
Starting again from (5) and taking logs yields:
(9)
qijt = fj (v ijt , kijt ; β) + ωit + ϵijt ,
where small letters indicate logs of physical output and inputs, respectively. All inputs
can be combined together in the vector xijt = {v ijt , kijt }. The functional form implies that
productivity term, ωit is Hicks-neutral, log-additive, firm-specific and identical across products
within a firm. The reason why the productivity term is forced to vary only across firms but
not products within a firm is because otherwise the input allocation shares cannot be retrieved
as discussed later.
The main challenge with (9) is that we do not observe all inputs in physical units with
the exception of output (quantity produced in various measurement units) and labour input
(number of FTE employees). The Danish data further provides information on the total
wage bill that a firm pays and the value of gross fixed assets. The literature on productivity
estimation has usually proceeded by deflating inputs by PPI, industry-specific deflator for the
given input or at best by a firm-specific input deflator.14 Subsection B in the Appendix shows
that any input in the vector xijt , can be expressed as:
(10)
13 The
x
xijt = ρijt + x̃it − wijt
,
input allocation share, ρ̃ijt denotes the actual share of input v that goes into product j and ρ̃ijt = exp (ρijt ).
a non-exhaustive list of studies that use deflated inputs and output as a proxy for physical inputs, see Mairesse and
Jaumandreu (2005); Foster, Haltiwanger and Syverson (2008); Topalova and Khandelwal (2011); Smeets and Warzynski
(2013).
14 For
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MARKUPS AND IMPORT COMPETITION
23
where x generally denotes any static or dynamic input used in the production process,
ρijt = ln (ρ̃ijt ), x̃it is log of total expenditures on input x deflated by an industry-specific price
x is the log deviation of the product-firm specific price of input x from the
index and finally wijt
industry average price. All the product-firm-specific inputs prices can be collected together in
a vector wijt . Plugging (10) into (9) can be expressed generally as:
(11)
qijt = fj (x̃it ; β) + A (ρijt , x̃it ; β) + B (wijt , ρijt , x̃it ; β) + ωit + ϵijt ,
where fj (x̃it ; β) denotes the same functional form of the production function and takes only
the deflated firm-level input expenditures, B (wijt , ρijt , x̃it ; β) depends on the product-firminput specific prices, the allocation shares and deflated input expenditures and is function
that collects all terms containing wijt and finally A (ρijt , x̃it ; β) is a function of the allocation
shares and deflated input expenditures.15
Equation (11) shows that when relying only on deflated inputs, the terms A (·) and B (·)
are left out in the composite error term, which biases the β coefficients as both terms depend
on the deflated inputs x̃it . To overcome this issue and obtain unbiased estimates, I estimate
(11) on a sub-sample of single product firms as suggested by De Loecker et al. (2016). By
definition, single product firms allocate all their production inputs to a single good only,
effectively eliminating the unobserved input allocation term, A (·). The single product version
of (11) reads as:
(12)
qit = f (x̃it ; β) + B (wijt , x̃it ; β) + ωit + ϵit ,
where all terms involving ρijt and the product subscript j are dropped as the equation
is estimated on a sub-sample of single product firms. Obtaining unbiased estimates of (11)
requires dealing with the unobserved input prices in wit and the simultaneity bias due to
the correlation between input choices and firm-specific productivity shocks. The literature on
productivity estimation has dealt with the latter issue by assuming that unobserved productivity, ωit can be inverted and expressed as a function of observable and that the evolution of
productivity follows a first-order Markov process (Olley and Pakes, 1996; De Loecker, 2011;
Levinsohn and Petrin, 2003; Ackerberg, Caves and Frazer, 2015). The parameters of interest
are then estimated by using GMM based on the moments that exploit the orthogonality of the
innovations in the productivity shock and the covariates.
The former bias due to unobserved firm- or product-firm-specific input prices is explicitly
addressed in De Loecker et al. (2016). To back out estimates of firm-specific input prices,
15 The
derivation of (11) is presented in subsection B.B1.
24
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
they use a control function approach, where the assumption is that firms’ output prices can
be indicative of input prices. The observation that firms selling more expensive goods also
use higher priced and higher quality inputs has been well documented in the trade literature
(Verhoogen, 2008; Kugler and Verhoogen, 2012; Manova and Zhang, 2012a). The approach
proxies for unobserved input prices by using information about the firm’s output quality:
x = w (v ). The idea is based on Khandelwal (2010) who uses a nested logit to express
wit
t it
quality as a function of market shares, output prices and product characteristics, approximated
here by various CN product level dummies: vit = vt (pit , msit , pr_dumi , expit , impit ), where
pit is the unit value, proxying for the output price, msit is a vector of marketshares of firm i,
pr_dumi are 2-, 3-, 4- and 6-digit CN product dummies, which aim to control for productspecific characteristics and finally expit and impit are binary variables taking the values of 1 if
a firm exports or imports, respectively.16 I extend the set of variables that determine output
quality by including the indicator for exporting and importing, as recently the trade literature
has shown that companies successfully engaged in exporting produce higher quality final goods
and that international sourcing allows firms to vary the quality scope of products (Fan, Li and
x and
Yeaple, 2015; Bas and Strauss-Kahn, 2015). Combining together the expressions for wit
vit and substituting for wit in B (·), yields:
B (·) = B ((pit , msit , pr_dumi , expit , impit ) , x̃it ; β, δ)
(13)
= B ((pit , msit , pr_dumi , expit , impit ) × x̃ait ; β, δ) ,
where δ is an additional vector of parameters to be estimated and x̃ait = {1, x̃it } denotes that
the variables in the input price control function enter by themselves but also as interactions
with deflated inputs, x̃it as shown in subsection B.B1. Note that δ contains the parameters
that identify the elements from the input price control function entering alone in B (·).
The final step in the estimation procedure is to deal with unobserved productivity, which
is correlated with the input choices that firms make. To confront this issue, I follow the rich
literature on productivity estimation, which offers solutions to the aformentioned problem (see
Levinsohn and Petrin (2003); Olley and Pakes (1996)). The estimation follows the two step
procedure suggested by Ackerberg, Caves and Frazer (2015).17 In similar spirit to Levinsohn
and Petrin (2003), I use a demand equation for material inputs to proxy for unobserved
productivity. Material demand depends on the amount of capital, labour, state variables and
productivity:
16 For
a formal model of output quality and input price differentiation, see Appendix A in De Loecker et al. (2016).
the first stage, no production function parameters are estimated. The only purpose of the first stage is to purge
output of measurement error. The second stage expresses productivity as a function of the parameter estimates and
constructs moments based on the productivity law of motion to obtain estimates by using GMM.
17 In
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MARKUPS AND IMPORT COMPETITION

(14)
25

m̃it = mt x̃it , ωit , pit , msit , pr_dumi , expit , impit , ICit  ,
|
{z
}
uit
where vector uit collects all variables that could lead to a different demand for materials,
except for deflated inputs and productivity. ICit is the import competition variable with
support [0; 1]. Since the estimation sample at the current stage contains only single product
firms, I do not need to compute a weighted average import competition measure at the firm
level. The reason this measure may have an effect on material demand is because import
competition can discipline firms in their choice of intermediate goods. Equation (14) can be
inverted for ωit , provided that mt (·) is monotonic in ωit (see De Loecker (2011)):
(15)
ωit = gt (x̃it , uit ) ,
where gt (·) is a non-parametric function, approximated by a higher-order polynomial in its
elements. Plugging (15) into (12), output quantity of a single product firm can be expressed
as:
(16)
qit = ϕt (·) + ϵit ,
where ϕt (·) = f (x̃it ; β) + B (wit , x̃it ; β) + gt (x̃it , uit ) and is equal to output net of measurement error. Predicted output is then given by ϕ̂it and can be obtained by estimating (16)
and approximating ϕt (·) by a third-order polynomial in its elements. Hence, for any set of
parameters β and δ, productivity can be computed as:
ωit (β, δ) = ϕ̂it − f (x̃it ; β) − B ((pit , msit , pr_dumi , expit , impit ) × x̃ait ; β, δ) ,
where wit is expressed in terms of the elements in the input price control function in (13).
Next, I proceed by estimating productivity non-parametrically, assuming that it evolves according to a first-order Markov process:
ωit (β, δ) = E [ωit (β, δ) |ωi,t−1 (β, δ) , expi,t−1 , impi,t−1 , ICi,t−1 , P rit , Sit ] + ξit
= E [ωit (β, δ) |Ii,t−1 ] + ξit
(17)
= ht (ωi,t−1 (β, δ) , expi,t−1 , impi,t−1 , ICi,t−1 , P rit , Sit ) + ξit ,
where ht (·) is a higher-order polynomial, P rit is the probability that a firm survives in
26
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
a given period and Sit is the probability that a single product firm becomes multi-product.
As pointed out in the recent literature, exporting can endogenously affect the evolution of
productivity (Smeets and Warzynski, 2013; De Loecker, 2011, 2013). The mechanism put
forward is that firms, active on export markets, learn about best practices and adopt newer
technologies, which subsequently improve their efficiency. Importing and import competition
can affect productivity by giving access to higher price-adjusted quality inputs that can also
imperfectly substitute domestic inputs and by incentivizing firms to eliminate inefficiencies in
their production processes once they get hit by a tougher competitive environment (Halpern,
Koren and Szeidl, 2015; Kasahara and Rodrigue, 2008; Kasahara and Lapham, 2013; Amiti
and Konings, 2007; ?). First, the survival of firms is non-random. A wealth of theoretical
contributions have depicted a mechanism where only the most productive firms are capable
of participating in international trade and the least productive firms are forced to exit the
industry (Melitz, 2003). To implement this insight, I follow Olley and Pakes (1996), who
run a probit model to obtain the probability of exit. Second, the estimation sample includes
only single product firms and many of them expand their product portfolios. The growing
theoretical literature on multi-product firms, productivity and trade, has pointed towards
product specialization within firms, implying that companies focus foremost on their core
products and add new items in a decreasing order of efficiency. Hence, the process of becoming
a multi-product firm is also non-random, which requires the inclusion of Sit in the productivity
process as in De Loecker et al. (2016). Both Sit and P rit have theoretical underpinnings, which
requires a consistent treatment in (17).
Equation (17) allows to recover the idiosyncratic shock to productivity, ξit as a function of
the parameters by non-parametrically regressing ωit (β, δ) on the elements in ht (·):
ξit (β, δ) = ωit (β, δ) − E [ωit (β, δ) |Ii,t−1 ] .
The parameter vectors β and δ are estimated by GMM, forming moment conditions with
ξit (β, δ):
E (ξit (β, δ) I) = 0 ,
where I is a vector containing lagged material and wage expenditures, current capital, lagged
output prices, interaction and higher order terms between appropriately lagged prices and production inputs. A few comments on the identification assumptions are in place. First, capital
is treated as a dynamic input since it takes times to accumulate or adjust the stock, where
the observable capital at time( t is decided
at time t − 1. The parameter of capital is identi)
fied based on the moment E ξit k̃it = 0 as current shocks to productivity are uncorrelated
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MARKUPS AND IMPORT COMPETITION
27
with current levels of capital.18 The intermediate inputs coefficient is identified based on past
input expenditures, m̃i,t−1 as current material expenditures are correlated with contemporaneous productivity shocks ξit , which leads to the moment: E (ξit m̃i,t−1 ) = 0. The coefficient
for labour (wages) is identified based on the lagged values as labour is considered to be a static
input, which can adjust in the same period and would be correlated with idiosyncratic productivity shocks. This assumption fits well with the Danish flexicurity labour market, which
features easy hiring and firing for firms and a wide safety net for employees in case of a job
loss (Andersen and Svarer, 2006). The main identification insight hinges on the serial correlation between current and lagged values of intermediate inputs, labour, export and import
participation of the firm and output prices. Finally, note that the input price control function
also includes interactions together with production inputs x̃it . These coefficients are identified based on lagged values of output prices and market shares as current values can react to
productivity shocks at time t.
The described procedure above provides unbiased coefficient estimates of the production
function using a sample of single product firms. Depending on the functional form of fj (·),
the elasticity of output with respect to materials can be computed easily
( in the case of Cobb)
v
v
Douglas, ζ̂ijt = β̂m . In the case of a translog specification, ζ̂ijt = ζt β̂, x̃it , ρ̂ijt , ŵijt is a
function of the production function coefficients, deflated input expenditures, allocation shares
across products within firms and estimated input prices.19 Relying on the translog production function, requires estimates of the input allocation shares, ρ̂ijt . The innovative method
proposed by De Loecker et al. (2016) uses numerical optimization to find the optimal input
allocation shares that solve simultaneously a system of equations for each firm-year pair and
impose the restriction that all shares should sum up to one.20 The necessary assumptions to
get estimates of ρijt are that ωit is firm-specific, log-additive and inputs are divisible across
final products as in (5). In this numerical exercise, I provide several starting values for the allocation of input shares. Intuitively, products that generate a big share of firm revenues can be
thought of as being the firm’s specialty or core product. This would imply that more expensive
goods, which are of high quality require more expensive inputs, hence higher marginal costs.
This line of argumentation suggests that core goods should use a greater fraction of inputs
in their production. This is why the initial starting value is product’s revenue share. From a
(
)
the coefficient for capital could also be identified off the moment condition: E ξit k̃i,t−1 = 0. To
identify the parameters of the input price control function, I form moments based on past observations for output prices,
marketshares and international status of the firm.
19 The elasticity with respect to materials under the translog is ζ v
ˆ
ijt = β̂m + 2β̂mm mijt + β̂lm lijt mijt + β̂lm lijt +
18 Alternatively,
β̂lk kijt + β̂lmk mijt kijt . Since the vector xijt = {mijt , lijt , kijt }, containing physical inputs at the product-firm level is
not observed, one can make use of imputed input prices, ŵijt and the ρ̂ijt to obtain x̂ijt . This elasticity depends not only
on β̂m but also on the levels of the other inputs and their elasticities, generating additional variation across product-firm
pairs compared to the Cobb-Douglas case where the elasticity is constant across product-firm pairs and the only variation
in product-firm markups comes from differences in αvijt in equation (8).
20 For complete description of the methodology, see De Loecker et al. (2016) and Appendix B.B2, which shows several
intermediate results of the procedure.
28
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
methodological point of view it is relevant to discuss whether using revenue shares is a good
proxy for the actual (imputed) input allocation suggested in the procedure. If one observes
that the backed out input allocation shares are highly correlated with revenue shares, then empirical researchers could rely on the readily available shares in the data to obtain product-firm
specific inputs and circumvent the computationally intensive task of backing out ρijt s. Using
the Danish data, I find a correlation coefficient of 0.51 between product revenue shares and
the actual input allocations. The moderate correlation indicates that observed revenue shares
should be treated with caution if they are to be used as proxies for the fraction of an input
that is allocated to individual products.21 Now we are equipped to estimate firm-product-year
specific markups by using the empirical equivalent of equation (8):
(
(18)
µ̂ijt =
M
ζ̂ijt
Pijt Qijt
exp (ρ̂ijt ) T EitM
)
,
where recall that T EitM are deflated total firm-level expenditures on materials, defined at the
v V v = exp (ρ ) T E v for a given static input v. Naturally, having
end of section III.A as Wijt
ijt
ijt
it
an estimate of markups at the product-firm level, allows to back out marginal costs, mcijt by
using the available unit values in the data. Investigating how markups react to higher import
competition is important as trade liberalization can lower manufacturing costs by forcing firms
to import cheaper quality-adjusted inputs or look for new suppliers. This is also one of the
main objectives of the paper - to investigate the change in marginal costs due to intensified
import competition.
IV. Empirical results
This section begins by presenting several stylized facts about the evolution of prices, markups
and marginal costs during the sample period from 1999 to 2012. Then, the main estimation
results are presented which establish the relationship between import competition and product
level markups. Since the aim of the paper is to investigate the within firm responses across
products, additional results are presented in relation to the heterogeneous effects within firms
and also across products.
A.
Stylized facts - Evolution of prices, markups and marginal costs
Before studying the role of import competition in firm’s decision to adjust markups, it is
worth understanding the aggregate developments in the main variables of interest for product
pairs that were both manufactured in 1999 and 2012. Figure 4 plots the densities of demeaned
21 In De Loecker et al. (2016) the correlation coefficient is 0.4036 using Indian product-firm level data. I thank Frederic
Warzynski for the useful suggestion to investigate the link between the numerically computed ρijt s and the product
revenue shares.
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MARKUPS AND IMPORT COMPETITION
29
units values (prices), marginal costs and markups for these surviving goods. The price and
marginal costs in the figure are deflated to 1999 levels using industry-specific deflators. The
plots reveal that the distribution of markups have shifted significantly to the left, indicating that overall the product markups in Danish manufacturing have declined through time.
Marginal costs, on the other hand, have seen an increase, where the overall distribution has
shifted to the right. Product prices of surviving products, on average, have remained largely
unchanged with the exception that in 2012 there was more mass in right tail of the distribution
and less in the left tail.22
The aggregate patterns are consistent with a story where firms upgrade quality, which
is costly. For example, Khandelwal and Amiti (2013) investigate the link between import
competition and quality upgrading and find that indeed Indian producers invest in quality
improvements of their products. Since it is costly for producers to improve the quality, appeal or functionality of products, such cost increases will be reflected in the marginal costs of
products. In fact, the observed product-firm pairs may have survived precisely because of improvements in their products, which have allowed these firms to insulate themselves for higher
competitive pressure. The empirical distributions also hint towards imperfect pass-through
between marginal costs and prices, as overall shift in the marginal costs has not reflected in
an equal shift in the price distribution. This emphasizes the role of variable markups and
imperfect pass-through of costs to prices as also shown by De Loecker et al. (2016) for the case
of India.
With these stylized facts on the evolution of prices, marginal costs and markups, the next
section studies the role of import competition in those aggregate patterns and particularly
focuses on the markup setting of Danish manufacturers.
Table 5 shows median and mean markups estimated from the sample of firms in Danish manufacturing.23 For most industries, the markup estimates appear reasonable and well above 1.
However, two industries are exceptions. The median and average markups for the textiles
and apparel industries along with chemicals have very low values, which indicates that the
output elasticities for these industries are not well behaved or that the ratio of material expenditures to sales behaves oddly. Since the production function estimates are obtained from a
sub-sample of single-product firms from each industry, Table B1 in the appendix reveals that
input coefficients are estimated based on the smallest samples. The returns to scale parameter
is way below 1 for the industry CB, which raises concerns as to the quality of the estimates for
that industry. Hence, in the robustness section, I pay special attention to these two industries
and run alternative specifications where they are excluded to verify that they do not affect
the markup responses to import competition substantially. Putting the markup estimates into
22 Figure XXX in Appendix subsection XXXX shows the CDF of prices, marginal costs and markups. Following
Delgado, Farinas and Ruano (2002) I implement the non-parametric one-sided Kolmogorov-Smirnov test on each of the
empirical distributions to investigate whether the observed differences between 1999 and 2012 are statistically significant.
23 The elasticities from the production function estimation are reported in Table B1 in Appendix A.
−1.0 −0.8 −0.5 −0.3
0.0
0.3
0.5
0.8
1.0
1.0
Density
0.6
0.2
0.0
0.0
0.0
0.2
0.5
0.4
Density
1.0
Density
0.4
0.6
0.8
1.5
0.8
2.0
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AARHUS UNIVERSITY WORKING PAPER
1.0
30
−2.0
−1.5
Log unit values
1999
−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
−2.0
−1.5
−1.0
−0.5
Log marginal costs
2012
1999
0.0
0.5
1.0
1.5
2.0
Log markups
2012
1999
2012
Figure 4. Distribution of real unit values, marginal costs and markups in 1999 and 2012
Note: The density plots include only firm-product pairs that are both present in 1999 and 2012. Observations above and below the 97th and 3rd
percentile are excluded. The unit values, marginal costs and markups are demeaned, by product-firm fixed effects and the residuals are plotted. The
distribution of unit values and marginal costs are deflated using sector-specific deflators and are expressed in real 1999 DKK.
perspective, I can directly compare them with the estimates by De Loecker et al. (2016) for the
case of India. Overall, the markups in Danish manufacturing are substantially lower, which
indicates a more fierce degree of competition. Even though both samples have a tendency to
overrepresent bigger firms, the markup dispersion is smaller in the Danish case and can be interpreted as featuring a more disciplined industry with fewer frictions. Having established the
overall development in markups, prices and marginal costs, I now proceed with the empirical
analysis and the effects of import competition.
Table 5—Median and average production function elasticities by NACE Rev. 2 industry
NACE 2-letter manufacturing product industry
Median markup, µ
Average markup, µ
CA - Food products, beverages and tobacco products
1.53
1.41
CB - Textiles, apparel, leather and related products
0.25
0.67
CC - Wood and paper products, and printing
1.20
2.82
CE - Chemicals and chemical products
0.06
0.65
CG - Rubber and plastics products, and other non-metallic mineral products
1.07
1.99
CH - Basic metals and fabricated metal products, ex. machinery and equipment
1.11
2.37
CI - Computer, electronic and optical products
1.37
2.41
CJ - Electrical equipment
1.26
2.23
CK - Machinery and equipment n.e.c.
1.21
2.68
CL - Transport equipment
1.25
1.62
CM - Other, repair and installation of machinery and equipment
1.24
4.48
Note: The table reports the estimated average and median elasticities from a translog production function. The values in brackets are standard
deviations of the estimates. The RTS columns report the returns to scale parameter which is the sum of the labour, material and capital input
elasticities. The number of observations column shows based on how many single-product firm observations have been included in the estimation of
the production function coefficients.
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MARKUPS AND IMPORT COMPETITION
31
B. Econometric model
In this section, I outline the main econometric model, which investigates the link between
product-firm level markups, marginal costs, prices and import competition. The main regression equation looks as follows:
′
(19)
ln (µijt ) = β1 ICjt + Xijt δ + τk + τt + ϵijt ,
where the dependent variable is the log of markups at the 8-digit CN level, ICjt is the
import share at the same level of product disaggregation, Xijt is a vector of controls that
includes covariates that vary both at the firm level, such as firm-specific productivity, ωit ,
size of the firm measured by the log of the number of employees, number of products, n and
also product level variables, such as marginal costs and product rank within the firm. As
recent empirical contributions have pointed out that high quality goods sell at higher prices
and also use more expensive inputs, I employ an indicator variable denoting differentiated
versus homogeneous products following Rauch (1999). Furthermore, I exploit the variation
in product-firm level markups by running different combinations of fixed effects: τk , where
k = {i, ij, j} are firm-, product- and product-firm fixed effects, and τt are time fixed effects
that account for aggregate macroeconomic shocks that are common to all product-firm pairs
and across sectors in the economy. Finally ϵijt is an idiosyncratic error, which assumed to
be uncorrelated with the main covariates in the estimation equation. Note that the following
specification exploits several different levels of variation in markups and import competition
in order to identify the β1 coefficient of interest. I first begin the econometric exercise by
exploiting the variation in markups, prices and marginal costs and import competition as
defined in equation (1) within products and across firms.
C.
Import competition, prices, markups and marginal costs
Table 6 shows the regressions, which related markups, marginal costs and prices of products.
The timing assumption is that product-level markups can react to heightened competitive
pressure during the same period. This assumption is relaxed in 7 where the assumption
is that it takes time for firms to embrace the changed competitive environment and adjust
markups. These results are meant to inform and confirm results obtained at the firm level.
For each outcome variable, I run several specification where various control variable are added
sequentially. Starting with the markup response, columns 1-4 reveal that import competition
is highly and negatively correlated with markups across all models. One interesting feature
is that after controlling for marginal costs, the markup response halves in size and remains
significant at the 1% level. The β coefficient captures the semi-elasticity as ICijt = {0; 1}.
The interpretation is that a 1% point increase in import competition leads to a reduction
32
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
in markups by 0.7% to 0.3%. Since on average, import penetration shares have increased
by around 10-15% points during the past 15 years, the estimates imply that markups have
declined due to import competition by around 3%-11%, which is a sizable economic effect.
Marginal costs on the other hand exhibit a positive relationship with import competition.
This may seem surprising at first, but such an observation would be consistent with the fact
that when firms are faced with greater competitive pressure, one way to soften the effect
of competition is by investing in higher quality, improved product functionality and appeal.
The literature has shown evidence that quality upgrading is costly and is thus related to an
increase in marginal costs. In sub-section IV.D I provide evidence for this potential mechanism by showing that products, having a greater scope for quality differentiation, are partly
shielded from import competition, charge higher markups and are less responsive to import
competition. Furthermore, in the case of marginal costs, I also control for the overall firm-level
productivity, backed out from the numerical optimization for multi-product firms. Consistent
with hypothesis that more productive firms, on average, have lower marginal costs finds support in columns 1-4 for marginal costs. Prices, have also been pressured downwards and exhibit
similar pattern of adjustment as markups. Conditional on import competition, marginal costs
display an imperfect pass-through to prices. The coefficient is in the ballpark of 0.33-0.34,
which is comparable to the size that De Loecker et al. (2016) find for India.
Table 6—Prices, markups, marginal costs and import competition at the CN8 product-firm level. (Variation
within products across firms)
Import competition (CN8)ijt
Markup (1)
Markup (2)
Markup (3)
Markup (4)
MC (1)
MC (2)
MC (3)
MC (4)
Price (1)
Price (2)
Price (3)
Price (4)
-0.670***
(0.092)
-0.291***
(0.043)
-0.319***
(0.044)
-0.303***
(0.044)
0.706***
(0.097)
0.660***
(0.102)
0.678***
(0.105)
0.614***
(0.105)
-0.097**
(0.046)
-0.291***
(0.043)
-0.319***
(0.044)
-0.303***
(0.044)
-0.661***
(0.011)
-0.658***
(0.011)
-0.655***
(0.011)
0.339***
(0.011)
0.342***
(0.011)
0.345***
(0.011)
-0.056***
(0.010)
-0.033***
(0.011)
-0.056***
(0.010)
-0.033***
(0.011)
Marginal costijt
Log # employeesit
Number of productsit
0.036
(0.022)
-0.005***
(0.001)
0.018***
(0.004)
Firm productivityit
Constant
R2
Adjusted R2
Number of clusters
Product fixed effects
Year fixed effects
Observations
-0.069**
(0.031)
-0.359***
(0.021)
-0.352***
(0.020)
-0.361***
(0.020)
-0.005***
(0.001)
-0.264***
(0.040)
-1.505***
(0.032)
-1.259***
(0.055)
-1.298***
(0.056)
-1.904***
(0.045)
-1.108***
(0.070)
-1.290***
(0.132)
-1.059***
(0.153)
-2.141***
(0.026)
-1.505***
(0.032)
-1.259***
(0.055)
-1.298***
(0.056)
0.47
0.45
4,555
0.81
0.80
4,555
0.81
0.80
4,555
0.81
0.80
4,555
0.70
0.69
4,481
0.68
0.66
2,121
0.68
0.66
2,121
0.68
0.67
2,121
0.90
0.89
4,555
0.93
0.93
4,555
0.93
0.93
4,555
0.93
0.93
4,555
77595
77595
77595
77595
77595
61341
61341
61341
77595
77595
77595
77595
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. All specifications are estimated using OLS. The product level is at 8-digit CN.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
To understand how responsive markups are to alternative timing assumptions, I run the
reduced-form model from (19) by used lagged import penetration shares and also lagged covariates. This specification is preferred as it alleviates potential endogeneity concerns stemming
JULY 2016
MARKUPS AND IMPORT COMPETITION
33
from simultaneous shocks that could affect current markups and current import competition.
Table 7 shows that even under this alternative specification, the signs and magnitudes remain comparable albeit lower. All regressions cluster standard errors at the level of the firm,
which allows arbitrary correlation between markups within firms. Across all specifications,
the standard errors are obtained by bootstrapping. However, I conduct only 100 iterations
due to computational burden required to compute markups at the product-firm level. The
estimating procedure requires resampling and re-estimating markups and allocation shares at
every iteration.
Table 7—Prices, markups, marginal costs and lagged import competition at the CN8 product-firm level.
(Variation within products across firms)
Import competition (CN8)ij,t-1
Markup (1)
Markup (2)
Markup (3)
Markup (4)
MC (1)
MC (2)
MC (3)
MC (4)
Price (1)
Price (2)
Price (3)
Price (4)
-0.440***
(0.086)
-0.205***
(0.056)
-0.238***
(0.057)
-0.217***
(0.056)
0.515***
(0.093)
0.448***
(0.096)
0.461***
(0.098)
0.420***
(0.097)
-0.057
(0.047)
-0.181***
(0.046)
-0.212***
(0.047)
-0.201***
(0.047)
-0.531***
(0.010)
-0.529***
(0.010)
-0.524***
(0.010)
0.308***
(0.011)
0.310***
(0.011)
0.313***
(0.011)
-0.059***
(0.011)
-0.023*
(0.013)
-0.054***
(0.012)
-0.035***
(0.013)
Marginal costij,t-1
Log # employeesi,t-1
Number of productsi,t-1
R2
Adjusted R2
Number of clusters
Product fixed effects
Year fixed effects
Observations
-0.081**
(0.031)
-0.313***
(0.021)
-0.309***
(0.020)
-0.316***
(0.020)
-0.007***
(0.001)
0.018***
(0.004)
Firm productivityi,t-1
Constant
0.023
(0.023)
-0.004***
(0.001)
-0.285***
(0.038)
-1.271***
(0.036)
-1.010***
(0.060)
-1.074***
(0.064)
-1.858***
(0.044)
-1.195***
(0.070)
-1.312***
(0.128)
-1.085***
(0.146)
-2.112***
(0.027)
-1.524***
(0.034)
-1.282***
(0.062)
-1.317***
(0.064)
0.48
0.45
4,016
0.70
0.69
4,009
0.70
0.69
4,009
0.70
0.69
4,009
0.72
0.71
3,953
0.70
0.68
1,915
0.70
0.68
1,915
0.70
0.68
1,915
0.90
0.90
4,016
0.93
0.92
4,009
0.93
0.92
4,009
0.93
0.92
4,009
62385
61479
61479
61479
62256
48848
48848
48848
62385
61479
61479
61479
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. All specifications are estimated using OLS. The product level is at 8-digit CN.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
Across both Tables 6 and 7, the coefficient of interest, β1 is identified purely from the
variation within a given product and across firms.
• The specification with firm-product fixed effects is the most demanding one. First,
the key parameter of interest, β1 is identified purely from the variation within a give
product-firm pair. In other words, all heterogeneity that is constant across time within a
product-firm pair is absorbed by these fixed effects. For example, factors such as product
image, firm brand value, national appeal of a good produced by a domestic manufacturer,
which can be thought of being constant across time and that are specific to the given
product-firm pair would be captured by the fixed effect.
Even in the most demanding specification, the result remains significant at conventional levels.
The slightly weaker significance should also be regarded in light of the fact that the average
duration across which a given product-firm pair is observed is 5 years. Hence, the decreased
strength of the import competition effect may stem from the shorter time span across which
34
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
the coefficient β is identified. In the last set of specifications the parameter is purely identified
from the variation within a given 8-digit product-firm pair.
Next, we proceed by investigating how markups respond to import competition by using
the variation within firms and across products. Hence, for now, we employ an additional set
of instruments to control for variant and invariant product characteristics. In the estimation
specification, I control for product rank within the firm, the type of product - intermediate,
consumption or capital types of manufactured goods by Danish firms both at the product and
product firm level.
• As we can see, Danish manufacturers of intermediate goods charge on average lower
markups than producers of capital and consumption goods. The interaction between
the good type and import competition shows that this effect is even more magnified
for intermediate goods, which suffer and even greater decline in their markups. This is
consistent with the observations that in the past 15 years imports of intermediate inputs
have been rising faster than imports in the final goods. Hence, globalization has partly
hit these type of manufacturers stronger than for example producers of consumption
goods as shown in column.
The following table examines the variation within firms across products.
D.
Product differentiation and import competition
Having markups at the product-firm level allows the researcher to investigate additional
margins along which import competition can affect product markups. Naturally, goods which
have a wider scope for quality differentiation can be partly shielded from tightened competitive
pressure due to distinct features, higher quality, design, etc. Furthermore, consumers may have
preferences for a specific brand or variety, which differs along various product characteristics.
Despite the rise of imports from Far East Asian countries, such goods would be less prone to
markup and price reductions due to product differentiation.
The economic literature has identified several ways of capturing product differentiation at
the product level. First, the elasticity of substitution among varieties of a given good gives an
indication of how substitutable different product varieties are.24 A high elasticity of substitution indicates that varieties are highly substitutable among each other. As pointed out by
Broda and Weinstein (2006), the median elasticity of substitution for US imports has gradually
declined, providing evidence that internationally traded goods have become more differentiated i.e varieties of the same good imported from many countries exhibit a low elasticity of
substitution.
24 The question of what is the exact definition of variety a multifaceted one. The literature has defined a variety in
several ways (see Feenstra (1994)), but this paper follows the logic of Broda and Weinstein (2006) and the definition put
forward by Armington (1969) that a given product-country pair is a unique variety. Chinese socks of cotton and Indian
socks of cotton are a different varieties of socks (product).
JULY 2016
MARKUPS AND IMPORT COMPETITION
35
Table 8—Prices, markups, marginal costs and import competition at the CN8 product-firm level. (Variation
within firms across products)
Markup (1)
Markup (2)
Markup (3)
MC (1)
MC (2)
MC (3)
Price (1)
Price (2)
Price (3)
Import competition (CN8)ijt
-0.517***
(0.066)
-0.443***
(0.066)
-0.284***
(0.057)
1.006***
(0.107)
0.297**
(0.118)
0.377***
(0.113)
-0.517***
(0.066)
-0.443***
(0.066)
-0.284***
(0.057)
Marginal costijt
-0.657***
(0.016)
-0.630***
(0.017)
-0.670***
(0.015)
0.343***
(0.016)
0.370***
(0.017)
0.330***
(0.015)
# of product sellersit
-0.009***
(0.001)
-0.005***
(0.001)
-0.015***
(0.001)
-0.010***
(0.001)
-0.009***
(0.001)
-0.005***
(0.001)
NOT core productijt
-0.800***
(0.050)
-0.709***
(0.046)
1.806***
(0.053)
1.823***
(0.051)
-0.800***
(0.050)
-0.709***
(0.046)
Number of productsit
-0.002
(0.002)
0.019***
(0.003)
-0.002
(0.002)
BEC Intermediate goodj
-2.354***
(0.156)
-1.871***
(0.179)
-2.354***
(0.156)
BEC Consumption goodj
-1.180***
(0.148)
-1.667***
(0.176)
-1.180***
(0.148)
Firm productivityit
Constant
R2
Adjusted R2
Number of clusters
Firm fixed effects
Year fixed effects
Observations
-0.263***
(0.026)
-0.315***
(0.025)
-0.313***
(0.024)
-1.386***
(0.045)
-0.693***
(0.069)
0.525***
(0.128)
-1.443***
(0.093)
-2.267***
(0.107)
-1.171***
(0.168)
-1.386***
(0.045)
-0.693***
(0.069)
0.525***
(0.128)
0.67
0.65
4,555
0.70
0.68
4,555
0.73
0.72
4,548
0.60
0.58
2,121
0.65
0.63
2,121
0.66
0.65
2,121
0.88
0.87
4,555
0.89
0.88
4,555
0.90
0.89
4,548
77595
77595
77559
61341
61341
61338
77595
77595
77559
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. All specifications are estimated using OLS. The reference group for type of product is capital good according to the BEC classification.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
The discussion about markups and quality is highly relevant in the context of production
differentiation. For example, the data reveals that the manufacturers of the same CN8 goods
charged different markups and sell at different prices. This observation reveals that quality
and markup choices are important especially in the context of the import competition. The
main concern in establishing a clear link between markups and quality is that the quality of
a given good is not directly observed. In fact, certain aspects of quality are subjective as
they are determined by consumer perceptions (hedonic and unobserved characteristics) and
not purely by observable and cardinal product characteristics. To understand better the link
between quality, I employ several measures, which have been shown to proxy for quality in
the literature. The first measure is the “elasticity of substitution”. Broda and Weinstein
(2006) provide estimates for U.S. imports. Overall, products with lower (higher) elasticity of
substitution are thought to be more differentiated (homogeneous) goods. Economic intuition
postulates that goods with a larger scope for differentiation are less substitutable to each other,
allowing firms to charge higher markups. The second measure aims at capturing the quality
content of a good conditional on prices and market shares. I rely on the structural model
36
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
Table 9—Prices, markups, marginal costs and lagged import competition at the CN8 product-firm level.
(Variation within firms across products)
Markup (1)
Markup (2)
Markup (3)
MC (1)
MC (2)
MC (3)
Price (1)
Price (2)
Price (3)
Import competition (CN8)ij,t-1
-0.604***
(0.074)
-0.459***
(0.074)
-0.313***
(0.065)
0.900***
(0.115)
0.199
(0.124)
0.288**
(0.119)
-0.474***
(0.074)
-0.409***
(0.075)
-0.248***
(0.064)
Marginal costij,t-1
-0.541***
(0.016)
-0.501***
(0.017)
-0.540***
(0.015)
0.301***
(0.017)
0.327***
(0.018)
0.280***
(0.015)
# of product sellersi,t-1
-0.008***
(0.001)
-0.004***
(0.001)
-0.015***
(0.002)
-0.010***
(0.001)
-0.010***
(0.001)
-0.006***
(0.001)
NOT core productij,t-1
-0.941***
(0.051)
-0.847***
(0.047)
1.672***
(0.057)
1.693***
(0.055)
-0.743***
(0.055)
-0.639***
(0.049)
Number of productsi,t-1
-0.006***
(0.002)
0.018***
(0.003)
-0.000
(0.002)
BEC Intermediate goodj
-2.129***
(0.156)
-1.943***
(0.194)
-2.492***
(0.178)
BEC Consumption goodj
-0.953***
(0.152)
-1.662***
(0.191)
-1.224***
(0.166)
Firm productivityi,t-1
Constant
R2
adj. R2
Number of clusters
Firm fixed effects
Year fixed effects
N
-0.115***
(0.026)
-0.149***
(0.026)
-0.146***
(0.025)
-1.167***
(0.055)
-0.437***
(0.077)
0.651***
(0.135)
-1.754***
(0.099)
-2.470***
(0.112)
-1.337***
(0.181)
-1.423***
(0.055)
-0.757***
(0.082)
0.486***
(0.151)
0.55
0.52
4,009
0.58
0.55
4,009
0.61
0.58
4,007
0.61
0.60
1,915
0.66
0.64
1,915
0.67
0.66
1,915
0.88
0.87
4,009
0.89
0.88
4,009
0.90
0.89
4,007
61479
61479
61460
48848
48848
48846
61479
61479
61460
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. All specifications are estimated using OLS. The reference group for type of product is capital good according to the BEC classification.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
byKhandelwal (2010) to obtain estimates at the CN8 product level.
In this paper, the elasticity of substitution is estimated for Danish imports following the
methodology suggested by Soderbery (2015), who shows that previously estimated elasticities
are biased upwards by up to 35%.25 The fact that the number of countries supplying each
good almost doubled serves as prima facie evidence of a startling increase in the number of
varieties. For example, reductions of trade costs may have made it cheaper to source new
varieties from different countries. Alternatively, the growth of economies like China, Korea,
and India has meant that they now produce more varieties that the United States would like
to import. But, of course, if these goods are differentiated by country, then this implies that
there must be some gain from the increase in variety—a point that we will address in the next
section.
• Exploring dynamics within firm portfolios can have import repurcussions for welfare
25 The suggested approach accounts for two important shortcomings: the small sample bias and infeasible estimates
of the elasticity of demand and supply. In the standard estimators, such as those in Feenstra (1994) and Broda and
Weinstein (2006), apply equal weighting to hyperbolaes introducing a bias. The alternative method by Soderbery (2015),
weights outliers using a LIML estimator. In case of economically unfeasible estimates of the elasticity (see p. 566 in
Broda and Weinstein (2006)), the final step constraints the grid search only to the feasible region.
JULY 2016
MARKUPS AND IMPORT COMPETITION
37
gains. As this new within firm channel of adjustment is import for firm profitability,
product survival and consequently product scope, the competitive effects within the firm
can have important aggregate implications. To test the central hypothesis that firms’
core products are more affected than their peripheral goods can be tested within the
empirical framework by studying the interaction between the product rank and import
competition. In what follows, I study these dynamics by estimating several specifications
of the main equation. First, I start by identifying the β coefficient purely from the
variation across products and within firms. To take into account other confounding that
can be correlated with import competition, I control for a wealth of product-firm, firm,
product and industry level controls. The equation taken to the data looks as follows:
′
ln (µijt ) = β1 ICijt + β2 rankingijt + β3 ICijt × rankingijt + Xijt δ + τi + φBEC
+ κt + ϵijt ,
j
The hypothesis about the effects along the product ladder within a firm, would imply that the
effect of import competition should intensify as a product moves closer to the core competency
of the firm.
From specification XXXX, the main interest lies in the heterogeneous effect of import competition across the firm’s product ladder. Formally, the change in markups due to import
competition is given by:
∂ ln (µijt )
= β1 + β3 rankingijt ,
∂ICijt
where the hypothesis is that β1 < 0 and β3 > 0, implying that import competition has a
greater impact on the core products of multi-product firms.
E. Response of Product scope to import competition
The trade literature has documented that one margin of adjustment to trade liberalization
and tighter import competition is via product portfolio changes for multi-product firms. The
focus has mainly been targeted at understanding the extent firms undertake changes in their
portfolios, but not so much on which products in fact get dropped. This sub-section fills this
gap by bring novel findings about the heterogeneous intrafirm adjustments with respect to
product markups. I test the hypothesis whether the products with already lower markups are
more likely to be discontinued from the production lines relative to products that are priced
with a higher markup by firms.
V. Robustness checks
VI. Conclusion
This paper studies the effects of import competition stemming from increased imports in
Denmark and the responses that firms make in the face of increased competitive pressure. The
38
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
Table 10—Markups and import competition effects across the product ladder.
Contemporaneous import competition
(1)
Markup
(2)
Markup
(3)
Markup
(4)
Markup
Import competition (CN8)ijt
-0.890***
(0.142)
-0.541***
(0.088)
-0.544***
(0.088)
-0.251***
(0.052)
Product rank x Import competition (CN8)ijt
0.058***
(0.014)
0.033***
(0.008)
0.037***
(0.010)
0.021***
(0.005)
Product rankijt
-0.171***
(0.034)
-0.086***
(0.023)
-0.112***
(0.017)
-0.071***
(0.013)
Lagged import competition
(5)
Markup
(6)
Markup
(7)
Markup
(8)
Markup
Import competition (CN8)ij,t-1
-0.951***
(0.125)
-0.713***
(0.085)
-0.456***
(0.089)
-0.308***
(0.062)
Product rank x Import competition (CN8)ij,t-1
0.064***
(0.018)
0.044***
(0.013)
0.044***
(0.011)
0.035***
(0.007)
Product rankij,t-1
-0.161***
(0.037)
-0.090***
(0.027)
-0.108***
(0.018)
-0.070***
(0.014)
Marginal costijt
-0.548***
(0.025)
-0.587***
(0.013)
0.024
(0.025)
-0.019
(0.011)
# of productsit
0.020***
(0.008)
0.018***
(0.004)
Single product firmit
0.229***
(0.065)
0.128***
(0.028)
Log # employeesit
Marginal costij,t-1
-0.439***
(0.026)
-0.471***
(0.012)
Log # employeesi,t-1
0.127***
(0.035)
-0.003
(0.014)
# of productsi,t-1
0.013**
(0.007)
0.011***
(0.003)
Single product firmi,t-1
0.307***
(0.068)
0.141***
(0.029)
Constant
R2
Adjusted R2
Number of clusters
Firm fixed effects
Year fixed effects
Product fixed effects
Sector fixed effects
Observations
0.687***
(0.128)
-1.170***
(0.130)
0.262***
(0.055)
-1.195***
(0.061)
0.552***
(0.141)
-1.309***
(0.160)
0.059
(0.090)
-1.060***
(0.067)
0.51
0.48
4,555
0.71
0.69
4,555
0.57
0.56
4,555
0.83
0.82
4,555
0.45
0.42
4,016
0.58
0.55
4,009
0.55
0.53
4,016
0.72
0.70
4,009
77595
77595
77595
77595
62385
61479
62385
61479
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. The reference group for type of product is capital good according to the BEC classification.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
results suggest that import competition does have a significant negative effect on product-firm
level markups. A 10% point increase in import competition reduces markups by around 4% to
12%, all else equal. These are sizeable effects and even after tackling potential endogeneity by
an instrumental variable approach, the magnitude increases up to 25%. These are sizeable and
economically significant effects, which suggest that trade policy and the increase in globalization have caused firms to adjust their operations by also reducing markups. Most importantly,
I provide evidence of heterogeneous responses along the product ladder within firms. Across
JULY 2016
MARKUPS AND IMPORT COMPETITION
39
Table 11—Prices, markups, marginal costs and import competition at the CN6 product level - Robustness.(Variation within products across firms)
Import competition (CN6)ijt
Markup (1)
Markup (2)
Markup (3)
Markup (4)
MC (1)
MC (2)
MC (3)
MC (4)
Price (1)
Price (2)
Price (3)
Price (4)
-0.556***
(0.096)
-0.290***
(0.047)
-0.322***
(0.048)
-0.303***
(0.047)
0.559***
(0.105)
0.496***
(0.111)
0.515***
(0.114)
0.444***
(0.112)
-0.154***
(0.052)
-0.290***
(0.047)
-0.322***
(0.048)
-0.303***
(0.047)
-0.661***
(0.011)
-0.659***
(0.011)
-0.655***
(0.011)
0.339***
(0.011)
0.341***
(0.011)
0.345***
(0.011)
-0.056***
(0.010)
-0.033***
(0.011)
-0.056***
(0.010)
-0.033***
(0.011)
Marginal costijt
Log # employeesit
Number of productsit
0.035
(0.022)
-0.005***
(0.001)
0.018***
(0.004)
Firm productivityit
Constant
R2
Adjusted R2
Number of clusters
Product fixed effects
Year fixed effects
Observations
-0.071**
(0.031)
-0.005***
(0.001)
-0.360***
(0.021)
-0.353***
(0.020)
-0.362***
(0.020)
-0.310***
(0.041)
-1.508***
(0.033)
-1.262***
(0.055)
-1.302***
(0.057)
-1.846***
(0.047)
-1.037***
(0.072)
-1.214***
(0.133)
-0.980***
(0.155)
-2.122***
(0.027)
-1.508***
(0.033)
-1.262***
(0.055)
-1.302***
(0.057)
0.47
0.45
4,555
0.81
0.80
4,555
0.81
0.80
4,555
0.81
0.80
4,555
0.70
0.69
4,481
0.68
0.66
2,121
0.68
0.66
2,121
0.68
0.66
2,121
0.90
0.89
4,555
0.93
0.93
4,555
0.93
0.93
4,555
0.93
0.93
4,555
77595
77595
77595
77595
77595
61341
61341
61341
77595
77595
77595
77595
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. All specifications are estimated using OLS. The product level is at 6-digit CN.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
Table 12—Prices, markups, marginal costs and lagged import competition at the CN6 product level Robustness.(Variation within products across firms)
Import competition (CN6)ij,t-1
Markup (1)
Markup (2)
Markup (3)
Markup (4)
MC (1)
MC (2)
MC (3)
MC (4)
Price (1)
Price (2)
Price (3)
Price (4)
-0.376***
(0.095)
-0.223***
(0.061)
-0.258***
(0.061)
-0.236***
(0.061)
0.407***
(0.107)
0.330***
(0.112)
0.343***
(0.114)
0.301***
(0.113)
-0.134**
(0.053)
-0.207***
(0.050)
-0.239***
(0.050)
-0.227***
(0.050)
-0.531***
(0.010)
-0.529***
(0.010)
-0.525***
(0.010)
0.308***
(0.011)
0.310***
(0.011)
0.313***
(0.011)
-0.059***
(0.011)
-0.023*
(0.013)
-0.054***
(0.012)
-0.035***
(0.013)
Marginal costij,t-1
Log # employeesi,t-1
Number of productsi,t-1
0.022
(0.023)
-0.007***
(0.001)
0.018***
(0.004)
Firm productivityi,t-1
Constant
R2
Adjusted R2
Number of clusters
Product fixed effects
Year fixed effects
Observations
-0.082***
(0.031)
-0.004***
(0.001)
-0.313***
(0.021)
-0.309***
(0.020)
-0.316***
(0.020)
-0.310***
(0.040)
-1.267***
(0.037)
-1.005***
(0.060)
-1.070***
(0.065)
-1.817***
(0.047)
-1.147***
(0.073)
-1.259***
(0.131)
-1.031***
(0.149)
-2.086***
(0.029)
-1.517***
(0.035)
-1.274***
(0.063)
-1.309***
(0.065)
0.48
0.45
4,016
0.70
0.69
4,009
0.70
0.69
4,009
0.70
0.69
4,009
0.72
0.71
3,953
0.70
0.68
1,915
0.70
0.68
1,915
0.70
0.68
1,915
0.90
0.90
4,016
0.93
0.92
4,009
0.93
0.92
4,009
0.93
0.92
4,009
62385
61479
61479
61479
62256
48848
48848
48848
62385
61479
61479
61479
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. All specifications are estimated using OLS. The product level is at 6-digit CN.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
several specifications, the findings suggest that product markups closer to the core competency
of the firm are more sensitive to import competition than peripheral products.
The policy implication of this study is that multi-product firms do not respond in the same
way as single product firms. The evidence corroborated here suggest that firms adjust the
markups of their core products more compared to their peripheral goods. Ignoring this level
of adjustments misses an important aspect of how trade induces within product and within
40
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
Table 13—Prices, markups, marginal costs and import competition at the CN6 product level - Robustness.(Variation within firms across products)
Markup (1)
Markup (2)
Markup (3)
MC (1)
MC (2)
MC (3)
Price (1)
Price (2)
Price (3)
Import competition (CN6)ijt
-0.527***
(0.069)
-0.470***
(0.070)
-0.290***
(0.061)
0.907***
(0.105)
0.219*
(0.112)
0.297***
(0.108)
-0.527***
(0.069)
-0.470***
(0.070)
-0.290***
(0.061)
Marginal costijt
-0.659***
(0.016)
-0.631***
(0.017)
-0.670***
(0.015)
0.341***
(0.016)
0.369***
(0.017)
0.330***
(0.015)
# of product sellersit
-0.009***
(0.001)
-0.005***
(0.001)
-0.015***
(0.001)
-0.010***
(0.001)
-0.009***
(0.001)
-0.005***
(0.001)
NOT core productijt
-0.808***
(0.050)
-0.715***
(0.046)
1.822***
(0.053)
1.842***
(0.051)
-0.808***
(0.050)
-0.715***
(0.046)
Number of productsit
-0.002
(0.002)
0.019***
(0.003)
-0.002
(0.002)
BEC Intermediate goodj
-2.357***
(0.156)
-1.859***
(0.179)
-2.357***
(0.156)
BEC Consumption goodj
-1.187***
(0.148)
-1.655***
(0.175)
-1.187***
(0.148)
Firm productivityit
Constant
R2
Adjusted R2
Number of clusters
Firm fixed effects
Year fixed effects
Observations
-0.267***
(0.026)
-0.317***
(0.025)
-0.315***
(0.024)
-1.388***
(0.044)
-0.683***
(0.069)
0.533***
(0.129)
-1.388***
(0.091)
-2.240***
(0.105)
-1.158***
(0.168)
-1.388***
(0.044)
-0.683***
(0.069)
0.533***
(0.129)
0.67
0.65
4,555
0.70
0.68
4,555
0.73
0.72
4,548
0.59
0.58
2,121
0.65
0.63
2,121
0.66
0.65
2,121
0.88
0.87
4,555
0.89
0.88
4,555
0.90
0.89
4,548
77595
77595
77559
61341
61341
61338
77595
77595
77559
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. The reference group for type of product is capital good according to the BEC classification.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
firm reallocation and how welfare gains from trade are realized. These novel findings are the
main contribution of the paper, which emphasizes the importance of multi-product firms and
the within firm heterogeneous effects. Furthermore, I show evidence that quality differentiation
can help alleviate competitive pressure for firms.
This paper also leaves open several avenues for your future research. For example, the
current paper assess the import competition from all countries on markups. However, an
interesting question is whether import competition from certain geographical regions has had
a differential effects on markups. Here I have taken a global view on import competition in
order to also shed light on globalization’s impact on firm behavior at the most disaggregated
level. Another natural extension of this line of research, which emphasizes the importance
of multi-product firms and various performance measures, would be to study in a unified
framework markups, quality and import competition. It is highly possible that firms may
improve the quality of their core products, which would then allow firms to partly shield
themselves from competitive pressure. This paper has only hinted towards the fact that firms
that produce differentiated goods charge higher markups and that the response to import
JULY 2016
MARKUPS AND IMPORT COMPETITION
41
Table 14—Prices, markups, marginal costs and lagged import competition at the CN6 product level Robustness.(Variation within firms across products)
Markup (1)
Markup (2)
Markup (3)
MC (1)
MC (2)
MC (3)
Price (1)
Price (2)
Price (3)
Import competition (CN6)ij,t-1
-0.618***
(0.078)
-0.494***
(0.078)
-0.322***
(0.070)
0.828***
(0.117)
0.151
(0.123)
0.240**
(0.119)
-0.499***
(0.079)
-0.455***
(0.079)
-0.267***
(0.070)
Marginal costij,t-1
-0.543***
(0.016)
-0.501***
(0.017)
-0.541***
(0.015)
0.300***
(0.017)
0.327***
(0.018)
0.280***
(0.015)
# of product sellersi,t-1
-0.008***
(0.001)
-0.004***
(0.001)
-0.015***
(0.002)
-0.010***
(0.001)
-0.010***
(0.001)
-0.006***
(0.001)
NOT core productij,t-1
-0.948***
(0.052)
-0.854***
(0.047)
1.682***
(0.057)
1.705***
(0.054)
-0.749***
(0.055)
-0.644***
(0.050)
Number of productsi,t-1
-0.006***
(0.002)
0.018***
(0.003)
-0.000
(0.002)
BEC Intermediate goodj
-2.131***
(0.156)
-1.936***
(0.194)
-2.492***
(0.178)
BEC Consumption goodj
-0.961***
(0.152)
-1.653***
(0.190)
-1.230***
(0.166)
Firm productivityi,t-1
Constant
R2
Adjusted R2
Number of clusters
Firm fixed effects
Year fixed effects
Observations
-0.118***
(0.027)
-0.151***
(0.026)
-0.147***
(0.025)
-1.163***
(0.055)
-0.418***
(0.078)
0.664***
(0.136)
-1.712***
(0.099)
-2.452***
(0.112)
-1.330***
(0.182)
-1.413***
(0.056)
-0.734***
(0.083)
0.500***
(0.152)
0.55
0.52
4,009
0.58
0.55
4,009
0.61
0.58
4,007
0.61
0.60
1,915
0.66
0.64
1,915
0.67
0.66
1,915
0.88
0.87
4,009
0.89
0.88
4,009
0.90
0.89
4,007
61479
61479
61460
48848
48848
48846
61479
61479
61460
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors clustered at the firm level. All specifications are estimated using OLS. The reference group for type of product is capital good according to the BEC classification.
Note: The reason why the number of observations in the estmiation of MC falls is because we included firm-level productivity control. However, this
estimate is only available for multi-product firms and is derived from the numerical optimization procedure. Hence, the subsample of single-product
firms does not have an estimate for productivity.
competition becomes less pronounced compared to manufacturers of homogeneous products,
which do not have a scope for vertical differentiation. Another interesting area of research
is the link between product churning and within firm portfolio adjustments and markups. A
research agenda to study jointly the effects of import competition on quality, markups and
product churning in multi-product firms would be highly complementary to recent studies such
as Manova and Zhang (2012b) and Iacovone and Javorcik (2010). I leave these new horizons
and unexplored areas for future research.
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Appendix A: Data
This section sheds further light on the data management routines adopted in the paper and
offers additional descriptive results.
A1. Data cleaning algorithms
In this subsection I discuss the data cleaning and merging process among the different
datasets used in the paper. The objective is to shed light on some practical issues and how I
overcome them in order to obtain the final dataset. To facilitate the discussion, Figure A1 maps
the different databases and shows how they are linked together to obtain the final estimation
sample. This is the dataset that is used for the econometric analysis of import competition on
product-firm level markups. As discussed in Section III.A, I rely on single product firms to
estimate the parameters of the production function as this allows me to circumvent the input
allocation bias at this stage and still obtain consistent and unbiased estimates.
Figure A1. Data structures
VARS - Firm-product level data
for manufacturing firms
Period: 1999-2012
Product classification: CN8/CN8+
# firm-product-year obs: 90,331
Frequency: Annual
FIRE - Firm-level balance sheet
and accounting data for all firms
Period: 1999-2012
Industry classification: NACE Rev.2
# firm-year obs: 31,479
Frequency: Annual
UHDI - Firm-product-country
level data on all imports/exports
Period: 1998-2012
Product classification: CN8/CN8+
# firm-product-year obs: > 13M
Frequency: Annual
BACI - Country-product level
data on global imports/exports
Period: 1998-2012
Product classification: HS6/HS6+
# coun.-product-year obs: > 95M
Frequency: Annual
Estimation sample
Final sample after cleaning containts
the information to estimate markups
and conduct the econometric analysis.
No missing values for the key
Single product firms sample for
productivity estimation
Period: 1999-2012
Industry classification: NACE Rev.2
# firm-product-year obs: 17,378
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VARS - Survey of manufacturing firms
The dataset based on the survey of manufacturing firms in Danish firms is essential to
conduct the analysis. First, the level of observation is quarterly, which requires the aggregation
up to annual level to match with the other datasets. Firms do not always produce a given good
in each quarter. This requires some additional care as for some observations in a quarter firms
do not report quantity, whereas in other quarters they do. The implication of this caveat is
that for certain product categories the unit values may get highly inflated because of missing
quantity in some quarters. The data revealed that across quarters within a product-firm-year
triplet the measurement unit does not change at the CN10 nor at the CN8 level, which allows
the product data to be aggregated to the yearly level and further to CN8. Second, a lot
of firms report goods with either missing quantity or measurement unit. This constitutes a
problem as simply dropping products for which the unit price cannot be calculated, leads to
a severe bias in the actual number of products that a firm manufactures. Especially, in the
context of this study, observing as much as possible of the actual product units that a firm
produces is essential. Consider, for example, dropping a firm that reported in a given year the
production of 10 different varieties. Value of production is reported for all 10 products but
quantity units are provided for only 5 products. Since prices and unit values are unobserved
in the data, they are calculated by dividing the total value of production by the quantity
manufactured within disaggregated product categories. The missing 5 products have to be
dropped from the analysis as prices cannot be computed. The manufacturing output database
has around 26% of all product-firm-year observations quantity information is missing and for
12.3% of the observations measurement units are unavailable. The problem could be ignored
if, for example, all products with missing information are reported by firms that have missing
values for all products in their production portfolio. Such a scenario would allow me simply
to drop those firms with missing values and preserve only firms that reported their products’
information without gaps.
I develop an algorithm which allows me to make an informed decision regarding which
product-firm pairs can be dropped and where the “missing product” bias will not pose a
threat to the estimation. First, for 19% of the total observations, firms report products in
their portfolio for which they never report quantity throughout the sample. In other words,
these are goods that exist in their product range but due to missing quantity, they cannot
be used in the estimation. In those specific cases, I drop these products and make sure that
such products with a complete series of missing quantity do no represent more than 20%
of the total sales. Furthermore, I make sure that firms manufacturing two products without
reporting quantity for one of them are not erroneously treated as single-product firms. I simply
drop the entire firm series from the sample. After adopting this cleaning procedure only 8.5%
of observations do not have quantity. These instances feature products where firms provide
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quantity for some years and not for others during the sample period. Hence, I calculate a
the ratio between the number of years with no quantity information for a given firm-product
pair relative to the total number of years that this product-firm pair has existed. The applied
criterion is:

keep if T _ij_missingij ≤ 20%
T _ij_totalij
1
crij
=
drop if T _ij_missingij > 20% ,
T _ij_totalij
where entire product-firm series are dropped if for more than 20% of the observed duration
there is no reported quantity. It is important to account for these instances as simply dropping
the observation for which the econometrician does not observe quantity would introduce a
bias related to product introduction and dropping behavior of firms. Capturing true product
dropping is crucial for the analysis of portfolio adjustments and markups. When a product-firm
pair is preserved, I simply leave the quantity as missing.
To assess the severity of the zero quantity observations in the remaining cases, I construct
two variables. The first one indicates the total number of unique products, N prodit (including
products for which value is available but quantity is missing) produced by a firm in a given year
and the second one counts the total number of products with positive quantity information,
N prod_qit . The decision rule whether to drop an entire firm series is based on a criterion:
2
crit
=

keep
it −N prod_qit
if N prodN
≤ 20%
prodit
drop if N prodit −N prod_qit > 20%.
N prodit
In cases where products with missing quantity represent more than 20% of the product
portfolio in a given year, I discard not only the products with missing quantity information
but the entire firm series, which also may included product for which the product information
is available. This strategy does not result in many firms suddenly entering and exiting the
sample due to this cleaning approach. After dropping those firm-year observations, I am left
with a sample of firms, which in general systematically report information about product value
and quantity.
The final step in cleaning VARS is to concord the annual 8-digit CN codes across time
following the methodology by Beveren, Bernard and Vandenbussche (2012). By definition, this
approach creates a synthetic classification where several product codes are collapsed into one
or alternatively, even expanded into more. This concordance exercise is essential to study the
dynamic responses of markups and import competition. The end result is a sample of 90,331
observations, uniquely identified by CN8+ product-measurement unit-firm-year combination.
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MARKUPS AND IMPORT COMPETITION
49
Concordance of production and trade data
The Combined Nomenclature (CN) product classification cannot be mapped 1:1 to NACE
industries as a direct correlation table is not available between the two. Instead, I adopt
a two-step procedure, which allows me to link each 8-digit CN code and the industry to
which it belongs at the 3- and 4-digit NACE Rev. 2 classification. In most countries of
the European Union, production data is recorded at the 8-digit level using the PRODCOM
(PC) classification. It has the beneficial feature that the first four digits denote the industrial
affiliation of the manufacturing enterprise according to NACE and the remaining digits specify
the product at a more disaggregated level. In the first step I map the individual PC8 code to its
industry. In the second step, I rely on the concordance method developed in Beveren, Bernard
and Vandenbussche (2012) to link PC8 to CN8 in a cross section for a given year. A big
majority of PC8 codes have a corresponding CN equivalent, however certain codes belonging
to the category of animals are unclassified in PC8. In total, 94% of all product codes from
VARS are successfully mapped with their corresponding PC8 code. The final step links CN8
products to their primary industry affiliation at the 3- and 4-digit NACE Rev.2 classification.
Establishing this link has the benefit that market shares, used in the input price estimation
can be defined according to an alternative market definition, which is product-based (CN)
instead of firm industry-based (NACE).
In 2003 NACE Rev. 1.1 underwent a slight revision and in 2008 a substantial change in the
industry codes led to the introduction of NACE Rev. 2. Since Table A1 shows the mapping
for a cross-section in 2010, the PC8 codes are based on the NACE Rev. 2. Beveren, Bernard
and Vandenbussche (2012) provide a mapping key for 2003 and 2005 between NACE Rev. 1.1
and PC8. I extend the methodology to also allow the linking to NACE Rev. 2 as this is the
version adopted in the empirical analysis. The important element in this mapping of products
to industry affiliation is that each CN8 code belongs to only one 3- or 4-digit NACE code.
Alternatively, one may attempt to concord the NACE Rev. 1.1 with Rev. 2 using the officially
provided keys by Eurostat or Statistics Denmark. The issue with this approach is that the
classifications feature codes that get expanded or split during the conversion from the old to
the new system.
FIRE - Balance sheet and accounting data
This dataset provides the necessary firm-level information for the markup estimation, where
variables at the firm level, such as capital, labour and material inputs are needed. For this
purpose, I preserve the information on revenue, material expenditures, labour in fulltime
equivalent units (FTE), total wages and compensation paid by firms, industry affiliation by
NACE Rev. 2, value-added, total fixed assets, material fixed assets along with industry-specific
deflators provided by Statistics Denmark. Table provides descriptive statistics on the sectoral
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(2-let.)
NACE
CB
CG
13.20
13.10
(4-dig.)
NACE
(2-dig.)
13
22
22.11
22.19
Row description
Table A1—Excerpt of the mapping among PC8, CN8 and NACE Rev. 2 classifications
CN2010
13107200
13107200
13107200
53089019
53089012
53082090
53082010
53081000
Yarn of other vegetable textile fibres; other and paper yarn
Yarn of other vegetable textile fibres; paper and ramie yarn measuring less than 277,8 decitex (exceeding 36 metric number)
Yarn of other vegetable textile fibres; paper and ramie yarn measuring 277,8 decitex or more (not exceeding 36 metric number)
Yarn of other vegetable textile fibres; paper and true hemp yarn, put up for retail sale
Yarn of other vegetable textile fibres; paper and true hemp yarn, not put up for retail sale
(8-dig.)
PC2010
Manufacture of textiles
Textiles and leather products
13107200
53089050
Yarn of other vegetable textile fibres; paper and coir yarn
13107200
Yarn of other vegetable textile fibres; other
Preparation and spinning of textile fibres
13107200
...
53089090
13201330
53091900
53091190
53091110
Woven fabrics of flax, containing less than 85 % by weight of flax, unbleached or bleached
Woven fabrics of flax, containing 85 % or more by weight of flax, other
Woven fabrics of flax, containing 85 % or more by weight of flax, bleached
...
...
13107200
13201330
53092100
Woven fabrics of flax, containing 85 % or more by weight of flax, unbleached
13201330
Woven fabrics of flax, containing less than 85 % by weight of flax, other
Weaving of textiles
13201360
...
53092900
...
...
13201360
Manufacture of rubber and plastic products
Manufacture of plastic and glass
22111357
22111355
22111100
40114000
40113000
40112090
40112010
40111000
New pneumatic tyres of rubber of a kind used on motorcycles
New pneumatic tyres of rubber of a kind used on civil aircraft
New pneumatic tyres of rubber of a kind used on buses or lorries with a load index exceeding 121
New pneumatic tyres of rubber of a kind used on buses or lorries with a load index not exceeding 121
New pneumatic tyres of rubber of a kind used on motor cars
22111370
New pneumatic tyres of rubber of a kind used on bicycles
Manufacture of rubber tyres and tubes; retreading and rebuilding of rubber tyres
22111200
...
40115000
40101200
40101100
Conveyor or transmission belts or belting, of vulcanised rubber, other
Conveyor or transmission belts or belting, of vulcanised rubber, reinforced only with textile materials
...
...
22111200
22194050
40101900
Conveyor or transmission belts or belting, of vulcanised rubber, reinforced only with metal
22194050
Manufacture of other rubber products
22194050
Note: The CN8 to PC8 conversions are based on the codes from 2010 and are based on the approach by Beveren, Bernard and Vandenbussche (2012). This link is cross-sectional and is easily
extended across the sample period thanks to the intertemporal mapping of CN8 to CN8+ codes. The 4-digit NACE codes are based on the first 4 digits of the PC code and correspond to the
classification from Rev. 2. The letter codes in the first row represent the 36 industry groupings constructed by Statistics Denmark. Most of the letter codes represent a more aggregated grouping of
the 2-digit NACE Rev. 2 codes. Not all CN codes have an equivalent PC code.
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MARKUPS AND IMPORT COMPETITION
51
composition, number of single product firms, average wage, revenue, number of products and
employees by industrial sector in the sample.
BACI - World trade database
This dataset contains in essence the universe of global trade transactions at the productimporter-exporter country-year level observed annually. The product information is reported
according to the 6-digit Harmonized System (HS) classification used to report world trade
data. The BACI dataset is based on the United Nations’ COMTRADE database (Gaulier
and Zignago, 2010) and maintained at the French research institute CEPII. The 8-digit CN
and 6-digit HS classifications share a common base where the first 6-digits are identical. This
allows me to link the production data coming from Danish manufacturing firms (VARS) with
the world trade database at a highly disaggregated level. It is important to note that the
HS classification has gone through only four rounds of revisions whereas CN is revised on a
yearly basis, which requires the researcher to concord products that change their codes in both
classifications.
The data in BACI for the period 1998-2012 is reported in the HS96 version, which implies
that all product codes are already harmonized across sample years. To link this information
with the CN product codes from the manufacturing survey it is only required to concord the
HS96 codes to CN8 and then to CN8+ codes in a single year and then extend the mapping
across years in the BACI database. From the global trade dataset, I can construct the world
export supply (WES) of all countries from which Denmark imports. The rationale behind
WES is that it captures global exports to all countries excluding Denmark.
A2.
Supplementary descriptive statistics
Table A2 shows that all IC measures are positively correlated with the strength declining as
CN 8
the product definition becomes more aggregated. The most disaggregated measures - ICjt
CN 6 posit a correlation coefficient of 0.87, which is sensible given that in the sample
and ICjt
there are 2,694 unique varieties at the CN8 level and 1,912 unique CN6 products.
Appendix B: Estimation routines
This section of appendix provides further technical details in relation to the markup estimation algorithm, closely following De Loecker et al. (2016). In what follows, the allocation
and input biases bias arising in multi-product firms are discussed together. Consider the
product-level production function:
(B1)
qijt = fj (xijt ; β) + ωit + ϵijt ,
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AARHUS UNIVERSITY WORKING PAPER
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Table A2—Correlations between IC measures at different product level aggregations
CN 8 IC CN 6 IC CN 4 IC CN 3 IC CN 2 IC CN −N ACE
ICjt
jt
jt
jt
jt
jt
CN 8
ICjt
1.00
CN 6
ICjt
CN 4
ICjt
CN 3
ICjt
CN 2
ICjt
CN −N ACE
ICjt
0.87
1.00
0.68
0.78
1.00
0.49
0.56
0.72
1.00
0.46
0.53
0.66
0.87
1.00
0.35
0.40
0.47
0.54
0.55
1.00
−1.0
−0.5
0.0
0.5
Log unit values
1999
1.0
1.0
0.0
0.2
0.4
CDF
0.6
0.8
1.0
0.8
0.6
CDF
0.4
0.2
0.0
0.0
0.2
0.4
CDF
0.6
0.8
1.0
Note: All correlation coefficients are significant at the 1% level. The IC measures are computed at different levels of aggregation, where the
subscript signifies the number of product digits according to CN . The last IC measure is computed at the NACE Rev. 2, 36 groupings classification
(CN − N ACE), described in Table A1. The final estimation sample consists of 10 NACE 2-letter industries, shown in Table 1. All CN 8 products
belonging to a given 2-letter NACE are summed together and the variable is computed as in equation (2). Only products that are included in the
final sample of manufacturing goods are used in the construction of the correlation table.
−2.0
−1.0
0.0
1.0
Log marginal costs
2012
1999
2.0
−2.0
−1.0
0.0
1.0
2.0
Log markups
2012
1999
2012
Figure A2. Cumulative distribution of real unit values, marginal costs and markups in 1999 and 2012
Note: The CDF plots include only firm-product pairs that are both present in 1999 and 2012. Observations above and below the 97th and 3rd
percentile are excluded. The unit values, marginal costs and markups are demeaned, by product-firm fixed effects and the residuals are plotted.
where the subscript j denotes the product, i indexes the firms and t the time period. Output
in physical units is denoted by qijt , xijt = {v ijt , kijt } are the log of static and dynamic inputs
to the production function, ωit is Hicks-neutral productivity and ϵijt is a measurement error or
unexpected shocks to productivity that are uncorrelated with inputs. Properly estimating (B1)
requires that all inputs are in physical units. With the exception of labour, all other inputs
such as capital, materials and energy are obtained from firms’ balance sheets, which only report
the monetary value but not the actual units used. This poses a problem for the econometrician
due to the unobservability of key production inputs. The standard approach in the literature
has been to rely on deflated inputs, where the monetary values of materials and capital are
divided by industry-specific deflators as no firm dataset provides detailed information on the
-1.315***
(0.056)
-0.005***
(0.001)
-0.032***
(0.011)
-0.655***
(0.011)
-0.262***
(0.044)
-0.324***
(0.037)
-0.324***
(0.082)
(5)
Markup
-1.285***
(0.036)
-0.531***
(0.010)
-0.162***
(0.056)
(6)
Markup
0.81
0.80
4,555
77595
0.47
0.45
4,555
77595
77595
0.81
0.80
4,555
-0.022*
(0.013)
-0.525***
(0.010)
-0.166***
(0.056)
(8)
Markup
77595
0.81
0.80
4,555
62385
0.47
0.45
4,016
61479
0.70
0.69
4,009
61479
0.70
0.69
4,009
61479
0.70
0.69
4,009
77595
0.47
0.45
4,555
-0.349***
(0.040)
-0.439***
(0.092)
(9)
Markup
77595
0.81
0.80
4,555
-1.518***
(0.033)
-0.661***
(0.011)
-0.260***
(0.047)
(10)
Markup
77595
0.81
0.80
4,555
-1.278***
(0.055)
-0.055***
(0.010)
-0.659***
(0.011)
-0.281***
(0.048)
(11)
Markup
77595
0.81
0.80
4,555
-1.318***
(0.057)
-0.005***
(0.001)
-0.032***
(0.011)
-0.656***
(0.011)
-0.263***
(0.047)
(12)
Markup
62385
0.47
0.45
4,016
-0.345***
(0.039)
-0.268***
(0.091)
(13)
Markup
61479
0.70
0.69
4,009
-1.279***
(0.037)
-0.531***
(0.010)
-0.186***
(0.061)
(14)
Markup
61479
0.70
0.69
4,009
-1.023***
(0.060)
-0.058***
(0.011)
-0.529***
(0.010)
-0.210***
(0.061)
(15)
Markup
61479
0.70
0.69
4,009
-1.087***
(0.064)
-0.007***
(0.001)
-0.022*
(0.013)
-0.525***
(0.010)
-0.189***
(0.061)
(16)
Markup
Note: The markup is always estimated at the CN8 product-firm level. The table reports additional robustness results regarding the timing of the import competition effect and also allows for a wider
range of products to impact markups at the CN8 level.
Standard errors clustered at the firm level. All specifications are estimated using OLS.
* p < 0.10, ** p < 0.05, *** p < 0.01
Standard errors in parentheses
Adjusted R2
Number of clusters
Product fixed effects
Year fixed effects
Observations
R2
-1.030***
(0.059)
-0.058***
(0.011)
-0.529***
(0.010)
-0.184***
(0.056)
(7)
Markup
-1.094***
(0.063)
-1.276***
(0.054)
-0.055***
(0.010)
-0.659***
(0.011)
-0.278***
(0.044)
(4)
Markup
Constant
-1.516***
(0.032)
-0.661***
(0.011)
-0.259***
(0.043)
(3)
Markup
-0.007***
(0.001)
-0.304***
(0.039)
-0.552***
(0.088)
(2)
Markup
Number of productsi,t-1
Log # employeesi,t-1
Marginal costij,t-1
Number of productsit
Log # employeesit
Marginal costijt
Import competition (CN6)j,t-1
Import competition (CN6)jt
Import competition (CN8)j,t-1
Import competition (CN8)jt
(1)
Markup
Table A3—Markup responses and import competition at the CN6 and CN8 product level
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MARKUPS AND IMPORT COMPETITION
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AARHUS UNIVERSITY WORKING PAPER
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prices paid for its inputs. The implication of these data limitations are two fold. First, the
researcher can only observe the log of a deflated inputs, x̃ijt instead of the actual quantities of
each input used. This causes a bias in the production function estimate coefficients. Second,
under the input divisibility assumptions in the theoretical model of De Loecker et al. (2016),
one also needs the input allocation share across products. In other words, the econometrician
needs to know the share of materials that are used for the production of a given good by a
firm. Denote by ρijt the input allocation share for product j, manufactured by firm i at time
t. The bias arising from not observing the input allocation shares, ρijt and the physical inputs
used, xijt can be expressed as follows. All the input expenditures that a firm has are simply
the sum of all input prices they pay for the materials needed in the production of a given
∑
x
x
x
product:
j Wijt Xijt = T Eit , where T Eit denotes the total expenditure on input x by firm i
in period t. The expenditure on input x for product j, can be expressed as :
x
Wijt
Xijt
(B2)


∑
x
= ρ̃ijt 
Wijt
Xijt 
=
j
x
ρ̃ijt T Eit
The adopted method in the literature has been to deflate total expenditures on a given input
by PPI or a materials price index available from National statistical offices. Dividing both
sides of Equation (B2) yields:
(B3)
x X
Wijt
ijt
Pdt
= ρ̃ijt
T Eitx
,
Pdt
where the subscript d denotes an industry to reflect the fact that the price index is comT Ex
puted at a higher level of aggregation. Define X̃it ≡ Pdtit , which simply is the deflated total
expenditure on input x. This is the measure which has been most often used in production
functions as both the numerator and denominator are observed in the data. Equation (B3)
can be re-expressed using X̃it and after taking logs yields:
(
x X )
(
)
Wijt
ijt
ln
= ln ρ̃ijt X̃it
Pdt
x
wijt
− pdt + xijt = ρijt + x̃it ,
x −p
where all smallcase variables are in logs and ln (ρ̃ijt ) = ρijt . Note that wijt
dt denotes
the product-firm-specific input price deviation from the industry average. Finally, the log of
a given input x is:
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MARKUPS AND IMPORT COMPETITION
55
( x
)
xijt = ρijt + x̃it − wijt
− pdt ,
(B4)
which shows that production inputs will generally depend on the allocation share, ρijt and the
X − p .26 Not taking
deviation of firm-specific input prices from the industry level prices, wijt
it
into account the bias arising from the unobserved input prices and allocation shares across
products, would lead to biased production function coefficients.
B1. Input price and Allocation bias in production functions
To formally obtain the general form of the estimation equation that takes into account the
input price and allocation biases, consider a translog production function in three inputs:
labour, Lijt , materials, Mijt and capital, Kijt . We maintain the previous notation where
small letters denote logs. The following additional derivations lead to the final expressions in
De Loecker et al. (2016). Using the result from (B4) and substituting it into the following
expression
2
2
qijt = βl lijt + βk kijt + βm mijt + βll lijt
+ βkk kijt
+ βmm m2ijt + βlk lijt kijt
(B5)
+βlm lijt mijt + βmk mijt kijt + βlkm lijt kijt mijt + ωit + ϵijt ,
shows that the translog production function can be segmented into several parts:
qijt
=
[
]
[
]
[
]
l
k
m
βl ρijt + l̃it − wijt
+ βk ρijt + k̃it − wijt
+ βm ρijt + m̃it − wijt
[
]
( )2 (
)2
l
l
l
+ 2ρijt l̃it − 2l̃it wijt
− 2ρijt wijt
+βll ρ2ijt + l̃it + wijt
[
]
( )2 (
)2
k
k
k
+βkk ρ2ijt + k̃it + wijt
+ 2ρijt k̃it − 2k̃it wijt
− 2ρijt wijt
[
]
( m )2
m
m
+βmm ρ2ijt + (m̃it )2 + wijt
+ 2ρijt m̃it − 2m̃it wijt
− 2ρijt wijt
[
]
k
k
l
k
l
k
+βlk ρ2ijt + ρijt k̃it − ρijt wijt
+ ρit l̃it + l̃it k̃it − l̃it wijt
− ρijt wijt
− k̃it wijt
+ wijt
wijt
[
]
m
m
l
m
l
m
+βlm ρ2ijt + ρijt m̃it − ρijt wijt
+ ρit l̃it + l̃it m̃it − l̃it wijt
− ρijt wijt
− m̃it wijt
+ wijt
wijt
[
]
k
k
m
k
m k
+βkm ρ2ijt + ρijt k̃it − ρijt wijt
+ ρit m̃it + m̃it k̃it − m̃it wijt
− ρijt wijt
− k̃it wijt
+ wijt
wijt
m
m
l
l
l̃it
− ρijt wijt
− ρ2ijt wijt
+ ρ2ijt m̃it + ρijt m̃it l̃it − ρijt m̃it wijt
+βlkm [ρ3ijt + ρ2ijt l̃it − ρ2ijt wijt
m l
l
l
+ρijt wijt
wijt + ρ2ijt k̃it + ρijt l̃it k̃it − ρijt wijt
k̃it + ρijt m̃it k̃it + m̃it l̃it k̃it − m̃it wijt
k̃it
m
m
m l
k
k
l
k
k
−ρijt wijt
k̃it − wijt
l̃it k̃it + wijt
wijt k̃it − ρ2ijt wijt
− ρijt l̃it wijt
+ ρijt wijt
wijt
− ρijt m̃it wijt
(B6)
k
l
k
m k
m
k
m l
k
−m̃it l̃it wijt
+ m̃it wijt
wijt
+ ρijt wijt
wijt + wijt
lit wijt
− wijt
wijt wijt
] + ωit + ϵijt .
The deflated firm-level input expenditures, their squared and cross-product terms form a
26 In
the main text this is referred to as simply product-specific input prices.
56
AARHUS UNIVERSITY WORKING PAPER
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translog production function and simplify the expression to:
qijt
=
[
]
[
]
[
]
l
k
m
fj (x̃it ; β) + βl ρijt − wijt
+ βk ρijt − wijt
+ βm ρijt − wijt
[
]
(
)2
l
l
l
+βll ρ2ijt + wijt
+ 2ρijt l̃it − 2l̃it wijt
− 2ρijt wijt
[
]
(
)2
k
k
k
+βkk ρ2ijt + wijt
+ 2ρijt k̃it − 2k̃it wijt
− 2ρijt wijt
]
[
( m )2
m
m
− 2ρijt wijt
+ 2ρijt m̃it − 2m̃it wijt
+βmm ρ2ijt + wijt
[
]
k
k
l
k
l
k
+βlk ρ2ijt + ρijt k̃it − ρijt wijt
+ ρit l̃it − l̃it wijt
− ρijt wijt
− k̃it wijt
+ wijt
wijt
[
]
m
m
l
m
l
m
+βlm ρ2ijt + ρijt m̃it − ρijt wijt
+ ρit l̃it − l̃it wijt
− ρijt wijt
− m̃it wijt
+ wijt
wijt
[
]
k
k
m
k
m k
+βkm ρ2ijt + ρijt k̃it − ρijt wijt
+ ρit m̃it − m̃it wijt
− ρijt wijt
− k̃it wijt
+ wijt
wijt
l
l
m
m
+βlkm [ρ3ijt + ρ2ijt l̃it − ρ2ijt wijt
+ ρ2ijt m̃it + ρijt m̃it l̃it − ρijt m̃it wijt
− ρ2ijt wijt
− ρijt wijt
l̃it
l
l
m l
k̃it + ρijt m̃it k̃it − m̃it wijt
k̃it
+ρijt wijt
wijt + ρ2ijt k̃it + ρijt l̃it k̃it − ρijt wijt
k
k
l
k
k
m
m
m l
− ρijt m̃it wijt
− ρijt l̃it wijt
+ ρijt wijt
wijt
l̃it k̃it + wijt
wijt k̃it − ρ2ijt wijt
k̃it − wijt
−ρijt wijt
m l
k
k
m k
m
k
k
l
] + ωit + ϵijt ,
wijt wijt
lit wijt
− wijt
wijt + wijt
−m̃it l̃it wijt
+ m̃it wijt
wijt
+ ρijt wijt
where x̃it is a vector of deflated inputs and fj (·) is translog production function. The next
step is to collect together all elements that contain the product-firm-input-specific prices, wijt
into a function B (·) and all remaining elements into A (·), which yields:
qijt
=
fj (x̃it ; β) + βl ρijt + βk ρijt + βm ρijt
[
]
[
]
[
]
+βll ρ2ijt + 2ρijt l̃it + βkk ρ2ijt + 2ρijt k̃it + βmm ρ2ijt + 2ρijt m̃it
[
]
[
]
[
]
+βlk ρ2ijt + ρijt k̃it + ρit l̃it + βlm ρ2ijt + ρijt m̃it + ρit l̃it + βkm ρ2ijt + ρijt k̃it + ρit m̃it
[
]
+βlkm ρ3ijt + ρ2ijt l̃it + ρ2ijt m̃it + ρijt m̃it l̃it + ρ2ijt k̃it + ρijt l̃it k̃it + ρijt m̃it k̃it
+B (wijt , ρijt , x̃it ; β) + ωit + ϵijt .
Finally, all remaining terms can be combined into A (ρijt , x̃it ; β), which allows us to rewrite
(B5) and illustrate the biases that arise due to unobserved ρijt and wijt :
(B7)
qijt = fj (x̃it ; β) + A (ρijt , x̃it ; β) + B (wijt , ρijt , x̃it ; β) + ωit + ϵijt .
The translog functional form significantly augments the number of parameters to be estimated and introduces many cross-term products between input prices, allocation shares and
inputs. The derivations showed that the input price correction in function B (·) enters nonlinearly in (B7). The translog offers considerably higher flexibility in in the markup estimates
compared to the Cobb-Douglas form, where the output elasticity with respect to the materials
is constant, equal to βm .
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57
Table B1—Median and average production function elasticities by NACE Rev. 2 industry
NACE 2-letter manufacturing product industry
Median elasticities
CA - Food products, beverages and tobacco products
CB - Textiles, apparel, leather and related products
CC - Wood and paper products, and printing
βl
βm
βk
RTS
0.32
0.72
0.04
1.07
0.06
0.41
CE - Chemicals and chemical products
0.69
CG - Rubber and plastics products, and other non-metallic mineral products
CH - Basic metals and fabricated metal products, ex. machinery and equipment
CI - Computer, electronic and optical products
0.53
0.42
0.36
CJ - Electrical equipment
0.35
CK - Machinery and equipment n.e.c.
0.50
CL - Transport equipment
0.37
CM - Other, repair and installation of machinery and equipment
0.46
0.82
0.58
0.37
0.46
0.50
0.46
0.50
0.52
0.59
0.56
-0.16
0.04
0.02
0.05
0.03
0.04
0.07
0.01
0.02
0.03
0.69
1.03
1.06
1.05
0.96
1.00
0.95
1.03
0.99
1.03
Average elasticities
βl
βm
βk
Number of
RTS
observations
871
0.31
0.76
0.05
1.12
(0.11)
(0.10)
(0.06)
(0.12)
0.62
0.14
-0.56
0.19
(0.33)
(0.42)
(0.38)
(0.91)
0.47
0.60
0.00
1.08
(0.10)
(0.04)
(0.06)
(0.09)
0.87
0.10
0.16
1.13
(0.31)
(0.30)
(0.14)
(0.25)
0.52
0.47
0.04
1.04
(0.19)
(0.07)
(0.07)
(0.06)
0.38
0.51
0.05
0.94
(0.13)
(0.05)
(0.07)
(0.08)
0.39
0.59
0.07
1.05
(0.24)
(0.12)
(0.09)
(0.06)
0.37
0.55
0.04
0.96
(0.07)
(0.07)
(0.06)
(0.08)
0.44
0.55
0.01
0.99
(0.06)
(0.04)
(0.03)
(0.06)
0.41
0.70
0.01
1.12
(0.14)
(0.09)
(0.06)
(0.24)
0.34
0.51
-0.03
0.81
(0.42)
(0.23)
(0.12)
(0.39)
236
1,206
110
1,128
3,361
534
973
1,946
425
1,984
Note: The table reports the estimated average and median elasticities from a translog production function. The values in brackets are standard
deviations of the estimates. The RTS columns report the returns to scale parameter which is the sum of the labour, material and capital input
elasticities. The number of observations column shows based on how many single-product firm observations have been included in the estimation of
the production function coefficients.
B2. Estimation of input allocation shares across products
An inherent problem in all datasets is that the econometrician does not observe how firms
allocate total input expenditures to specific products, nor the quantity used in the manufacturing process. To this end, I briefly revisit the suggested methodology for backing out
the input allocation shares across products, ρijt . To be as specific as possible, consider the
specification in (B5). Predicted output purged from measurement error can be defines as
q̂ijt ≡ E [qijt |ϕt (x̃it , uit )], where ϕt (·) = fj (xijt ; β) + ωit and recall that ωit = gt (x̃it , uit ) from
(15). The physical inputs at the product-firm-year level can be expressed as a function of
allocation shares, firm-year level input expenditures and estimated input prices as in equation
(B4), such that:
(B8)
(
)
q̂ijt = fj xijt ; β̂ + ωit
(
)
= fj x̃it , ŵijt , ρijt , β̂ + ωit .
Applying the translog production function leads to the result in (B6). Note that in reality
58
AARHUS UNIVERSITY WORKING PAPER
JULY 2016
x for x = {l, k, m}.
the estimates of the inputs prices are common across all inputs: ŵijt = wijt
As in De Loecker et al. (2016), the elements in( (B6) can be separated
into two functions:
)
one that contains all input allocation shares, f2 x̃it , β̂, ŵijt , ρijt and one, which collects the
(
)
remaining terms, f1 x̃it , β̂, ŵijt . The former is given by:
(
)
f2 x̃it , β̂, ŵijt , ρijt
=
(
)
(
)
ρijt (β̂l + β̂k + β̂m + 2β̂ll l̃it − ŵijt + 2β̂kk k̃it − ŵijt + 2β̂mm (m̃it − ŵijt )
)
)
(
)
(
(
+β̂lk k̃it + l̃it − 2ŵijt + β̂lm m̃it + l̃it − 2ŵijt + β̂km k̃it + m̃it − 2ŵijt
(
)
2
+β̂lkm m̃it l̃it − 2m̃it ŵijt − 2ŵijt l̃it + 3ŵijt
+ l̃it k̃it − 2ŵijt k̃it + m̃it k̃it )
(
(
))
+ρ2ijt β̂ll + β̂kk + β̂mm + β̂lk + β̂lm + β̂km + β̂lkm l̃it − 3ŵijt + m̃it + k̃it
+ρ3ijt β̂lkm
(B9)
=
âijt ρijt + b̂ijt ρ2ijt + ĉijt ρ3ijt ,
where âijt , b̂ijt and ĉijt can be directly computed using the available β̂, ŵijt and x̃it . After
x for x = {l, k, m}, it
knowing the elements in f2 (·) and making use of the fact that ŵijt = wijt
is possible to obtain f1 (·), which includes all terms that do not contain ρijt :
(
)
f1 x̃it , β̂, ŵijt
(B10)
=
[
]
[
]
β̂l l̃it − ŵijt + β̂k k̃it − ŵijt + β̂m [m̃it − ŵijt ]
]
[( )
]
[( )
2
2
+β̂ll l̃it + (ŵijt )2 − 2l̃it ŵijt + β̂kk k̃it + (ŵijt )2 − 2k̃it ŵijt
[
]
[
]
2
+β̂mm (m̃it )2 + (ŵijt )2 − 2m̃it ŵijt + β̂lk l̃it k̃it − l̃it ŵijt − k̃it ŵijt + ŵijt
[
]
[
]
2
2
+β̂lm l̃it m̃it − l̃it ŵijt − m̃it ŵijt + ŵijt
+ β̂km m̃it k̃it − m̃it ŵijt − k̃it ŵijt + ŵijt
[
]
2
2
2
3
+β̂lkm m̃it l̃it k̃it − m̃it ŵijt k̃it − ŵijt l̃it k̃it + ŵijt
k̃it − m̃it l̃it ŵijt + ŵijt
m̃it + ŵijt
lit − ŵijt
.
Note that all elements in (B10)
( are known
) from( the data or have
) been estimated. From
(B8) it is known that q̂ijt = f1 x̃it , β̂, ŵijt + f2 x̃it , β̂, ŵijt , ρijt + ωit . Let ω̂ijt = q̂ijt −
(
)
f1 x̃it , β̂, ŵijt and use the result in (B9) to obtain Jit + 1 equations in Jit + 1 unknowns
(ρi1t , ..., ρiJt t , ωit ) for each firm-year:
ω̂i1t
=
âi1t ρi1t + b̂i1t ρ2i1t + ĉi1t ρ3i1t + ωit
···
J
∑
ω̂iJt t
=
âiJt t ρiJt t + b̂iJt t ρ2iJt t + ĉiJt t ρ3iJt t + ωit
exp (ρijt )
=
1,
j=1
where the last equation is the economic constraint that the sum of all input allocation shares
cannot exceed one. This system is solved numerically for each firm-year following the algorithm
JULY 2016
MARKUPS AND IMPORT COMPETITION
59
by De Loecker et al. (2016). The procedure yields estimates of ρ̂ijt and ω̂it , which are used to
compute product-firm markups as in equation (18) of the main text.
B3. Execution programmes
The econometric analysis and markup and production function estimation are performed in
STATA 13.1 SE and in Matlab R2015b at the research server of Statistics Denmark.