The Comparative Advantage of Firms

Johannes Boehm
Sciences Po, Centre for Economic Performance, London School of Economics, and Centre
for Economic Policy Research

Swati Dhingra
Centre for Economic Performance, London School of Economics, and Centre for Economic
Policy ResearchJohn Morrow
Kings College London, Centre for Economic Performance, London School of Economics, and Centre
for Economic Policy Research

Resource-based theories propose that firms grow by diversifying into products that use common capabilities. We provide evidence for commoninput capabilities, using a policy that removed entry barriers in input
markets to show that the similarity of a firm’s and an industry’s input
mix determines firm production choices. We model industry choice andeconomies of scope from input capabilities. When the model is estimatedfor Indian manufacturing, input complementarities make firms 5% more
likely to produce in an industry and are quantitatively as important
as time-invariant drivers of coproduction rates. Upstream entry barriers
were equivalent to a 9.5% tariff on inputs.

I. Introduction
Multiproduct firms dominate production and export activity. They aremuch larger than their single-product counterparts, and their productWe are grateful to Andy Bernard, Keith Head, Beata Javorcik, Kalina Manova, Thierry Mayer,
Veronica Rappoport, and John Sutton, as well as audiences at many seminars and conferences,
Electronically published October 25, 2022
Journal of Political Economy, volume 130, number 12, December 2022.
© 2022 The University of Chicago. All rights reserved. Published by The University of Chicago Press.
https://doi.org/10.1086/720630

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turnover contributes substantially to aggregate output growth.1 Recent
work in international economics and industrial organization examines how
many products firms make and the impact of economic changes on thesechoices. It emphasizes the importance of core products for firm growth(Bernard, Redding, and Schott 2010, 2011; Eckel and Neary 2010; Iacovone
and Javorcik 2010; Mayer, Melitz, and Ottaviano 2014), but less is known
about why these products are “core.” This paper examines firm decisions
to make products across different industries and provides reduced-form
evidence and structural estimates for comparative advantage arising from
input capabilities and industrial coproduction.
Early theoretical and empirical work recognizes the sizable contributionof product diversification toward firm growth and aggregate productivity
and examines explanations for product diversification within firms (suchas Stigler 1951 and Scherer 1982, summarized in Chandler 1992 and Montgomery 1994). Explanations on the demand side include gaining market
power through horizontal and vertical integration or internalizing demandcomplementarities and network externalities across products (e.g., Bernheim and Whinston 1990; Willig, Salop, and Scherer 1991; Jovanovic andGilbert 1993; Hoberg and Phillips 2016). On the supply side, agency-based
theories of the firm suggest that diversification is motivated by internal labor and capital markets of the firm. For example, managers choose to diversify to reduce their human capital risk, to gain rents from utilizing free cash
flows, or to obfuscate when their own division is doing badly (Amihud and
Lev 1981; Jensen 1986; Morck, Shleifer, and Vishny 1990). This explained
early trends of reduced firm valuations from diversification (e.g., Lichtenberg 1992; see Maksimovic and Phillips 2013 for a survey). Resource-based
theories of the firm, dating back to Penrose (1955), take a competing viewthat diversification enables firms to grow beyond the limits imposed by thefor helpful comments. An earlier version of the paper was titled “Swimming Upstream:
Input-Output Linkages and the Direction of Product Adoption.” Boehm thanks the Sciences
Po/Banque de France partnership for financial assistance and the International Economics
Section at Princeton for hospitality. Morrow thanks the London School of Economics–Tata
Institute of Social Sciences–Tata grant for financial assistance. Dhingra thanks the European
Research Council for financial assistance under Starting Grant 760037. Shania Bhalotia and
Yan Liang provided excellent research assistance. Replication files are available in a zip file.
This paper was edited by Chad Syverson.
1
For example, in the United States, multiproduct firms account for over 90% of manufacturing output, and multiproduct exporters account for over 95% of exports. They arelarger than single-product firms in the same industry in terms of shipments (0.66 log
points), employment (0.58), labor productivity (0.08), and total factor productivity(TFP; 0.02). About 89% of multiproduct firms vary their product mix within 5 years,
and these changes in the product mix make up a third of the increase in US manufacturing
output (Bernard et al. 2007; Bernard, Redding, and Schott 2010). In India, multiproductfirms (that produce in more than one of 262 different industries) account for 32% of firms
and 62% of sales (as we discuss below). Among publicly listed firms, Goldberg et al.
(2010b) find that multiproduct firms, which produce in more than one of 108 4-digit
NIC (National Industrial Classification) industries, make up 47% of firms and 80% of sales.
They are 107% bigger in output than single-product firms within the same industry.

comparative advantage of ﬁrms

3027

size of a single-product market. Entering new products requires resources,
such as know-how or inputs, that are costly to acquire and to transfer outside the firm. Firms therefore gain economies of scope by diversifying into
products that require similar know-how or inputs to what their existingproducts use, as experienced during wartime, when auto manufacturers
quickly switched to making tanks, chemical companies to making explosives, and radio manufacturers to making radar (Teece 1982; Wernerfelt
1984; see Baumol 1977; Panzar and Willig 1981).
Theories of product diversification have influenced a vast literature ineconomics, finance, and management that examines which products firms
choose to make.2 For example, recent microdata reveal that firms aremuch more likely to produce in certain pairs of industries (Bernard, Redding, and Schott 2010). Many firms that make fabricated metal products
also make industrial machinery. A challenge, however, has been to movebeyond systematic correlations in coproduction and product characteristics to disentangling evidence for specific theories of the firm. In the example, systematic coproduction of metal and machinery could arise because
they share common inputs and technologies such as metal and metalworking (as in the resource-based view). Or it could arise because consumers
who order fabricated metal products also need industrial machinery (asin demand-side theories) or still further because machinery and metal
are produced in firms with excess capital (as in agency-based theories).
This paper examines product diversification within firms in the light ofthese theories of the firm and with a view to understanding the comparative advantage of firms in the product space.
Using plant-level data from Indian manufacturing, this paper starts
with the striking observation that product diversification within firms
is systematically related to shared input use across these products. Figure 1 shows that firms produce more in pairs of industries that require
similar intermediate inputs. Figure 1A illustrates the extent of coproduction of industry pairs within plants (across 1–253 different industries),and figure 1B is for the input similarity between industry pairs.3 This isalso borne out in findings from the United States, where stark examples
2
In early work, Scherer (1982) estimates technology flows across industries to examine
business lines within firms and the related slowdown in aggregate productivity growth in
the United States. Recent work has built on these findings to show a systematic relationshipbetween demand relatedness, technological relatedness or input relatedness of products
made by firms, and various firm performance measures (e.g., Robins and Wiersema 1995;
Fan and Lang 2000; Bowen and Wiersema 2005; Rondi and Vannoni 2005; Bryce and Winter2009; Liu 2010).
3
The coproduction cells contain the size-weighted average sales shares of plants that derive the largest share of revenue from products in the row industry. Darker values indicate
higher shares. The input similarity cells contain the inner product of the industries’ vectorof intermediate-input expenditure shares, calculated from single-product plants in eachindustry.

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F IG . 1.—Coproduction and input similarity. A, For plants with primary sales in the row
industry, the fraction of sales coming from products in the column industry. B, Inner product between the row and column industry’s intermediate-input expenditure share vectors.
Intermediate-input shares (B) are constructed from single-industry plants only. Darker colors indicate larger relative values within each panel.

of industry pairs that are coproduced and have similar input requirements include textiles and apparel, lumber and paper, and primary metaland fabricated metal (Bernard, Redding, and Schott 2010).4
To disentangle input-based product diversification from other explanations, the paper leverages plausibly exogenous variation in input supply to relate product choices within firms with input similarity acrossproducts. Starting in the late 1990s, the Indian government dismantled
size-based entry barriers in several products that were previously reserved for production by small-scale firms. The removal of entry barriers
was driven primarily by an agenda to reform postindependence economic
policy.5 As the entry barriers were lifted, firms acquired better accessto inputs. Those firms that intensively used these inputs became more
likely to grow by diversifying into products that are intensive in the useof liberalized inputs. To give a concrete example, when entry barriers tocotton are lifted, a cotton apparel maker becomes more likely (than asilk apparel maker) to move into cotton textile production (than into silk
textile production). In fact, even within the cotton apparel industry, a4
Similar patterns emerge in firm-level data from the United Kingdom and Belgium(Hutchinson, Konings, and Walsh 2010; Bernard et al. 2019), and early work by Wernerfelt(1984) suggests systematically examining these patterns through “resource-product” matrices.
5
The original aim of the reservation policy was employment generation through smallscale units that were expected to be more labor intensive than larger firms (though Martin,
Nataraj, and Harrison 2017 show that the dismantling of this policy in fact generated relatively more employment).

comparative advantage of ﬁrms

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firm that is relatively more intensive in cotton use becomes relatively more
likely to move into cotton textile production. In other words, firms diversified into industries in which they had input-based comparative advantage.
This paper examines the extent to which better input supply enables
firms to acquire comparative advantage in industries related by common inputs. According to comparative-advantage theory, industries differ in theiruse of technologies or factor requirements, and countries differ in theirtechnological prowess or factor endowments. Countries therefore produce
relatively more in industries in which they are more capable through better
technologies or greater reliance on abundant factors. Translating this fromcountries and technologies/factors to firms and inputs, we examine
whether firms produce more in their input-intensive industries relative
to the typical firm in those industries and relative to other industries thatfirms could enter. Common input requirements provide well-measured
proxies for shared technical know-how across products, which overcomes
long-standing constraints associated with measuring technologies and intangible know-how (Atalay et al. 2019). The focus on intermediate inputs
enables direct examination of the empirical relevance of economies ofscope and the extent to which these economies are determined by policy
choices. In concrete terms, firms intensively using metal inputs have metalworking know-how and skills, and the policy change in metal inputs provides variation in supply complementarities that can be directly linked to
production outcomes.
While the policy episode is best suited to examining economies of scopethrough inputs, the setting is amenable to disentangling competing explanations for product diversification. The production data can be used to
distinguish various resources within firms, such as intermediate inputs
and primary factors, that have been shown to be important constraints tofirm growth in developing economies (Tybout 2000; Bloom et al. 2010).
The rich microdata can also be leveraged to construct measures suggested
by competing theories, such as vertical upstream/downstream linkages,
capital intensity, and the diversification discount. In particular, firm-time,
firm-industry, and industry-time fixed effects control for unobserved reasons
such as firms’ financial and managerial conditions, industry technologicalshifts, and other time-invariant firm-industry reasons for coproduction.
In the absence of direct measures of substitutability/complementarities
across products and their evolution, industry-mix fixed effects can also
be included to account for unobservable demand-side reasons for coproduction. Accounting for the different theories of the firm, we find thatthe dominant explanation in our context and policy episode is that firms
specialize in products where they have comparative advantage based onshared input use.
Having established the importance of input-based comparative advantage for firms, the paper provides a theoretical framework for input

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capabilities and their contribution to firm sales. Starting from the primitive of industry-specific production functions, differences across industries arise from differences in their input requirements. Differences acrossfirms arise from their endowed industry productivities and from their decisions to invest in input capabilities, which can be shared across industries.
Economies of scope induce coproduction in industries that are intensivein the use of dynamically acquired input capabilities. Removal of entry barriers in input markets provides better access to those inputs and confers anadvantage to firms that have higher use for those inputs. These firms step
up production, but much more so in industries that use these inputs more.
In sum, policy-induced improvements in input supply enable firms to diversify into industries in which they have input-based comparative advantage relative to other firms, even within their industry.
The theory allows for love or hate for input variety, and a key insight ofour framework is that economies of scope within multiproduct firms imply
that production choices and input capabilities are jointly determined.
Since firms are heterogeneous in their costly-to-transfer resources, thisjoint determination of downstream input capabilities and production
choices is around the revealed “core competencies” of the firm, resulting
in input-based comparative advantage. The framework generates structural
estimating equations that explain the portfolio of industries a firm adopts
on the basis of contemporaneous input similarity with each industry. The
latter, in turn, is determined by policy changes that improve access to inputs
and by demand and supply shocks that interact with a firm’s industry mix.
The theory guides estimation of common industry demand innovations
and policy changes in input supply to predict contemporaneous input
similarity, which in turn determines industry choice.
The estimates show that input capabilities are quantitatively importantin determining the industry choice and scope of firms. On average, inputbased comparative advantage makes single-industry firms 5.2 percentage
points (pp) more likely to produce in an industry. Multi-industry firms exhibit a distribution of such premia. Shared input capabilities provide advantages across multiple industries, but this decays as a firm diversifies into
industries with more varied inputs. For instance, triple-industry firms are
6.1 pp more likely to enter their first industry, 2.3 pp more likely to enter
their second industry, and only 1.9 pp more likely to enter their third industry. However, as multi-industry firms are larger across the board, sizeweighted premia range as high as 46.8 pp, showing that they are importantfor firm growth. Overall, input-based comparative advantage is quantitatively as important a determinant of firm entry into industries as timeinvariant industry-pair determinants of coproduction rates.
Related literature.—The results relate to the multiproduct-firm literature, which usually focuses on how many, not which, products firms
make. We contribute to this literature by identifying the role of input

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3031

linkages as a determinant of the core competencies of multiproductfirms.6
A large literature studies the role of access to inputs on firm productivity.7
While we ask a different question, the focus on input supply is consistent
with these studies. Specifically, Goldberg et al. (2010b) highlight the importance of input supply in Indian manufacturing. They find that large firms
in India increased the range of products they offered in response to India’s
input tariff liberalization of the nineties. Their focus is on the number of
products firms make. We instead examine which products firms make and, in
doing so, uncover input capabilities–based comparative advantage of firms.
Goldberg et al. (2010a) differentiate the role of price and new variety channels of imported inputs in expanding firm product scope, finding a crucialrole for new imported varieties and allowing for potential technologicalcomplementarity within firms or product lines, something we also find andstructurally model. Vandenbussche and Viegelahn (2018) also show thatIndian firms move away from inputs facing domestic antidumping measures by decreasing sales of products using these inputs. Similarly, we findthat intermediate inputs drive output decisions. Distinct from their work,
our reduced-form analysis examines measures suggested by competingtheories of product diversification, and we provide a structural estimating
equation for the relationship between input linkages and output decisions.
While our focus is on supply-side policies in a developing-country context, the approach of characterizing firms and industries is similar to thatof Bloom, Schankerman, and Van Reenen (2013) and Conley and Dupor(2003). Bloom et al. construct technological and product market proximity measures to identify the causal effect of R&D spillovers across US firms
by using changes in federal and state tax incentives for R&D. Conley andDupor construct input similarity measures between sectors. They show thatcross-sector productivity covariance tends to be greatest between sectorsthat are similar in inputs and that this channel contributes substantiallyto the variance in aggregate productivity. We build on these ideas and show
how plants internalize input linkages to achieve product diversification.
The question of product choice in a developing-country setting is related to work by Hausmann, Hwang, and Rodrik (2007) and Hidalgo
et al. (2007), who examine the product space of countries and the network structure of their products. They propose that products differ in
6
See also Foster, Haltiwanger, and Syverson (2008), Eckel and Neary (2010), Liu (2010),
Dhingra (2013), Mayer, Melitz, and Ottaviano (2014), and Eckel et al. (2015) in the multiproduct literature and Hottman, Redding, and Weinstein (2016) and Bernard et al. (2022)
in the firm-heterogeneity literature.
7
See, e.g., Acemoglu, Antràs, and Helpman (2007), Amiti and Konings (2007), Kasahara
and Rodrigue (2008), Kugler and Verhoogen (2009, 2012), Antràs and Chor (2013), andHalpern, Koren, and Szeidl (2015). In recent work, Lu, Mariscal, and Mejía (2016) model
the inherently dynamic process of accumulating input capabilities and its role in increasing
firm productivity.

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the capabilities needed to make them and that countries differ in the capabilities they have. Countries make products for which they have therequisite capabilities, and they tend to move to goods close to those they
are currently specialized in (Hidalgo et al. 2007). Introducing quality capabilities to this framework, Sutton and Trefler (2016) show a nonmonotonic relationship between advances in countries’ wealth and changes intheir product mix and quality. We apply these ideas at the microeconomic
level of a production unit and find empirical support for input-based diversification of the product space. This confirms the view of Hausmannand Hidalgo (2011) that developing a regional jet aircraft is likely to beless costly for those who have previously developed a transcontinental aircraft and a combustion engine, compared to those who previously produced only raw cocoa and coffee.
In innovative work at the firm level, Flagge and Chaurey (2014) use amoment-inequality methodology to estimate bounds on the costs of adding products, including the role of product-proximity measures. Like
theirs, our work connects to studies documenting relatedness across products made by firms, though we differ in using policy variation to identify
input-based comparative advantage. Using a different approach, Aw andLee (2009) focus on four Taiwanese electronics industries and estimate
cost functions to arrive at the incremental marginal cost of the core product when the firm adds a new product. The industrial policy we exploit
eased entry barriers in previously reserved industries and has been of interest in understanding competition, employment generation, productivity
growth, and misallocations in manufacturing (Bollard, Klenow, and Sharma
2013; García-Santana and Pijoan-Mas 2014; Galle 2015; Martin, Nataraj,and Harrison 2017). We show a new channel, input-side complementarities, through which the policy affected the economy.
Our work is related more broadly to the literatures on industry linkages
and entry barriers.8 We quantify entry barriers in terms of tariff rates thathave equivalent effects on firm decisions to move into industries. On average, entry barriers from the policy to reserve products for small-scale plants
are equivalent to input tariffs of 9.5%. Domestic policies, such as size-based
entry barriers, are well understood to be a nontariff barrier to doing business. Given their prevalence as a protectionist tool, a large literature in international economics has tried to quantify such policies in terms of tariffs
that have an equivalent effect on outcomes of interest. But such quantification is typically fraught with difficulties for reasons such as limited variation

8
There are a growing number of studies relating linkages to productivity (see the handbook chapter by Combes and Gobillon 2015). In particular, López and Südekum (2009)find that upstream, but not downstream, linkages are associated with higher productivity,
perhaps in part because of the stronger effect of upstream linkages on product adoptionthat we find.

comparative advantage of ﬁrms

3033

in policies and correlation of policy changes with other shocks.9 The Indian
context overcomes these problems to reveal the constraints placed by domestic policy on firms and its comparison with trade policy. Recent work
has started to examine international trade as a driver of product choiceof firms (Ding 2019; Rachapalli 2021).
The paper is also relevant for macroeconomic studies that stress the importance of input linkages in amplifying micro shocks and policy effects.10
The development literature emphasizes their role in aggregate productivity and volatility (Koren and Tenreyro 2013) and in motivating policies,
such as domestic content requirements, that have interested governments
across the developing world (Harrison and Rodríguez-Clare 2010). While
we do not look at product linkages across firms, our results for within-firm
product linkages demonstrate the existence of cross-product spillovers
through inputs. These have been harder to identify across firms becauseof confounding factors, such as unobserved demand shocks. Looking
within firms controls for many of these confounding factors and provides
a causal interpretation of shared input capabilities in product choice bydrawing on variation driven by policy changes.
The remainder of the paper is organized as follows. Section II contains
a description of the context, data, and stylized facts. Section III shows theempirical relationship between input similarity and the industry mix offirms. Section IV presents a model of capability choice and limit-pricing
suppliers, deriving structural estimation equations and an instrumentation strategy. Section V contains the results from estimation and quantification of input capabilities. Section VI concludes.
II. Data and Stylized FactsA.

Data Description

We use annual data on manufacturing firms from the Annual Survey of Industry (ASI), which is conducted by the Ministry of Statistics and Programme Implementation (MOSPI) of the Government of India. The ASI
is the Indian government’s main source of industrial statistics on the formal
manufacturing sector and consists of two parts: a census of all manufacturing plants that are larger than 100 employees and a random sample ofone-fifth of all plants that employ between 20 and 100 workers (between
10 and 100 workers if the plant uses power). The ASI’s sampling methodology and product classifications have changed several times over the course
9
In their handbook chapter, Bown and Crowley (2016, 78) summarize that “the existing
literature and data sources are not sufficiently developed” to answer key questions such as
the extent to which domestic policies affect economic activity and how they compare withtrade policy instruments.
10
For example, Acemoglu et al. (2012), di Giovanni, Levchenko, and Méjean (2014),
and early work by Jovanovic (1987) and Durlauf (1993).

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of its history. In order to ensure consistency, we focus on the time frame of
the fiscal years (April–March) 2000–2001 to 2009–10.
The ASI has two unique aspects that make it particularly suitable for ouranalysis. First, it contains detailed information on both intermediate inputs
and outputs, hence allowing us to link the firm’s input characteristics to theirproduct-mix decisions. All sales figures include exports, and all purchases
include imports. The same product codes are used to describe both inputs
and outputs of plants. The data report inputs and outputs at the 5-digit
level (of which there are 5,204 codes). To look at the question of production
in multiple industries, we aggregate these codes to the 3-digit level, whichcorresponds to 253 codes, which we call “industries” and take to be our unitof analysis for diversification choices. We focus on 3-digit industries because
the purpose is to capture differences in input needs across products. It also
avoids the possibility of misclassification, which is more acute at finer levels.
Importantly, it keeps our analysis computationally feasible.11
The 3-digit industries are in 60 2-digit sectors. To give a sense of the levelof detail in this classification, consider the sector “cotton, cotton yarn, andfabrics” (ASIC [ASI commodity code] 63), which has various 3-digit industries, such as “cotton fabrics including cotton hosiery fabrics” (ASIC 633),“made up articles of cotton including apparel” (ASIC 634), and “processing or services of cotton, cotton yarn and fabrics” (ASIC 638). To take another example, the 3-digit industry “stainless steel in primary and finishedform” (ASIC 714) is an industry in the sector “iron & steel (incl. stainlesssteel), and articles thereof” (ASIC 71). A comparison of the dimensionalityof products with other sources and descriptive statistics are provided in
Boehm, Dhingra, and Morrow (2016, 2018).
Second, the ASI is collected with the definition that the unit of production (factory or factories) must have the same management, combined accounts, and resources that are not separately identifiable. This is particularly well suited for examining the capability (or resource) theory of the
firm. But it implies that we pick up plant-wide explanations and not all
firm-wide drivers of firm decisions. While we do not have firm identifiersand hence cannot aggregate plants under common ownership, we knowthat less than 7.5% of all plants are part of a multiplant firm with sister
plants that file separate survey returns. With that caveat in mind, we callthe units of observation in our data “firms.”
B. The Industry Mix of Indian Manufacturing Firms
We turn to documenting a set of facts related to the industry mix of firms inour sample. This set of facts motivates our subsequent empirical analysis.
11
According to the ASI, the product classification is stratified into 2-digit sectors, 3-digit
industries, and 5-digit products.

comparative advantage of ﬁrms
1.

3035

Multi-industry Firms Dominate Production

Like their counterparts in the United States and other countries, firmsthat span multiple industries account for a disproportionately large
share of economic activity. Table 1 shows the prevalence of multi-industry
firms in our sample. Multi-industry firms account for 32.2% of observations but 62.2% of all sales. Firms that span three or more industries(11.2% of all observations) still account for more than 39% of total sales.
This fact is well known and mirrors the results reported by Bernard, Redding, and Schott (2010) for the United States and by Goldberg et al.
(2010b) for the set of listed Indian firms.
2.

Coproduction Is Not Random

We now turn to the question of which industries the firms produce in.
Figure 1, in section I, shows two matrices. Figure 1A shows the degreeof coproduction between industries. Each row contains the size-weighted
average sales shares of plants (in the column industry) that derive thelargest share of revenue from products in the row industry. Darker colors
indicate higher shares. Hence, by construction, the diagonal contains thehighest value in each row. There is substantial coproduction across industries, as indicated by the off-diagonal dark areas. In particular, there ismuch coproduction occurring within the metal product and machinery
manufacturing sectors (the large shaded square on the bottom right)
and in the chemicals and pharmaceuticals industries (the industries withindices between 55 and 93), as well as within the textiles and apparel sectors (150–70). Firms from a diverse range of industries choose to have auxiliary outputs from the plastic and rubber industries (columns 100–112).

TABLE 1Frequency and Sales Shares of Multi-industry Firms
2-Digit Sectors
No. of Industries
1
2
3
4
5
6
7
8
9
101

3 -Digit Industries

Observations % Firms % Sales Observations % Firms % Sales
250,028
43,048
10,113
2,972
864
216
43
7
3

81
14
3
1
0
0
0
0
0

Source.—Authors’ calculations from ASI data.
Note.—Observations are firm-years.

50
28
12
7
2
1
0
0
0

208,881
63,99722,723
6,843
2,835
1,198
539
183
69
26

68
21
7
2
1
0
0
0
0
0

38
23
14
8
6
6
2
1
1
1

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journal of political economy

These patterns are similar to the coproduction documented by Bernard,
Redding, and Schott (2010) for the United States.
Figure 1B shows a matrix that captures the similarity of the row andcolumn industries’ mix of intermediate inputs. Each element (k, k0 ) is
the inner product of the industries’ vector of intermediate input expenditure shares:
InputSimilaritykk 5 ovik vik ,00iwhere vik is the sum of expenditure of single-industry firms that produce
only k on intermediate inputs from i, divided by total expenditure ofthese firms on intermediate inputs. This measure captures the overlap
in intermediate-input mixes between industries k and k0 . While not identical, the two matrices look very similar. The metal product and machinery industries all rely on primary metals as inputs; the textiles and apparelindustries share a dependence on textile fibers and yarns. Many basechemicals are applicable in different industrial processes. This correlation motivates an examination of firms’ input mixes in determining theircomparative advantage in the next section.
III. The Input Mix and Comparative Advantage
of Firms
Motivated by the strong positive relationship between coproduction andcommon use of intermediate inputs at the aggregate level, we focus inparticular on the role of firms’ intermediate-input mix in explaining revealed comparative advantage. We find that firms’ intermediate-input
mix explains their subsequent movements in the product space and thatthese input mixes interact with policy changes to shape revealed comparative advantage. Our regressions motivate a structural model of firm heterogeneity in input-biased productivity, which we present and estimate
in section IV. The estimating equation in that model bears a close resemblance to the reduced-form regressions from this section but provides a
structural interpretation to the estimated coefficients.
A.

Input Similarity

A natural way to bring the industry-level input similarity from above tothe firm level is to consider the inner product of the firm’s vector ofintermediate-input expenditure shares, vj, with the vector of intermediateinput expenditure shares of an industry k:
NInputSimilaritytjk 5 ovijt vik ,i51

comparative advantage of ﬁrms

3037

where i indexes the expenditure shares of spending on 3-digit inputs andt denotes time. We construct the aggregate intermediate-input shares vik
by aggregating the microdata of single-industry plants that produce only
in industry k. The input similarity measure ranges from zero, when firm jand sector k have no 3-digit inputs in common, to one, when the input
expenditure shares of firm j and sector k are identical. The crucial difference between this firm-level input similarity and the aggregate input similarity constructed in section II.B.2 is that this one incorporates idiosyncratic firm-specific variation in input mixes. The firm’s input mixes may
deviate from the one observed in input-output tables because of the firm
producing outputs belonging to multiple industries or because of othersources of variation. This firm-specific variation is quantitatively important: a set of input-output dummies explains only 61% of the overall variation in firm’s cost shares vij. The firm-industry input similarity measure isrelated to the measure of technological proximity of Bloom, Schankerman, and Van Reenen (2013). Our model in section IV provides a structural interpretation of the measure as the part of firm-level comparativeadvantage that comes from shared capabilities in intermediate input use.
B. Estimating the Role of Input Similarity
in Industry Adoption
We use the input similarity measure to predict firm movements in the
product space. To avoid the possibility that changes in the input mix predate an anticipated change in the product mix, we use the firms’ sales
and intermediate-input shares at the time of the first observation (anddenote the corresponding similarity measure by a “0” superscript).12
Our baseline specification is a linear model for the probability of firm
j adding industry k between time t and t 1 1:
Addjkt 5 b  InputSimilarity0jk 1 ajt 1 akt 1 akk t 1 εjkt :0(1)Here, Addjkt is 1 if and only if firm j does not produce in industry k at time
t but does so at time t 1 1; ajt is a firm-time fixed effect that captures theaverage rate of adding industries for each firm-year, leaving the regression
to identify only the direction of change in the industry mix and not changes
in the number of industries that the firm operates in; akt is an industry-time
fixed effect that captures any economic changes that determine entry
into a particular industry at a particular point in time (such as demand
shocks for k or input cost shocks that affect all potential k-producing firms
uniformly). In some specifications, we refine this to industry pair–time12That said, the data on reported intermediate-input use in the ASI are the expenditures
on intermediate inputs that are being consumed in the current year. Hence, purchases ofinventories should not show up in these variables.

3038

journal of political economy

fixed effects, akk t, with an additional dimension of the firm’s industry k0
from which it derives the highest fraction of revenue. These effects control
for all shocks that might make all firms in industry k0 more or less likely tostart producing in industry k. Finally, εjkt is an idiosyncratic error term. Appendix A shows summary statistics and correlation tables for all the variables in the regression.
Table 2 shows the results of estimating equation (1), with the inclusionof increasingly stringent fixed effects from left to right. The first specification contains only firm-year fixed effects, thereby estimating the direction of movement in the industry space. The estimated coefficient of
the input similarity measure is positive and statistically significant: firmsthat have an initial input mix that is relatively intensive in inputs thatan industry k relies on are more likely to start producing in k (than in
the average industry). The second specification additionally includes
industry-time fixed effects for every period, which control for any systematic demand or supply shocks that could affect the probability of firms
starting to produce in a particular industry. Finally, the third specificationof table 2 is very stringent, in that it absorbs the average rate of productadoption for each product k and the main industry of each firm k0 (asmeasured by sales) for each period through k  k 0  t fixed effects. Thismeans that any economic shock (supply, demand, technology, infrastructure, etc.) that might affect industry coproduction is accounted for andthat what remains are estimates of the direction of intraindustry productchanges driven by idiosyncratic input-output linkages of each firm within
its main industry. As the table shows, input similarity remains importanteven in this specification.
Our preferred specification is presented in column 2 of table 2, which
controls for annual rates of product adoption at the firm level in addition to annual supply and demand shocks that occur at the productlevel. A 0.10 unit increase in the similarity between firm and industry
0

TABLE 2
Industry Entry: Input Similarity
Dependent Variable: Addjkt

InputSimilarity0jk
Firm  year fixed effects ajt
Industry  year fixed effects aktk  k0  t fixed effects akk t
R2
Observations

(1)

(2)

(3)

.0391**(.0004)
Yes.0383**(.0004)
Yes
Yes.0281**(.0006)
Yes.0097
52,691,029.0117
52,691,029

0

Yes
.0575
52,666,907

Note.—Standard errors are in parentheses, clustered at the firm-industry level.
** p < .01.

comparative advantage of ﬁrms

3039

cost shares is associated with a 0.38 pp (or 75%) higher entry probability.
In distributional terms, a 1 standard deviation increase in input similarity is associated with a 174% higher industry entry rate.
As in previous work examining product diversification, the results above
constitute compelling correlations between firm characteristics and subsequent entry into industries by firms. To establish a causal channel anddistinguish from competing theories, we now turn to exploiting a policychange that interacted with the firm’s input mix to determine the direction of change in the output industry mix.
C. Dereservation of Products from Small-Scale Production
Since the 1950s, India has given particular attention to the developmentof its small-scale industry (SSI) sector, which contributes almost 40% togross industrial value added and is the second-largest employer after agriculture.13 Starting in 1967, the government implemented a policy of reservation of certain products for exclusive manufacture by SSI firms. The
stated aim of this policy was to ensure employment expansion, to achievea more equitable distribution of income and “greater mobilization of private sector resources of capital and skills” (Government of India 2009).
By the end of 1978, more than 800 products had been reserved; in 1996
it was more than a thousand.
By the early 1990s, the government realized that the reservation policy
was inconsistent with the vast liberalization that had begun in the late1980s and culminated in the new economic policy of 1991. According
to the expert committee set up by the government to look into SSI policy,
reservation did little to promote small enterprises and had negative consequences by keeping out large enterprises in these products. With freeimports of most goods after liberalization, the reservation policy was nolonger relevant. It also did not cover the large majority of products manufactured by the small-scale sector. Those industries that were covered,such as light engineering and food processing, were unable to growand invest in better technologies because of the limitations imposed by
SSI reservation. Consequently, the government was repeatedly advised
to dereserve products from the SSI list (Hussain 1997). Over the courseof the years 1997–2008, the government dereserved almost all products(see table 3). The remaining 20 products were dereserved in 2015.
The definition of SSIs, and therefore the scope of reservation, changed
over the period during which the reservation was in place. In 1955, an
SSI was defined as an establishment with fixed investments of less than

13
Development Commissioner, Ministry of Micro, Small, and Medium Enterprises, India(2018). Available at http://www.dcmsme.gov.in/publications/reserveditems/resvex.htm.

3040

journal of political economy
TABLE 3
Dereservation of Products, by YearYear

1997 1999 2001 2002 2003 2004 2005 2006 2007 2008 2010 2015

No. of products

15

9

15

51

75

85

108

180

212

107

1

20

Source.—Government of India, Ministry of Micro, Small and Medium Enterprises.

500,000 Indian rupees (Rs) that employed less than 50 workers whenworking with power or less than 100 workers when not working with power.
The employment criterion was dropped in 1960, and the SSI definition
was based on the original value of investment in plant and machinery.
The investment value was revised over time, and by 1999, the investment
ceiling was Rs10 million in plant and machinery (at historical cost).
The impact of the product dereservation on output markets has beenthoroughly studied in the literature. The consensus is that the dereservation policy was not systematically related to industry characteristics. In theofficial report to the government, Hussain (1997, §2.2) states that there
was “no explanation in official documents anywhere how the list of reserved items have been selected, . . . the choice of products was somewhat
arbitrary.” The dereservation policy led to entry of large firms into thedereserved markets, which boosted overall industry output and employment: Martin, Nataraj, and Harrison (2017) find that the aggregate employment response is, on average, above 40%, that output increased byabout 30% and wages by 6% and that the number of producers grew by
about 13%. Most of the policy response occurred among new firms entering the dereserved product space, rather than old firms adding new products (Amirapu, Gechter, and Smagghue 2018).
In contrast to the existing literature, we use the dereservation as an
unexpected change in the conditions that firms face on intermediateinput markets; we are thus looking at firms that are downstream fromthe dereserved markets. Unit values paid by downstream firms using inputs from dereserved markets drop by about 8%–12% upon dereservation(see the online appendix for full results of regressing log unit values ofdomestic 5-digit inputs on a dereservation indicator with various fixed effects). We use the policy to obtain variation in input supply that is plausibly
exogenous to the production decisions of using firms that were not in thesmall-scale sector.
D. Input Similarity Weighted by Dereservation
The official list of dereserved items is taken from the ministry’s website
and manually matched to 5-digit ASIC products. To define dereservation,
let dijt be 1 if and only if firm j at some point uses a 5-digit product in the
3-digit industry i that has been dereserved during or before year t 0 . We0comparative advantage of ﬁrms

3041

TABLE 4
Industry Entry: The Impact of Dereservation
Dependent Variable: Addjkt

InputSimilarity0jk

InputSimilarity-Dereservation0jkt

(1)

(2)

(3)

(4)

.0379**(.0004).0429**(.0025).0371**(.0004).0424**(.0024).0273**(.0006).0203**(.0024)

Yes

Yes
Yes

Yes

.0268**(.0006).0192**(.0024)2.0701**(.0095)
Yes.0098
52,691,029.0118
52,691,029

Yes
.0575
52,666,907

Yes
.0576
52,666,907

InputSimilarity-Tariff 0jkt
Firm  year FE ajt
Industry  year FE aktk  k0  t FE akk t
R2
Observations
0

Note.—Standard errors are in parentheses, clustered at the firm-industry level. FE 5
fixed effects.
** p < .01.

then interact the similarity measures by these dereservation indicators
as follows:NðInputSimilarity-DereservationÞtjkt 5 odijt vijt vik :
0

0

(2)

i51

This measure “selects” the portion of input industries in the inner product that have been dereserved.
To study how the dereservation interacts with firms’ input mix in shaping their comparative advantage, the specification of equation (1) is estimated with the input similarity measure weighted by dereservation. Table 4 shows that the estimated coefficient of the dereservation-weighted
input similarity coefficient is positive and statistically significant in all
specifications: when input i gets dereserved or faces reduced tariffs,
firms that have been using i intensively are more likely to add productsthat rely heavily on i. Column 4 includes a tariff-change-weighted input
similarity measure, analogous to the dereservation-weighted input similarity.14 Later in the paper, the structural estimation provides a tariff equivalent for dereservation.
To put these numbers in perspective, a firm experiencing a dereservation of one of its inputs gets a shock equivalent to a 0.30 increase in input
similarity for its most affected output industry and 0.19 and 0.12 increases
for its second- and third-most affected output industries, respectively. A
1 standard deviation increase in the initial input similarity–dereservation
measure is associated with an 18% higher industry entry rate, versus a
13% higher industry entry rate for the tariff-based measure, suggesting
14
This is constructed by replacing the dereservation indicator dijt with the change inIndia’s import tariffs Δtijt . For the precise definition and data description, see app. C.2.
0

0

3042

journal of political economy

a much larger direct role for removal of entry barriers, compared to input
tariff cuts.15
E. Case Study
Dereservation reduced firms’ input prices, and we use the policy to obtain variation in input supply that is plausibly exogenous to the production decisions of using firms that were not in the small-scale sector.
The reasoning for using the dereservation policy to study input-based
comparative advantage can be motivated by a notable example in comparative advantage driven by better input supply from dereservation.
India is the leading producer, consumer, and exporter of spices in theworld and produces 28% of the world’s spices. The spice industry in India
traditionally specialized in bulk spice commodity production but has now
become a world supplier of high-value spice products (including oleoresins, seasonings, sterilized spices, and nutraceuticals). According to the
Asian Development Bank, one of the main constraints faced by high-value
spice producers is the difficulty in getting high quality and reliable supplyof spices, for which they rely on small, unorganized firms.
Spices were reserved for small-scale production till 2008. On October 10, 2008, the government of India dereserved one of the main productcategories: ground and processed spices, which serves as an input into several related industries. The National Productivity Council of India documented that the dereservation led to a rise in employment per unit andan expansion in capital investment per unit in the ground and processed
spices industry.
Immediately after the dereservation in November 2008, the industry
magazine Spice India suggested that it is “for the spice industry now tomake use of the dereservation” to expand its processing capabilities
and to enhance development in high-value-added segments. One of the
top five sellers of spice oleoresins in the world is a good example of how
the product mix of firms changed with the dereservation of spices.
Headquartered in Cochin, Kerala, the Akay Group is a large Indian
firm with sales of over US$45 million in 2017. It exports mostly to theUnited States, Europe, and China and is a leading producer of high-value
spice products. It initially specialized in food coloring, certain spices, andflavored oil. Following the dereservation, Akay expanded its productofferings to new products that rely heavily on dereserved inputs, suchas spiceuticals (spice-based health supplements) and various oleoresins(which are semisolid spice oils such as capsicum oleoresin and cardamom
15
As the paper addresses mechanisms driving product entry of firms, we abstract fromindirect input-output linkages that could be important if the question of interest is the aggregate effect of dereservation or tariff policies.

comparative advantage of ﬁrms3043

oleoresin). Therefore, building on its earlier product portfolio, Akay has
scaled up operations in products that use related dereserved inputs. Similar examples of moving toward spice-intensive products can be found in
the ASI data for firms that were in related industries before the dereservation. Therefore, the case study provides a real-world example of thefindings from the reduced-form evidence.
F. Alternative Theories of Product Diversification
While the previous subsections control for a rich set of fixed effects toaccount for unobserved differences across firms, industries, and industry
pairs over time, coproduction could arise because of other rationales
suggested by theories of the firm, such as vertical integration and demand complementarities or substitutability. We discuss these in the remainder of this section and find that they are not confounding the findings for shared inputs driving product diversification.
1.

Vertical Diversification Measures

Firms could diversify up and down their value chain to gain vertical efficiency (e.g., Stigler 1951; Chandler 1992). We use the constructed inputoutput shares v to measure whether a sector k is upstream or downstream
from the firm’s current product mix. Let jzjt denote the sales of firm j inindustry z at time t, divided by the total of j’s sales at time t. Accordingly,
we defineN

Upstreamtjk 5 ojzjt vkz ,z51

NDownstreamtjk 5 ojzjt vzk ,

(3)

z51

where z runs over the set of 3-digit industries. To make sense of these definitions, consider the following analogy. Imagine a firm j with observed
sales shares jjt. Then, given the firm’s output mix jjt and the industry’s
average input expenditures for these outputs, one would expect the expenditure share upstream of j on k to be Upstreamtjk . This measure, forexample, is positive for the car components industry when the firm being considered is in the car industry, and the value of the upstream measure rises with the share of car sales of the firm and with the input shareof car components in making cars. Likewise, Downstreamtjk is proportional to the expected expenditure share of downstream industry k ona firm with the output mix jjt. It is positive, for example, for the car industry when the firm being considered makes car components, and thevalue of the downstream measure rises with the firm’s sales share in carcomponents and the input share of car components in the downstream
car industry.

3044
2.

journal of political economy

Output Similarity Measures

Firms might also enjoy other complementarities in outputs, by whichfirms that produce in one industry, or a certain set of industries, are able
to obtain relatively higher prices or sales for products from another industry. We construct a measure of output similarity analogously to our input similarity index as an inner product between firm j’s sales shares andthe aggregate industry k’s sales shares:
N

OutputSimilaritytjk 5 ojijt jik ,
i51

where i runs over the set of 3-digit industries. The vector jk denotes the(size-weighted) average jij among firms j 0 that derive their highest fraction of revenue from sales in k. Again, this measure captures the degreeof overlap between firm j ’s portfolio of sales (across industries) and theaverage portfolio of firms that sell most in k. We also construct an output
similarity weighted by the dereservation dummies analogous to the input
similarity measure in equation (2).
Output similarity summarizes similar distributions of sales, which would
be implied by the horizontal diversification motives of demand-side theories (e.g., Brander and Eaton 1984; Shaked and Sutton 1990; Willig, Salop,
and Scherer 1991; Jovanovic and Gilbert 1993; Dhingra 2013; Bernard
et al. 2019). If firms diversify to internalize demand complementarities
across products, it would show up as higher values of output similarity,and there would then be a positive relationship between the output similarity measure and firm’s product diversification. If firms diversify to gain
market power by taking over substitutable products, then output similarity would be low, and there would be a negative relationship with firm
diversification.
The advantage of the output similarity measure is that it encapsulates
various factors determining coproduction in a way that is broadly applicable, relying on information from input-output tables. But like many
inferred measures, output similarity embeds both demand- and supplyside motivations.16 For our purposes, this means that we cannot disentangle the different demand- and supply-side factors embedded in output
similarity, but we can assess whether these factors confound the effects
of input similarity in determining firm diversification.
0

16
Product substitutability has also been measured in related work by Broda and Weinstein (2006) and Hoberg and Phillips (2016), who construct demand substitutability measures through, respectively, trade data across various countries (where demand-side parameters are inferred structurally) and computational linguistic methods to determine productsimilarity from textual product descriptions (which correlate well with demand-side expenditures such as advertising). These methods either are applicable only to exported products
or rely on English-language descriptions, which makes them less suited to other settings.

comparative advantage of ﬁrms

3045

Output and input similarity would be positively correlated with eachother when the latter is an important contributor to coproduction, as suggested by figure 1. There is, however, substantial independent variation
across the two measures, especially when they are interacted with thedereservation policy. The correlation of the dereservation interactionsof input and output similarity is tiny because the dereserved products
could not generally be produced by firms (which were not “small,” according to the policy).
Table 5 shows the result of estimating equation (1) when controlling
for the output similarity variable, the dereservation-weighted version ofit, and the two vertical relatedness measures. Firms are also slightly more
likely to move upstream from their product mix and slightly less likely tomove downstream, showing again a role for inputs in product diversification. The estimated coefficient of output similarity is positive and significant, in particular in the specifications with k  k 0  t fixed effects. Putting the numbers in perspective, a 1 standard deviation higher output
similarity or upstream linkage is associated with a 62% or 152% higher
entry probability, respectively (based on col. 2). A 1 standard deviation
rise in the downstream linkage is associated instead with a 38% lower entry probability. The existence of these channels is not entirely surprising

TABLE 5
Industry Entry: Robustness
Dependent Variable: Addjkt

InputSimilarity0jk
InputSimilarity-Dereservation0jkt

(1)

(2)

(3)

(4)

(5)

.0379**(.0004).0429**(.0025).0251**(.0004).0383**(.0024).0136**(.0006).0344**(.0016).0335**(.0009)2.00826**(.0007).0245**(.0005).0378**(.0024).0136**(.0006).0334**(.0016).0315**(.0009)2.0076**(.0006).0199**(.0006).0155**(.0023).100**(.0018).0171**(.0022).0291**(.0030)2.0035*(.0014)

Yes

Yes

Yes
Yes

Yes

.0195**(.0006).0145**(.0023).100**(.0018).0171**(.0022).0291**(.0030)2.0036*(.0014)2.0640**(.0095)
Yes.00981
52,691,029.0122
52,691,029.0140
52,691,029

Yes
.0646
52,666,907

Yes
.0646
52,666,907

OutputSimilarity0jk
OutputSimilarity-Dereservation0jkt
Upstream0jk
Downstream0jk
InputSimilarity-Tariff 0jkt
Firm  year FE ajt
Industry  year FE aktk  k0  t FE akkt
R2
Observations
0

Note.—Standard errors are in parentheses, clustered at the firm-industry level. FE 5
fixed effects.
* p < .05.
** p < .01.

3046

journal of political economy

and could be suggestive of other complementarities, such as demand complementarities, motivating product diversification. Most importantly, theestimated coefficients of input similarity and dereservation-weighted input similarity remain positive and statistically significant across different
specifications. They are also economically more important than the othermeasures through higher estimated coefficients and larger values of themeasure on average.
3.

Alternative Output Complementarity Measures

A nonparametric way of capturing demand complementarities is to include a vector of output industry mix  year fixed effects for all observed
output combinations (i.e., fixed effects at the industry mix–time level
rather than just at the industry pair–time level). Table 6 shows the entry
regressions with fixed effects for k  K ðjÞ  t groups, where K(j ) is a setof dummies for the mix of goods produced by j at the time of first observation. These specifications show that among all producers of a particular
product mix at a given time and for a particular industry k, entry rates arehigher for firms that use input bundles more similar to those needed inindustry k. The output mix fixed effects absorb time variation in the entry
probabilities for combinations of industries, including those arising fromTABLE 6
Industry Entry with Output-Mix Indicators
Dependent Variable: Addjkt

InputSimilarity0jk
InputSimilarity-Dereservation0jkt

(1)

(2)

(3)

(4)

.0145**(.0006).0125**(.0025).0143**(.0006).0121**(.0025)2.0268**(.010).0147**(.0006).0122**(.0025).0145**(.0006).0118**(.0025)2.0269**(.010)
2.0228**(.0038).0066**(.0025).0039(.0080)2.0000(.0025)
Yes
Yes
.123
47,136,891

InputSimilarity-Tariff 0jkt
OutputSimilarity0jk
OutputSimilarity-Dereservation0jkt
Upstream0jk
Downstream0jk
Firm  Year FE ajt
k  K( j )  t FE akK( j)tR2
Observations

Yes
Yes
.123
47,136,891

Yes
Yes
.123
47,136,891

2.0228**(.0038).0066**(.0025).0039(.0080)2.0000(.0025)
Yes
Yes
.123
47,136,891

Note.—Standard errors are in parentheses, clustered at the firm-industry level. FE 5
fixed effects.
** p < .01.

comparative advantage of ﬁrms3047

demand complementarities. The coefficient of the input similarity measure remains positive and statistically significant. It is slightly smaller thanthe baseline specification with k  k 0  t fixed effects (in col. 3 of table 4),
as might be expected because the average input similarity effect is subsumed in the new fixed effects.
Table 6 confirms that input similarity is not confounded with demandside motivations for changes in the output mix of firms as controlled forby the k  K ðjÞ  t groups of all initial output mixes.17 It also reveals thatfirms move into industries similar in output to their main industry but
dissimilar in output from the rest of their industry mix. If output similarity is interpreted as capturing demand complementarities, then this isconsistent with diversification into industries that receive positive demand spillovers from the main industry and into industries that differentiate the firm from its competitors that have the same industry mix.
4.

Diversification DiscountAgency-based theories of the firm suggest that diversification reduces thevalue, growth, or productivity of firms and that managers undertake diversification to deploy distressed assets away from core activities. It therefore might be that firm diversification into industries with shared inputs
reflects weaker firms moving into new activities that would not be pursued by stronger firms to achieve growth. As a first examination of thisweak-firm hypothesis, table 7 estimates the heterogeneous effects acrossfirms on the basis of their initial size, which is often taken as a proxy forstronger performance. We run the baseline entry regressions but interact
input similarity (and the dereservation-weighted version) with log sales ofthe firm at the time of first observation (to proxy for “strong” vs. “weak”
firms). The regressions clearly show that larger firms have a stronger correlation between input similarity and industry entry. The negative coefficient on InputSimilarity0jk is completely dominated by the positive coefficient on the interaction, resulting in an almost-zero correlation for thesmallest firms (as log sales for the bottom percentile is about 12). The estimated coefficients are very similar to the ones from this table when log
sales at time t is used instead of that at the time of first observation. Therefore, there is little evidence to support that weaker firms select into inputsimilar industries.
It may, however, be that firms that diversify into input-similar industries
start to experience slower growth, which would again point toward weaker(low-growth) firms selecting into input-similar industries. Table 8 studies

17
See, for instance, Mayer, Melitz, and Ottaviano (2021), who use a similar approach tocontrol for firm-export destination effects.

3048

journal of political economy
TABLE 7
Revealed Comparative Advantage: Sales Interactions
Dependent Variable: Addjkt

InputSimilarity0jk

InputSimilarity  logSales
0
jk

0
jk

InputSimilarity-Dereservation0jkt
InputSimilarity-Dereservation0jkt logSales0jk

(1)

(2)

(3)

(4)

(5)

2.0346**(.0029).0042**(.0002)2.0102(.020)

2.0348**(.0028).0041**(.0002)2.00888(.020)

2.0328**(.0029).0040**(.0002)2.00314(.020)

2.0396**(.0029).0039**(.0002)2.0180(.019)

2.0382**(.0030).0038**(.0002)2.0139(.019).0029*(.0011).0028*(.0011).00201(.0011)

Yes

Yes
Yes

.0024*(.0011)
2.156
(.10)
.0047
(.0053)
Yes
Yes.00181(.0011)2.0898(.094).0024(.0049)Yes

InputSimilarity-Tariff 0jkt
InputSimilarity-Tariff 0jkt  logSales0jk
Firm  year FE ajt
Industry  year FE aktk  k0  t FE akkt
R2
Observations

Yes

Yes
Yes
.0100
.0120
.0121
.0577
.0577
52,691,029 52,691,029 52,691,029 52,666,907 52,666,9070Note.—Standard errors are in parentheses, clustered at the firm-industry level. FE 5
fixed effects.
1
p < .10.
* p < .05.
** p < .01.

the relationship between postentry sales growth and input similarity, andtables B8–B10 provide further checks with different sets of fixed effects tocompare across firms by their entering and continuing industries. In particular, we examine the specification
TABLE 8Postentry Growth: Within Entering Industries

InputSimilarity0jk
InputSimilarity-Dereservation0jkt

Dependent Variable:logðAvg Salest,jk ::: ,t13 Þ

Dependent Variable:logðAvg Salesjkt, ::: ,t15 Þ

(1)

(4)

(2)

1.5438** 1.4885**(.0859)(.0864)1.4308**(.3349)InputSimilarity-Tariff 0jkt
Industry  year FE akt
R2
Observations

Yes
.181
55,318Yes.181
55,318

(3)

(5)

(6)

1.3314** 1.7403** 1.6836**
1.5259**(.0878)(.0869)(.0875)(.0887)
1.0711**
1.4672**
1.1060**(.3313)(.3349)(.3275)221.5375**
221.6295**(1.3242)(1.3368)
Yes
Yes
Yes
Yes
.186
.188
.189
.194
55,31855,31855,31855,318Note.—Dependent variable is the log average sales by firm j in industry k between t 1 1
and t 1 h for h 5 3 or 5 years. Years where the firm is not surveyed are excluded in thecalculation of the average. Standard errors are in parentheses, clustered at the firm-industry
level. FE 5 fixed effects.
** p < .01.

comparative advantage of ﬁrms
3049!
ht51 Salesjkto
5 b0 InputSimilarity0jk 1 akt 1 εjkt
log
h
1
ð
firm
j
observed
at
t
Þ
ot51
on the sample of observations ( j, k, t), where firm j is entering industry k
between t and t 1 1 for h 5 3 or 5 years. The dependent variable is log
average sales of the firm in the industry it entered over a 3- or 5-year horizon, where the average is taken across all years where we observe thefirm (note that this may include zeros if the firm has exited the industry
during that time window).18 Table 8 includes industry-year fixed effects
and therefore compares firms entering the same industry k at time t that
may have produced different outputs before. We find that firms whose
input mix is more similar to k have higher postentry sales and not a diversification discount, as predicted by many agency-based theories.

5.

Other Explanations and Robustness

Within the resource-based view of the firm, our focus has been on sharedintermediate inputs because of the policy variation that we can directly
leverage. Primary factors, such as labor and capital, could also be sharedacross industries within the firm. This is explored in full detail in section V, after a simpler exposition with just intermediate inputs.
In appendix B, we report a number of additional results and robustness
checks: input similarity shapes revealed comparative advantage not only
through industry entry but also through the probability of dropping an industry from the mix and through the intensive margin of production. The
probability of dropping an industry falls with input similarity, while sales in
an industry rise with input similarity. This suggests that product turnover is
not driving the relationship between diversification and input similarity,
which is also reaffirmed in the postentry sales growth specifications. We
also show that results hold when focusing on (1) the set of large firms(≥100 employees) that are sampled every year in the ASI, (2) the set offirms that are single-plant firms, (3) the sample when excluding industry
pairs (k, k0 ) where there is never any coproduction, (4) the sample excluding few producing firms per industry-year, (5) the sample of firms that exclude those defined as wholesalers, and (6) the sample of firms that are
single product to begin with. Finally, the results are also robust to changing the estimator from OLS (ordinary least squares) to logit to better account for the discrete nature of the dependent variable. We conclude that18
We choose this dependent variable because in any given year, smaller firms are surveyed with only about 20% probability. Given that we are conditioning on entry, sales inyear t 1 1 are necessarily positive.

3050

journal of political economy

input-based comparative advantage is robust to a number of explanations
for product diversification proposed by theories of the firms.
The next section investigates these reduced-form findings by building
a structural model that explains them and quantifies the role of firmlevel comparative advantage based on input-output mechanisms.
IV. Theory of the Firm: Product Diversification
and Input Similarity
This section presents a theory of multiproduct firms including economies
of scope. We focus on the simplest setting, which yields a relationship between policy changes in the input market, supply of inputs, and production choices of multiproduct firms.
The model starts with the primitive of industry-specific production
functions, which firms use with their endowed industry-specific productivities. Economies of scope arise because firms can invest in acquiring inputspecific capabilities that can be shared across the industries that they produce in. This generates input-based comparative advantage, which makes
firms more likely to produce in industries that share inputs. Increases inthe depth of input supply, such as the removal of upstream entry barriers
or reductions in input tariffs, operate to heighten these economies ofscope. But as a firm goes on expanding its product range, its acquired capabilities get stretched further and the return to comparative advantage
declines, as in models of core competencies. This endogenizes the flexiblemanufacturing hypothesis of Eaton and Schmitt (1994), Eckel and Neary(2010), and Mayer, Melitz, and Ottaviano (2014), where unit costs of production rise as firms move away from their core competencies.19
The production model allows us to isolate upstream-downstream linkages and their role in multiproduct final-goods production. As we see below, even here the interdependency of suppliers’ entry choices and producers’ capability choices that allow them to use better-quality suppliers
opens up a rich framework. Key to establishing the existence of a supplierequilibrium is avoiding Jevons’s paradox, namely, that increased efficiency
of an input (as a result of more efficient coal engines) can result in a netincrease in demand for the input (coal), causing an outwardly spiraling
feedback loop. In our case, increased entry lowers the input costs of downstream firms, spurring further demand and therefore entry. The suppliermodel also shows that as parameters approach Jevons’s paradox, multiple
supplier equilibria are possible, precisely as one would get with textbook
19
This also rationalizes the finding of Fontagné, Secchi, and Tomasi (2018) that exporters have typical (essentially median) product vectors that are common across many markets but that there is also considerable fickleness of distinct product baskets across markets(perhaps because of country-specific demand).

comparative advantage of ﬁrms

3051

falling-average-cost-curve models. This echoes the literature on external
scale economies going back to Ethier (1982), although in our case thesearise endogenously from a downstream demand response to cutthroat competition by suppliers rather than from a technological assumption.
The model first solves for the optimal pricing and production choicesof downstream firms for fixed capabilities, then turns to supplier behavior and establishes their production, pricing, and entry choices. It thendetermines the capability choice of firms for exogenous industry-time
demand shifters.20 In that sense, the model is not completely closed, remaining agnostic about the relationship of the demand shifters, since
the empirics will allow for rich empirical substitution/complementarity
patterns over time.
The key insight from the model is that unit costs across industries for
multiproduct firms are interdependent through the portfolio of demanda firm faces, because capabilities are chosen to maximize total profits, notminimize costs in any single industry. This extends the pioneering workby Baumol (1977) and Panzar and Willig (1981), as the existence of economies of scope brings in joint-optimization considerations that alter theusual duality results. The framework generates an intuitive estimating
equation that mirrors and interprets the input similarity results of theprevious section. The portfolio of products a firm produces and the impact that policy changes have on observed portfolios are determined by afirm’s optimal input distance from an industry. Distance from an industry
carries a productivity penalty, as per the idea of core competency, which
examination shows contains the input similarity measure22 ov2ik ,2 o vijt 2 vik 5 2 ovijt vik 2
oi v2ijt
i
i
i|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}|ﬄﬄﬄﬄ{zﬄﬄﬄﬄ}|ﬄ{zﬄ}|ﬄ{zﬄ}
input distance penalty

input similarity

Hicks-neutral capability costindustry effectwhich can be interpreted in the light of theory. The theory motivates aninstrumental variable (IV) strategy that uses common industry-time demand shocks to approximate how endogenous firm revenue shares wouldchange, which maps onto input distance changes (separately from firmindustry-time changes holding last period’s capability choices constant).
This will allow us, in the next section, to use the structural estimates toquantify entry barriers in terms of equivalent tariffs and to determine the20
The closest piece to our model of supplier behavior is de Blas and Russ (2015), who
use Fréchet cost draws and limit pricing for a discrete number of firms that sell to end consumers, and our setting delivers analogs to their propositions 1 and 2. In contrast, we examine the interplay of supplier entry and downstream feedback effects through demandthat creates the possibility of Jevons’s paradox and multiple or nonexistence of equilibria
while still delivering a tractable model that can be readily estimated.

3052

journal of political economy

extent to which input-driven economies of scope explain the portfolios
of multiproduct firms.21
A.

Demand and Unit Costs

There are a finite number of downstream firms, which are large relative
to suppliers. Firm j can produce in multiple industries, indexed by k. In
period t, firm j pays a fixed cost of fkt to operate in industry k and faces
inverse demand in industry k of 22 
pjkt qjkt 5 Dkt qjktr21 ,where pjkt are prices, q jkt are quantities, and Dkt is an industry-time demand
shifter. To produce a quantity q jkt in industry k at time t, firm j combines
inputs from industry i, M ijkt, using a constant-returns-to-scale Cobb-Douglas
technology with industry input expenditure shares vik and industry productivity labeled Jjk.23 As firms pay a fixed cost to produce in any industry eachperiod, we can think of them as “production loci” with firm-industry productivity vector types Jj that produce different combinations of final goods
each period, depending on demand and supply conditions. At input prices
Sijtwit, the unit cost of firm j to produce in industry k at time t is therefore
YSijt wit v
cjkt ;
vik Jjk :i
ik

Thus, cjkt is a vector of unit costs that are influenced by input prices andindustry productivities.
B. Capabilities
Inputs Mijk at the industry level are a composite of quantities miijkt of varieties, indexed by i; Mijk is the CES aggregator of varieties of input i:ð∞ðj21Þ=jðj21Þ=j
5 miijkt di,
(4)
Mijkt
0

where variety i of input i has a price siit. Firms have capabilities of using
inputs with prices ½c ijt , ∞Þ, where c ijt is chosen by the firm. Here, a lower
21
In what follows, we take all prices in terms of a numeraire input or commodity (e.g.,labor).
22
As is well known, this structure can be microfounded with CES (constant elasticity of
substitution) preferences over varieties at the industry level. How one chooses to aggregate
across industries has implications for the patterns across {Dkt} each period. We remain agnostic to allow for flexibility in the estimation.
23
In keeping with this section’s focus on input capabilities,QJjk could be modeled as aCobb-Douglas aggregation of firm-input productivities: Jjk 5 i Aijv .
ik

comparative advantage of ﬁrms

3053

c ijt corresponds to both a greater variety of inputs and lower average prices.
This can be interpreted as firms screening their input suppliers by choosing a lower cost cutoff for suppliers that they meet. Firms then minimize
costs to produce Mijkt conditional on c ijt .
All firms have an innate capability for inputs from industry i, c i0 , andcan adjust this capability according to demand and supply conditions,subject to a Hicks-neutral cost across production in all industries.24
Letting c jt denote the vector of acquired capabilities, the unit costs ofa multiproduct firm are given by qðc jt Þcjkt in each industry, where


 

2
q c jt ; exp o ln c i0 2 ln c ijt =2 :i

A firm can use its acquired capabilities across any number of products
and reoptimizes by choosing c ijt each period. In order to simplify the subsequent notation, we normalize c i0 5 1.25
C. Upstream Suppliers
Suppliers can enter input market i by paying an entry cost fs and receive a
cost draw bi with Prðbi ≥ bÞ 5 ðb=sm Þ2l , with 0 < l < 1. The resulting massof entrants is Nit. Suppliers are monopolistically competitive across varieties i, but within varieties inputs are perfect substitutes, and so suppliers
engage in limit pricing akin to Bernard et al. (2003). Supplier i chooses
price siit, supplying a quantity miijt to downstream firm j, and earns profits
ziit by selling to any interested firms with the capability to purchase theirvariety. Since the minimum cost draw among Nit entrants is Prðbiit ≥ bÞ 5
ðb=sm Þ2Ω , with Ωit ; lNit , increases in entry uniformly decrease suppliercosts, which are passed on downstream, and prices drop even further
from limit pricing. It is noteworthy that supplier depth (per unit massof entry) l and the mass of entrants Nit both have similar price-reducing
effects through stochastic dominance in lower supplier prices.
it

D. Equilibrium
We are mainly concerned with how policies might influence supplier
depth and thereby capability choice and input distance with multiproduct firms. We therefore use a partial equilibrium setting in which suppliers enter, receive heterogeneous cost draws, but compete as in a Bertrand
model within their variety to supply downstream firms. Downstream firms
24
The innate capability is assumed to be common for econometric reasons. It can beheterogeneous but will then have to be estimated with fixed effects beyond the combination of industry-time.
25
This will not influence our estimating equations, as it is an industry-time effect.

3054

journal of political economy

are large, compared to suppliers, and purchase a continuum of input varieties, as determined by their choice of capabilities, to enter across industries
and maximize profits in the presence of scope economies across industries. The jointness of the mutiliproduct firm production and sourcing
decisions and the external scale economies of suppliers interact to provide a rich setting.26 Our equilibrium concept is as follows.
Deﬁnition. An equilibrium consists of choices in which firms andsuppliers compete under monopolistic competition in product markets
such that
1. Each firm j maximizes joint profits, given production technologies, {fkt}, {Dkt}, {wit}, {vik }, {Jjk}, sm, l, input price distributionsPrðsiit ≥ sÞ 5 ðs=sm Þ2lN , and {Nit} by choosing {qjkt}, {Mijt}, fc ijt g,and {miijt}.
2. Each supplier i in industry i maximizes profits, given the parameters and distributions above, {Nit}, and downstream firm choices{qjkt}, {Mijt}, and fc ijt g, by choosing price siit.
3. Suppliers enter until expected profits E[ziit] equal the entry cost fs.
it

We now solve for the optimal behavior of (upstream) suppliers and(downstream) firms.
E. Unit Costs
In what follows, we assume that Nit ≥ maxf1 1 ðj 2 2Þ=l, 1g, which is acontinuous analog of having at least two competitors and is sufficient forlimit-pricing effects from entry. While supplier entry is endogenous, wecharacterize when downstream demand from final-goods firms is sufficient to ensure this condition. In this setting, a downstream firm’s optimal choice of inputs can be summarized by the following proposition(all proofs are in app. D).
Proposition 1. Assume that Ωit > 1 2 j, which is necessary for nondegenerate variety choices. Define the cost index of input i for firm j as
Sijt for costs SijtMijkt.
1. The price index for input i for firm j is a function of capabilities c jit
and supplier entry Nit:
Sijt12j 5

lNit ϑit112j
smlN c 2lN,
jit
lNit 1 j 2 1
it

it

26
The model could be further closed with consumers who supply inputs to suppliers ingeneral equilibrium, but those features are not relevant to the subsequent analysis.

comparative advantage of ﬁrms
where

3055



j21
j 2 1 lðN 21Þ1j21
12:lðNit 2 1Þ 1 j 2 1
jitϑit ; 1 1

2. Since d ln Sijt =d lnc ijt 5 1 1 lNit =ðj 2 1Þ, it follows that when inputs
area. substitutes (j > 1), increasing varieties lowers costs (love for variety); or
b. complements (j < 1), decreasing varieties lowers costs (hatefor variety).
(3) Unit costs cjkt are given by
cjkt 5

1Jjk|{z}

firm-industry ð jkÞ"Y

1=ð12jÞ Ω =ð12jÞ #v Y 12Ω =ð12jÞ v
Ωit ϑit
sm
c ijt
wit
:

Ωit 1 ðj 2 1Þvikii
|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}


ik

it

ik

it

capability ð jktÞsupplier ðktÞWe next discuss the interplay between capabilities and supplier entry.
F. Supplier Entry
Since rRjk are expenditures by a firm j in industry k and vik is the share ofthose expenditures on input i, oj ok rvik Rjkt are total expenditures on input i. Expected profits corresponding to these revenues under limit pricing are calculated by multiplying revenues by the aggregate Lerner index Ljit 5 E½minf1=j, 1 2 b1 =b2 gjb1 ≥ c jit , where b1 =b2 is the ratio of thelowest to the second-lowest cost draw of suppliers of the same variety.
While the Lerner index varies by firm, the aggregate Lerner index depends only on the intensity of supplier competition at the industry level,
even though each firm buys from a fraction ðsm =c jit ÞlN of all suppliers.
Compared to the usual role of the Lerner index 1/j under CES preferences, this implies that limit pricing is eating into supplier profits andpassing the benefits of external scale economies downstream. The aggregate Lerner index is characterized by the following proposition.
Proposition 2. The aggregate Lerner index that converts supplierindustry revenues weighted by active suppliers into profits,
it

Lit ;

E½z iit 

lN ,

r
v
oj ok ik Rjkt sm =c jit

(5)

it

decreases in entry, approaches zero, and is given by
Lit 52lðN 21Þ211
j 2lðN 21Þ
1
j
12
1
j j21
lðNit 2 1Þ 1 1
j21
it

it

≤

1
:
j21

3056

journal of political economy

The aggregate Lerner index functions like an average markup that decreases with entry as a result of increased competition from limit pricing.
The free-entry condition is expected supplier profits per mass of entrants
E½z iit =Nit equal to the entry cost fs, which, with equation (5), gives the entry condition:
Lit 5

fs
:

lN

oj ok rvik Rjkt sm =c jit =Nit

(6)

it

Equation (6) will obtain if the left-hand and right-hand curves considered as functions of entry cross. The aggregate Lerner index decreases
in entry, so this has the potential to hold if the right-hand side increases
in entry, that is, if average weighted revenues oj ok rvik Rjkt ðsm =c jit ÞlN =Nitdecrease.
However, there is no reason this has to be the case. As the depth of suppliers increases, downstream input costs decrease, which spurs further
entry. Famously, this occurs under Jevons’s paradox, namely, that increased efficiency of an input (due to more efficient coal engines) canresult in a net increase in demand for the input (coal), causing an outwardly spiraling feedback loop. In our case, increased entry lowers the input costs of downstream firms, spurring further demand and therefore
entry. Even while fixing the complex interrelationship of capability choicewith input markets, it is crucial to examine whether this upstream-downstream feedback loop leads to Jevons’s paradox. This feedback loop canbe understood through profit shifting. Increased entry by suppliers decreases downstream costs through downward price competition that shifts
profits into cost savings downstream. This triggers the expansion of bothprofits and quantities downstream, spurring higher profits for suppliers
and therefore entry. Looking at this profit channel, it is intuitive that if
the profit taking downstream, as measured by the Lerner index 1 2 r, isgreater than the upper bound 1/j for all upstream Lerner indexes, thenthe paradox is avoided.27
Proposition 3. Holding downstream entry and capabilities constant, supplier entry drives average weighted revenues eventually down
to zero, including demand feedbacks from lower input costs, provided
that ð1 2 rÞj ≥ 1, which guarantees that downstream markups are highenough to absorb the upstream cost reductions.
it27
Famously, this occurs for inferior inputs, an idea dating at least to Jevons in 1865, whopointed to a paradox by which increased efficiency of an input (due to more efficient coalengines) can result in a net increase in demand for the input (coal). Hicks later refers tosuch inputs as regressive inputs, while subsequent work calls them Giffen inputs or inferior
inputs (see, e.g., Bear 1965; Portes 1968). In our case, if the “no-Jevons’s-paradox condition” ð1 2 rÞj ≥ 1 does not hold, then for high entry costs or low downstream demand,the market cannot support limit pricing, akin to markets that are too small to support
the entry of more than one firm.

comparative advantage of ﬁrms

3057

Returning to equation (6), one can picture the aggregate Lerner index,
drawn across levels of supplier entry, dropping from 1=ðj 2 1Þ toward anindex of zero, where limit pricing consumes all industry profits per unit
mass of suppliers and average weighted revenues fall toward zero, sweeping the right-hand side of equation (6) unboundedly upward. These curves
will cross so long as average revenues are high enough, which is true forsufficient downstream effective demand. This crossing need not be unique,as even for fixed downstream entry choices, expected supplier profits
E[ziit] (the product of the aggregate Lerner index and average revenues)
are not necessarily decreasing in entry. However, they will be, given thestronger conditions below, which further dampen the feedback loop thatis Jevons’s paradox. Once downstream entry is considered, then as input
costs drop from supplier entry, downstream firms may enter new industries, spiking up revenues abruptly, so for equation (6) to hold, supplier
entry must increase, potentially leading to multiple equilibria.28 We summarize these arguments and provide a sufficient condition for equilibrium holding downstream entry fixed in the following proposition.
Proposition 4. Holding downstream entry and capabilities constant, an equilibrium exists when average weighted revenues are at leastðj 2 1Þfs at supplier mass Nit 5 1 1 ðj 2 2Þ=l. Provided that j > 1 1 land ð1 2 rÞj ≥ 2, supplier entry drives average expected profits monotonically down to zero, including demand feedbacks from lower input
costs.
If capabilities are instead not held fixed, this implies that entry changes
for one input i will have cascading effects on input demand for all inputs
used in common production, causing changes in supplier entry in all
such inputs. Further analytical results would depend on demand structures (see Dhingra and Morrow 2019), and general results are not likely
because of the nonmonotonicities just detailed. Just as in models of thelocation of production, this is to be expected from a rich model ofinterlinkages that allows for “accidents of history” to occur.
When the condition of proposition 4 holds, equation (6) also provides
two comparative statics we appeal to in the empirical specification. First,
if supplier entry costs fs are reduced as from the removal of entry barriers,
the right-hand side of equation (6) shifts out, showing that the equilibrium
mass of suppliers increases. Second, suppose that some of the suppliers
are foreign and for expositional purposes, supply only to the domestic
market. For Nit fixed, if supplier costs are reduced as through a tariff decrease in industry i, it is easy to show that the price index Sit decreases, increasing average weighted revenues and again shifting out the right-hand28
However, the result implies average weighted revenues must decrease to zero barring
further entry, leading to an inductive proof of at least one equilibrium with the conditions
above.

3058

journal of political economy

side of equation (6) and increasing the equilibrium level of supplier entry.29 This yields the following proposition.
Proposition 5. Under the assumptions of proposition 4,
1. decreases in supplier entry costs increase supplier entry; and2. decreases in tariffs increase supplier entry.
G. Capability Choice
As derived above, unit costs are a function of chosen input capabilities,
which we now model. Economies of scope arise in this model because
firms can use their acquired capabilities across industries. The returns
to acquired capabilities, however, decrease as firms become active in moreindustries. Then, firms have to spread their input capabilities across alarger range of inputs and according to the different factor intensitiesof their outputs. The acquired capabilities are therefore not as tailoredto the needs of each industry as the industry mix gets wider.
Profits and revenues.—The profit function of firm j at time t across allindustries k is then 
pjt 5 opjkt 5 opjkt qjkt 2 ooq c jt Sit Mijkt
k

k



k

i

 

5 o D q 2 q c jt cjkt qjkt :r
kt jktk

A firm’s profit-maximizing capability and production choices, considering product markets jointly, are summarized in the following proposition.
Proposition 6. Assume that lNit > 1 2 j. For firm-input expenditure shares vijt, the optimal capability choice isln c ijt 5 2Θit vijt ,where Θit ; 1 1 lNit =ðj 2 1Þ is the elasticity of input price with respect
to capability. Firm-industry revenues are given by
Θ 21




r
ð12jÞ
21 1=ð12jÞ smvik lnwit ϑ1=
1
2
ΘlnRjkt 5 ln rr=ð12rÞ Dkt1=ð12rÞ 2
it
it
vik
|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} 1 2 r oi|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}
demand ðkt Þ
itsupplier ðkt Þ1
2 (7)rr
r
lnJjk 1
Θ2it v2ik 2Θ2it vijt 2 vik ,oo
12r2ð1 2 rÞ i2ð1 2 rÞ i
|ﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄ} |ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ
ﬄ} |ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}
RCA ð jk Þ

supplier-tech ðkt Þ

input distance ð jkt Þ|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}
comparative advantage ð jkt Þ(7)29This can be modeled as a decrease in iceberg transport costs or a first-order stochastic
shift downward in the cost distribution, since constant markups and limit pricing will passthis through into lower prices.

comparative advantage of ﬁrms3059

with the dimension of variation listed below each term (RCA 5 revealed
comparative advantage).
Since ln c ijt 5 2Θit vijt , it follows that firms sourcing from industry i increase their range of inputs under love for variety and decrease themunder hate for variety. Since competency is costly, firms do not invest incapabilities for inputs they do not source, that is, when vijt 5 0. The
addition to equation (7) of comparative advantage is beyond standard
models and yields input-based comparative advantage, highlighted by the
resource-based theory of the firm, through capability adjustment and different effective pools of suppliers for each firm.30 The demand and supplierterms can be estimated with industry-time fixed effects, which capture production shifts from the changing demand and supply environment. The
RCA terms capture idiosyncratic advantages a firm has across industries
that are static and can be estimated with industry-firm fixed effects, captured here with the interpretation of industry-specific combinations ofidiosyncratic input productivities.
The remaining comparative-advantage term captures the dynamic redeployment of input capability and is sensitive to the depth of input markets (through Nit in Θit). To interpret this term, we split it into two parts
to highlight the difference between single-product and multiproductfirms. The special case of the “average” single-product firm is useful withvijt 5 vik , in which case the input-distance term vanishes (the firm is exactly
in its “core” and tailors its inputs fully) and only a supplier-technology effect of the benefits from supplier depth by input intensity remains. To theextent that a multiproduct firm deviates from its core competency, this will
be reflected in input shares vijt deviating from each vik and penalizing industries far from the firm’s core. In the case of identical supplier depth
across markets—that is, Θit 5 Θ—the penalty takes the intuitive form ofa coefficient times Euclidean distance squared, oi ðvijt 2 vik Þ2 .
A final result stemming from profit-maximizing behavior is how firms
approximately update their core distance from changes in industry-level
demand {Dkt}, holding capabilities constant. We use this theory-driven relationship in the instrumentation strategy below to correct for potential
biases from unobserved firm-industry-level shocks.
Proposition 7. Input distance can be approximated by considering
each firm as holding capabilities constant and optimally updating to respond to industry demand shocks through the relationship

2

2

2
o vijt 2 vik ≈ o vijt21 2 vik 2 gkt oxjkt21 vijt21 2 vik ,
i

i

i

30
Following proposition 6, the effective mass of suppliers a firm chooses is Nit ðsm =c jit ÞlN 5 Nit smlN e lN ½11lN =ðj21Þv . Since the vector of expenditure shares vjt is a functionof contemporaneous demand and supply conditions and comparative advantage,
vjt ðDk , Nt , Jj Þ, there is firm heterogeneity in effective suppliers and ranks of supplier purchases from capability choice stemming from the joint production and sourcing decision.
it

it

it

it

ijt

3060

journal of political economy

where xjkt are revenue shares of industry k for firm j in year t and gkt is acommon industry demand innovation equal to 2ðDkt =Dkt21 2 1Þ=ð1 2 rÞ.
H. Estimating Policy Effects
Now consider an observable policy P that changes the depth of input
markets of the form Ωit 5 lNt 5 Ωi0 1 aP Pit . Linearizing equation (7)around the initial policy state Ωi0 and letting kx represent a fixed effectfor characteristic x yields the following estimating equation:


v2ijt
r
2Θi0
2

a
lnRjkt 5 kkt 1 kjk 1
v
Θ
1
ð
P
2
P
Þ
v
2
: (8)
i0
P
it
i0
ijt ik
j 21
2
12 ro
i
|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}
comparative advantage ð jkt Þ

The theory implies that Θit has the same sign as j 2 1, so estimating aP 
Θi0 =ðj 2 1Þ allows for testing hypotheses about the sign of aP.
Two policy changes over this period that can be expected to increase
the depth of the supplier market are dereservation and tariff changes,
which change the number of potential suppliers available. We model
these two policy changes as a discrete effect of entry barriers (reservation)aB within the 3-digit level (with Bijt equal to 1 if a 5-digit product the firm
ever uses is reserved in industry i and 0 otherwise) and a linear effect at oftariffs on entry for three digit tariffs tijt (these are aggregated at the firmlevel from observed average firm-level imports at the 5-digit level).
For ease of estimation, we impose that all supplier markets have the so thatsame depth Ωi0 5 Ω,
 1 aB Bijt 1 at tijt :Ωit 5 ΩIn light of the theory above, we can interpret these policy shifts as changing the depth of input markets with theory signing both aB and at to be is thenegative, so that with no entry barriers and zero tariffs, Ωi0 5 Ω“maximal” market depth. Therefore, equation (8) approximates arounda policy space of no entry barriers and no tariffs. This then implies theestimating equation


v2ijt
(9)
lnRjkt 5 kkt 1 kjk 1 k0 o vijt vik 2
2
i
(9)


2


v
ijt
:
1 k1 o aB Bijt 1 at tijt vijt vik 2
2iwith k0 5 Θ2i0 r=ð1 2 rÞ and k1 5 2Θi0 r=ð1 2 rÞðj 2 1Þ. This estimating
equation says that (log) firm revenues depend on industry-time demandand supply effects kkt, firm-industry effects kjk, a distance effect of industry
k from the firm’s core competency k0, and policy effects that exacerbate

comparative advantage of ﬁrms

3061

distance for each input i through k1aBBijt and k1attijt. Since deeper supply
increases the returns to capabilities and entry barriers and tariffs decrease supplier entry (proposition 5), k1aB and k1at should be negative.
The tariff equivalent of dereservation can then be computed fromaB k1 =at k1 5 aB =at . Because of the selection issues involved in log specifications of sales, we estimate the extensive margin of production impliedby equation (9) which accounts for zeros in firm-industry sales. Firms willproduce in industry k exactly when Rjkt > ð1 2 rÞfkt , so we estimate equation (9) as a linear probability model for the outcome that observed revenues of the firm-industry are positive each period.31 As we are estimating
probabilities, we can think of how comparative advantage shifts the production probability frontier of firms.
I. Structural Instrumentation
In equation (9), firm expenditure shares vijt are a function of timevarying input prices wit, demand shocks Dkt, firm-industry productivities
Jjk, and fixed technology vik . Input price and demand shocks are estimatedthrough industry-time fixed effects. Productivities are estimated throughfirm-industry fixed effects, expressed as RCA. Technology is estimatedwith a large number of observations, so the risk of measurement error
contaminating vik is small, and similarly for demand and input shocks.32
There might be omitted variables from our structural equation thatcause vijt to change, which could bias our estimates of the role of capabilities. For example, demand or cost shocks at levels more disaggregatedthan the firm-industry would change input expenditures and revenuesof a firm for reasons other than changes in input capabilities. It can beshown in these two cases, for instance, that bias will exist but run in opposite directions:• contemporaneous demand shocks Djkt at the firm level would bepositively correlated with input similarity through the compositionof firm activity; and31
This can be naturally extended to an extensive-margin formulation with a logit-typemodel; see app. D2. We implement this for the structural form as a robustness check
but have difficulties with IV-logit as a result of the high-dimensional parameter space andwell-known sensitivity of that estimator.
32
One potential concern is that dereservation systematically changes technology vik
(such as through price sensitivity of input shares for single-product firms), in which casewe could have instrumented for the change in input similarity with the interaction between
reservation and initial input similarity, under the assumption that better input supply affects revenues only through the channel of input expenditure shares. Regression coefficients of the percentage of reserved inputs within a 3-digit category on vik , however, havea mean of 20.010 with a standard deviation of 0.017, which is to say about zero in significance and magnitude. Since, in addition, the value percentage of reserved inputs is generally much less than 100%, the implied changes are negligible. See the online appendix
for the histogram of estimated coefficients.

3062

journal of political economy• contemporaneous supply shocks wijkt at the firm level would be negatively correlated with input similarity through the composition offirm activity away from industries intensive in using input i (highvik ).
A key econometric insight of proposition 7 is that omitted demand andsupply shocks interact with a firm’s industry mix, which alters their input
use and hence input similarity across industries, potentially introducing
bias in estimating economies of scope or policy impacts. The theory motivates a novel IV strategy that uses common industry-time demand shocks
to approximate how endogenous firm revenue shares would change input
use. The instrumentation strategy is based on the assumption of common
industry-level demand innovations Dkt =Dkt21 across firms, which can be estimated precisely from the large number of observations and projected onto
firm behavior through theory. Recovering these common demand shocks
allows us to predict changes in vijt on the basis of shifts in the within-firm
distribution of activity.33 In fact, examining the estimating equation (8),what is needed is not instruments for each vijt but rather an instrument
for terms of the form oi ðvijt vik 2 v2ijt =2Þ and oi ðPit 2 Pi0 Þðvijt vik 2 v2ijt =2Þ. The
key insight here is that we need to instrument for comparative advantage
and comparative advantage interacted with exogenous policy changes.
Proposition 7 motivates the following instrumentation strategy. The
current level of input similarity can be predicted from the levels of thepast period, plus a linear approximation of the change in acquired comparative advantage one would expect from common industry demand
shocks. Intuitively, this is akin to predicting current input expenditurelevels from the previous year (and the RCA they contain) and then projecting them forward one period with a Bartik-type instrument based on
input expenditures from the input-output table.34 In the case of a single
33
In doing so, we hold the role of capabilities constant in the instrumentation stage to
avoid nonlinearity, as the full expression for input similarity is recursive. Even assuming
common input markets for all inputs (lNit 5 Ω), the expression becomesoiovih vijt 5ivih ok vik Dkt

1=ð12rÞoDk1=ð12rÞ
kt

2½11Ω=ðj21Þ2

skt c 02½11Ω=ðj21Þ2

skt c 0i

ih ijt

o v v =Ji2r=ð12rÞ

ih ijt

o v v =Jjk

2r=ð12rÞ

jkQ
Ω=ð12jÞ  v
with skt ; i ðwit fΩ=½Ω 1 ðj 2 1Þg1=ð12jÞ sm=vik Þ .
34
While this instrumentation strategy works for contemporaneous shocks, if the omitted
shocks are serially correlated, they would appear in the previous-period terms that are thebasis for the IV strategy, and the exclusion restriction would fail. There are two potential
approaches to this problem: either (1) explicitly modeling the serial process, such as
shocks being AR(1), or (2) using even further lags in the first stage so that the serial correlation is lower. The former approach is popular but in our case would introduce anonlinear-in-parameters estimator that presents computational issues. The latter suffersfrom a large loss in observations, which would select toward larger firms because of the nature of the data sample.
ik

comparative advantage of ﬁrms

3063

instrument for terms of the form ðvijt vik 2 v =2Þ, the first stage of an IV
strategy following from proposition 7 is then
v2ijt21
v2ijt


v
v
v
2
1
k
1
l
v
2
5
k
kt
jk
oi ijt ik 2
oi ijt21 ik 2
(10)


2
v
ijt21
:
(10)
2 gkt oxjkt21 vijt21vik 2
2
i
2
ijt

Equation (10) is composed of three parts: the fixed effects found in themain structural equation for revenues, a lagged term for the endogenous
sum oi ðvijt vik 2 v2ijt =2Þ, and a linear adjustment based on predicted input
share changes from lagged revenue shares xjkt21 and contemporaneous
industry-level demand shocks gkt. This last term is essentially a (lagged)
sales-weighted “technological distance” measure of the firm away froman industry k times the magnitude of the demand innovation that predicts the change in oi ðvijt vik 2 v2ijt =2Þ between periods.
However, as we need to instrument for both changes in input sharesand these input shares interacted with two policy changes, we need three
instruments of the type in equation (10), one for the shares and two for
their two policy interactions. For this 2SLS (two-stage least squares) estimator, we also need a system that includes all instruments in each firststage prediction equation. Accordingly, define both ~vijkt ; ðvijt vik 2 v2ijt =2Þ
and x~ijkt ; xjkt ðvijt vik 2 v2ijt =2Þ and the following sums for parameters land the K  T vector g:M; lo~vijkt 2 gox~ijkt ,
Ijkt11
i

I

B
jkt11

I

t
jkt11

i

; loBijt ~vijkt 2 goBijt x~ijkt ,
ii

; lotijt ~vijkt 2 gotijt x~ijkt :ii

The resulting first-stage equations for our estimator are as follows:35






o~vijkt 5 kkt 1 kjk 1 IjktM l11 , g11 1 IjktB l12 , g12 1 Ijktt l13 , g13 1 hjkt , (11)ioB ~v 5 k 1 k 1 I

 21 21 
l , g 1 IjktB ðl22 , g22 Þ 1 Ijktt ðl23 , g23 Þ 1 hBjkt ,(12)

ot ~v 5 k 1 k 1 I

 31 31 
l , g 1 IjktB ðl32 , g32 Þ 1 Ijktt ðl33 , g33 Þ 1 htjkt :(13)

ijt ijkt

kt

jk

M
jkt

i

ijt ijkt

kt

jk

M
jkt

i

35
In practice, sales within a firm-industry group are unlikely to be a balanced panel, as
the extensive margin of a firm’s industries is liable to change (we in fact model and estimate this with a logit model). Consequently, our one-period-lag strategy may lose some observations, but it reduces the number of parameters that must be estimated simultaneously.

3064

journal of political economy

We implement the IV estimator of the structural coefficients in equation (9) as a manual 2SLS estimator, which allows us to calculate the fitted
values of the first stage without having to recover the high number of demand innovation coefficients gkt of the instruments in equations (11)–(13), and accordingly we do not report them. We correct for the wellknown misspecification of the residual variance estimator in manual
2SLS (see chap. 4.2.1 of Angrist and Pischke 2008) and cluster standard
errors at the firm-industry level, as proposed by Cameron and Miller(2015). The resulting estimator is equivalent to those obtained throughone-stage IV estimation with clustered standard errors.
V. Results and the Economic Relevanceof Input Capabilities
This section first presents our structural estimates of the industry portfolio of firms. The estimates predict which industries firms operate in following policy changes, showing how acquired comparative advantage
generates core competencies. We then turn to examples and counterfactuals that demonstrate the role of input capabilities in predicting firmindustry scope. A quantification of input-based comparative advantage
follows, relative to aggregate industry movements and coproduction rates,
before the section ends with an extension of the structural estimates to primary factors.
A.

Structural Estimates

Table 9 shows the OLS and IV estimates for the extensive-margin versionof equation (9). The estimated coefficient on the deviation of the input
similarity measure is k0 5 0:0086 in the OLS, which rises to 0.1630 in
the IV.36 The policy coefficient of interest for the entry barriers is k1 aB 5
20:0004 in the OLS, which increases in magnitude to 20.0016 in the
IV. Comparing this with the coefficient on tariffs interacted with the input
similarity deviation, k1 at 5 20:0168, the effect of entry barriers is a tenth
as large. Both entry barriers and higher tariffs reduce the role of input distance, since fewer suppliers disincentivize investing in input capabilities.
The tariff equivalent of dereservation is then aB =at 5 0:0016=0:0168 5
0:095. Entry barriers from reservation of inputs for small-scale firms therefore lower industry adoption, and their estimated effect is equivalent to a
9.5% tariff on inputs.

36
For the IV sample, the OLS coefficients for the right-hand-side variables are similar:
0.0092 (0.0002), 20.0004 (0.0002), and 20.0001 (0.0004) for k0, k1aB, and k1at, respectively.
Relevant summary statistics are in table A3.

comparative advantage of ﬁrms

3065

TABLE 9Structural Estimates for Multi-industry Sales Premium
Positive Sales for Plant j in Industry k (Rjkt > 0)
Input distance oi ðvijt vik 2 v =2Þ
2
ijt

Input distance oi Bijt  ðvijt vik 2 v2ijt =2Þ,entry barriers
Input distance oi tijt  ðvijt vik 2 v =2Þ,tariffs

(1)

(2)

(3)

(4)

.0085**(.0002).0086**(.0002).1362**(.0229).1630**(.0226)2.0004**(.0001)2.0004**(.0001)2.0016**(.0004)2.0016**(.0004)

Yes
Yes
OLS
77,745,382.762

2.0005(.0003)Yes
Yes
OLS
77,745,382
.762

Yes
Yes
IV
46,185,150.760

2.0168**(.0027)
Yes
Yes
IV
46,185,150
.760

2
ijt

kjk
kkt
Estimator
Observations
R2

Note.—Standard errors are in parentheses, clustered at the firm-industry level.
** p < .01.

B. Input-Based Comparative-Advantage Estimates
The structural estimates can be used to quantify the importance of input
capabilities in shaping firm-level comparative advantage. Input-based
comparative advantage (CA) can be summarized by the premium arisingfrom input linkages in the production probability frontier. By expandinglnRjkt , taking out industry-time, industry-firm, and firm-time fixed effects,
we have^ B Bijt 1 a^ t tijt vik vijt ,(14)
CA jkt ; ^k0 ovik vijt 1 ^k1 o aiiwhere parameters with a hat denote our IV estimates of the parameters.
Note that because of fixed effects, these estimates are within firm-industry,so they are inferred from shifts in comparative advantage, and they arealso within industry-time, so they measure shifts relative to other firms
in an industry. Therefore, this measure captures movements in comparative advantage.
Table 10 shows summary statistics of CA for firms across industries they
produce in by sales rank. CA increases a firm’s production probability by
4.3 pp on average, relative to that predicted by industry-wide demand andsupply factors (captured in the industry-time fixed effects). For the toptenth percentile, this increase is more than 13 pp. On average, CA is higher
for single-industry firms because they can choose their input capabilities ina way that is tailored to their industry. In line with the model, CA decreases
as firms are active in more industries, since firms have to spread their input
capabilities across a larger range of inputs and factor intensities.

3066

journal of political economy
TABLE 10
CA by Industry Sales Rank

Industry Rank
1
2
3
4
5
6
7
8
9
101
Total

Observations

Mean

10th Percentile

90th Percentile

307,294
98,41334,416
11,693
4,850
2,015
817
278
95
38

.054
.026
.017
.013
.011
.010
.009
.009
.008
.005

.004
.001
.000
.000
.000
.000
.000
.000
.001
.000

.153
.071
.040
.032
.028
.028
.024
.024
.018
.010

459,909

.043

.002

.132

We now study CA for industries that firms do not produce in, which isthe additional probability that a firm would produce in a new industry by
virtue of their input capabilities, holding fixed their capability choice.
Since the space of inputs is large and many industries will not have inputs
in common with the firm, CA is often close to zero for any given firm andindustry. But for more input-similar firm-industry combinations, as suggested by figure 1, CA is economically significant. Table 11 contrasts theaverage CA for single-product firms in three industries they might enter.
Single-industry firms in the edible fruits and nuts/edible vegetables industry (code 121), on average, enjoy a CA in the fruit and vegetable juices industry (135) of 8.5 pp, whereas the single-industry firms in the (perhaps
technologically more similar) industry of soft drinks and mineral water(152) would, on average, get only a 0.6 pp premium. In this example,
the edible fruits and nuts/edible vegetables industry is upstream to thefruit and vegetables juices industry and may therefore share intermediate
inputs. Many industry pairs where CA is economically relevant, however,
TABLE 11
CA for the Second Industry
Industry (3-Digit ASI Code)
Fruit and vegetable juices (135):
Edible fruits and nuts, edible vegetables (121)Soft drinks and mineral water (152)
Animal oils and fats (115):
Other produce of animal origin (119)Vegetable oils and fats (125)
Leather bags, purses, etc. (441):
Leather footwear (443)
Plastic footwear (423)

CA (pp)
8.5
.6
5.3
1.1
6.8
.4

Note.—Average firm-level comparative advantage among singleindustry plants of two contrasting industries for the italicized industry. “Other produce of animal origin” covers mostly bone, horn, andmeals thereof.

comparative advantage of ﬁrms

3067

are not vertically related. Consider the leather bags and purses industry(441), which is not vertically related to either leather footwear (443) orplastic footwear (423). Given the leather footwear industry’s shared input
use of leather with the leather bags and purses industry, its premium is
6.8 pp, whereas the plastic footwear industry’s premium is only 0.4 pp.
Table E1 states the average CA with the highest premium for 25 industries.
It shows that the examples below are not outliers: in many industries, input
capabilities shape firm-level comparative advantage to an extent that is economically relevant to firms.
Table 12 further highlights the core-competencies feature of inputbased comparative advantage. The columns contain the number of industries firms operate in, and the rows contain the firm sales rankingof each industry. For firms that produce in a single industry (top left), tailoring input capabilities to the needs of the industry increases production probabilities by 5.2 pp. Firms that produce in two industries experience a 6 pp premium on their core industry and about half of that, 2.9 pp,
on their secondary industry. As firms diversify into more industries, thereturns to capabilities for an individual industry decline. This occurs
along the rows and the columns, showing that the estimated industry adoption falls for firms that offer a wider industry mix and also for core industries, because the acquired capabilities are less tailored to the needs of asingle industry.
Table 12 shows that more diversified multiproduct firms experiencelower returns from input-based comparative advantage in percentage
terms. This, of course, conceals the large economic magnitudes of premia
associated with input-based comparative advantage in more diversified
firms, which are much bigger than other firms. To highlight this selection
effect, entries in table 13 contain the size-weighted CA of firms. We normalize sales weights by the average sales of a single-product firm in that industry, so that the interpretation is premia weighted by the equivalent
TABLE 12Core-Competency Sales Premium (in pp) from CA
Number of Industries with Positive Sales
Industry Rank

1

2

3

4

5

6

7

8

9

101

1
2
3
4
5
6
7
8
9
101

.052

.060
.029

.061
.023
.019

.033
.018
.015
.013

.026
.017
.013
.013
.011

.021
.016
.013
.012
.011
.010

.020
.014
.011
.011
.011
.010
.010

.019
.015
.011
.009
.009
.010
.009
.009

.014
.010
.014
.010
.011
.010
.009
.008
.008

.020
.022
.015
.016
.009
.006
.007
.008
.009
.005

3068

journal of political economy
TABLE 13Core-Competency Sales Premium (in pp) from
CA—Size Weighted
Number of Industries with Positive Sales (CA Weighted by Size)

Industry Rank

1

2

3

4

5

6

7

8

9

101

1
2
3
4
5
6
7
8
9
101

.055

.072
.005

.130
.012
.002

.157
.039
.005
.001

.143
.158
.007
.007
.004

.179
.301
.048
.057
.009
.004

.178
.266
.019
.017
.014
.007
.002

.284
.332
.041
.024
.008
.008
.006
.002

.468
.018
.245
.019
.019
.006
.005
.001
.005

1.727
3.499
1.375
.185
.047
.011
.019
.006
.004
.002

number of typical single-product firms. The single-industry premiumfrom acquiring capabilities is hardly changed at 5.5 pp, compared to thatof the typical single-industry firm. Firms in multiple industries now show
large premia even when we move along the rows of core industries forfirms that operate in more and more industries. For example, a firm operating in nine industries has a 46.8 pp higher (size-weighted) premiumin its core industry, compared to a 7.2 pp core premium for a two-industry
firm. Moving down the columns, firms see larger premia on their coreproducts, compared to their peripheral products. The lowest-ranked industries of a firm show small premia of under 1 pp. Examination of theanalogous tables for the model extended to factors of production in appendix F shows broadly the same patterns at roughly half the size.
Tables 12 and 13 therefore confirm the core-competencies feature of
input-based comparative advantage. Together they show that multiproduct firms experience growth as a result of economies of scope in inputs
but that these decline as firms diversify into more and more industries.
C. Economic SignificanceTo examine the economic importance of input-based comparative advantage, we compare the distribution of industry-level variation in coproduction, which is captured in the fixed effects, with the model-impliedcomparative-advantage terms. A large literature in international economics seeks to quantify the importance of alternative drivers of productivity and welfare, such as by decomposing the margins for welfare gains
from trade. Taking a similar approach, this subsection decomposes themargins of coproduction within firms. It relates them to potential underlying drivers, such as industry-level demand and supply shocks, which arecomparative advantage of ﬁrms

3069

being explicitly modeled in the theory and are being picked up in theform of fixed effects in the empirical analysis of sections III and V.
Figure 2A compares the distribution of CA, in lighter yellow, to the distribution of (unconditional) coproduction rates within industry-pair cells,in darker blue. Comparative advantage is estimated as in equation (14),while the unconditional coproduction rates capture, for example, demand complementarities such as left shoes being coproduced with rightshoes. The distributions overlap substantially, showing that input-based

F IG . 2.—Comparing CA with other drivers of entry. FE 5 fixed effects.

3070

journal of political economy

comparative advantage shifts entry probabilities to an extent that is similar to time-invariant coproduction rates within industry pairs. In otherwords, CA is as important in driving entry as summary statistics of observed coproduction rates across industries. Further, input-based comparative advantage explains much of the variation in entry probabilities
across industry pairs, implying a limited role that confounders could playin altering the contribution of CA toward entry into an industry.
Figure 2B compares the distribution of CA, in yellow, to the distribution of entry probabilities within industry-year cells (i.e., what an industryyear fixed effect would pick up), in blue. Although smaller, the overlap continues to be substantive. The quantitative importance of the model-implied
CA in driving production choices is therefore between the importance ofindustry pair–level drivers and that of industry-year shocks.
D. Extension to Primary Factors
The model and structural estimation can be readily extended to primaryfactors, such as capital and labor. This extension is motivated by productlevel findings of Schott (2004), who shows that countries’ within-productspecialization reflects factor-based comparative advantage. It is also related
to Crozet and Trionfetti (2013), which examines factor intensity and firm
exports, and to Fontagné, Secchi, and Tomasi (2018), which examines the
typical product vectors of firm exports.
Adding primary factors f in an analogous way to intermediate inputs(details in app. D4), the revenue equation then contains a factor similarity term as follows:




v2ijt
vijt vik 2
lnRjkt 5 kkt 1 kjk 1 o kI0 1 kI1 aB Bijt 1 at tijt
2
i


(15)
v2fjt
,
(15)
1 okF1 vfjt vfk 2
2fwith kI0 5 Θ2i0 r=ð1 2 rÞ, kI1 5 2Θi0 r=ð1 2 rÞðj 2 1Þ, and kF1 5 2Θf 0 r=ð1 2
rÞðj 2 1Þ. The IV estimator is analogous to the one above, with an additional instrument for firm-level factor shares to correct for biases fromfirm-factor shocks, detailed in appendix D4.
Taking the extended model to data, table 14 shows structural estimates accounting for primary factors capital K and labor L. It finds similar results, with a slightly smaller coefficient on the input similarity term
and minor reductions in the magnitudes of the interaction terms. The
results suggest that firms are also more likely to move into industries thathave a similar primary factor mix, and they provide some evidence fortheories of the firm suggesting coproduction in high-capital-intensity

comparative advantage of ﬁrms

3071

TABLE 14Structural Estimates for Multi-industry Sales Premium, with Primary Factors
Positive Sales Dummy (Rjkt > 0)
Input distance oi∉fK ,Lg ðvijt vik 2 v =2Þ
2
ijt

Factor distance of ∈fK ,Lg ðvfjt vfk 2 v2fjt =2Þ
Input distance oi Bijt  ðvijt vik 2 v2ijt =2Þ,entry barriers
Input distance oi tijt  ðvijt vik 2 v2ijt =2Þ,tariffskjk
kkt
Estimator
Observations
R2

(1)

(2)

(3)

(4)

.0068**(.0002).0084**(.0003).0068**(.0002).0084**(.0003).1277**(.0127).1094**(.0122).1112**(.0110).0600**(.0080)2.0000(.0002)2.0000(.0002)2.0040**(.0006)2.0036**(.0006)

Yes
Yes
OLS
77,745,382
.7622

.0008
(.0005)Yes
Yes
OLS
77,745,382
.7622

Yes
Yes
IV
46,185,150.7598

2.0210**(.0027)
Yes
Yes
IV
46,185,150.7598

Note.—Standard errors are in parentheses, clustered at the firm-industry level.
** p < .01.

industries. Tables B4 and B5 provide reduced-form results with primaryfactors.
VI.

Conclusion

Even though multiproduct firms account for a disproportionately large
share of economic activity, systematic theory and evidence examining
product diversification are thin. In this paper, we examine the role ofcommon use of input capabilities as a determinant of the evolution offirms’ product space. This formalizes the resource-based view of the firmin ways that enable an assessment of its economic significance. We bringthis theory to Indian manufacturing data to study the relevance of input
capabilities both in reduced form and through structural estimation. We
use the removal of size-based entry barriers in input markets to establish
a causal channel from input capabilities to the firm’s industry mix. Estimating the structural parameters that govern the elasticity of revenue
with respect to the capabilities component of cost, we find that input capabilities determine the content of a firm’s “core competencies” andthat they are quantitatively as important as time-invariant coproduction
rates across industries.
A key theoretical insight of our framework is that economies of scope
within multiproduct firms imply that production choices and input capabilities are jointly determined. Production choices are interdependent on
the relative demand and supply conditions a firm faces, and the portfolio
of industries a firm enters depends on the extent of its input similarity to3072

journal of political economy

that industry. The theory motivates an IV strategy that shows that input capabilities are quantitatively important in determining the production patterns of firms.
Broadly speaking, the fact that the mechanisms of this paper are quantitatively important underscores that multiproduct firms do not behave
like collections of single-product firms. Therefore, in aggregate, industries may respond to policy in ways that will not be captured by singleproduct firm models. Coupled with the obvious role of input-output
linkages central to economies of scope shown here, this calls for additional research on these linkages both between firms and at the macroeconomic level to look for policy effects within firms that so far may havebeen missed.
Appendix A
Descriptive Statistics
TABLE A1
Summary Statistics (N 5 52,637,029)

Industry Add Dummy
InputSimilarity0jk
InputSimilarity-Dereservation0jkt
InputSimilarity-Tariff 0jkt
OutputSimilarity0jk
OutputSimilarity-Dereservation0jkt
Upstream0jk
Downstream0jk

Mean

SD

Minimum

Maximum

.0011
.0110
.0005
2.0001
.0038
.0005
.0035
.0058

.0324
.0529
.0088
.0023
.0515
.0192
.0335
.0402

.00
.00
.00
2.33
.00
.00
.00
.00

1
1
1
0
1
1
1
1

InputSimilarity
OutputSimilarity0jk
InputSimilarity-Dereservation0jkt
OutputSimilarity-Dereservation0jkt
Upstream0jk
Downstream0jk

0
jk

1.00
.37
.17
.09
.46
.54

InputSimilarity0jk
1.00
.06
.37
.54
.45

OutputSimilarity0jk

1.00
.10
.05
.06

InputSimilarityDereservation0jkt

TABLE A2
Correlation Matrix of Similarity Indices

1.00
.10
.08

OutputSimilarityDereservation0jkt

1.00
.50

Upstream0jk

1.00

Downstream0jk

3074

journal of political economy
TABLE A3
Structural Summary Statistics

Indicator R jkt > 0 (OLS)oi ðvik vijt 2 v2ijt =2Þ
oi Bit  ðvik vijt 2 v2ijt =2Þ
oi tit  ðvik vijt 2 v2ijt =2Þ
Indicator R jkt > 0 (IV)oi ðvik vijt 2 v2ijt =2Þ
oi Bit  ðvik vijt 2 v2ijt =2Þ
oi tit  ðvik vijt 2 v2ijt =2Þoi ðvik vijt21 2 v2ijt21 =2Þ
oi Bit  ðvik vijt21 2 v2ijt21 =2Þ
oi tit  ðvik vijt21 2 v2ijt21 =2Þ
oi xjkt21 ðvik 2 vijt21 Þ2
oi Bit  xjkt21 ðvik 2 vijt21 Þ2
oi tit  xjkt21 ðvik 2 vijt21 Þ2

Count

Mean

SD

Minimum

Maximum

77,745,382
77,745,382
77,745,382
77,745,382
46,185,150
46,185,150
46,185,150
46,185,150
46,185,150
46,185,150
46,185,150
46,185,150
46,185,150
46,185,150.0059
2.35852.01422.0067.0060
2.34772.01282.00762.33742.01302.0061
.0000
.0011
.0001

.08
.15
.07
.02
.08
.15
.06
.03
.17
.07
.02
.00
.02
.01

.00
2.50
2.50
21.05
.00
2.50
2.50
2.83
21.46
21.00
2.91
.00
.00
.00

1
1
0
0
1
1
0
0
1
0
0
1
3
1

Appendix B
Robustness of Estimates and Further Results
B1.

Robustness of Industry Add, Drop, and Sales Regressions

Table B1 shows the results of the most stringent specification of the industry addition regressions on particular subsamples. Column 1 shows the benchmark results on the full sample. Column 2 shows results for single-plant firms. Given thatthe vast majority of plants are single-plant firms, the results are virtually unchanged. Column 3 shows results for the plants that get surveyed every year
(what the ASI calls the “census”: all plants that have more than 100 employees).
Finally, in column 4, we exclude all industries k that never have any coproduction
with the main industry (defined as the one where j has the highest amount ofsales). This removes about 90% of observations from the sample (which always
have zeros on the left-hand side). Table B2 shows how the probability to drop
an industry from the industry mix is shaped by input similarity. Table B3 shows
how log sales are correlated with input similarity with a wide range of input-output
linkage controls.
TABLE B1
Revealed Comparative Advantage: Robustness
Dependent Variable: Addjkt

InputSimilarity0jk

InputSimilarity-Dereservation0
jkt

OutputSimilarity0jk
OutputSimilarity-Dereservation0jkt

(1)

(2)

(3)

(4)

.0199**(.0006).0155**(.0023).100**(.0018).0171**(.0022).0196**(.0006).0146**(.0027).0970**(.0020).0178**(.0025).0251**(.0009).0110**(.0028).119**(.0025).0179**(.0030).0360**(.0011).0214**(.0042).0858**(.0019).0147**(.0021)TABLE B1 (Continued )Dependent Variable: Addjkt

0jk

Upstream

Downstream0jk
SampleFirm  year fixed effects ajt
k  k0  t fixed effects akk t
R2
Observations

(1)

(2)

.0291**(.0030)2.0035*(.0014)Full.0219**(.0032)2.0044**(.0016)
Singleplant firms
Yes
Yes
.0660
43,120,945

Yes
Yes
.0646
52,666,907

0

(3)

(4)

.0358**.0186**(.0041)(.0035)2.00384*2.0148**(.0020)(.0029)CensusCoproduction
plantsindustries
Yes
Yes
Yes
Yes
.0848
.0965
27,076,486
5,165,511

Note.—Standard errors are in parentheses, clustered at the firm-industry level.
* p < .05.
** p < .01.
TABLE B2
Industry Drop Regressions
Dependent Variable: Dropjkt

InputSimilarity0jk
InputSimilarityKL0jk
InputSimilarity-Dereservation0jkt
OutputSimilarity0jk
OutputSimilarity-Dereservation0jkt
Firm  year fixed effects ajt
Industry  year fixed effects aktk  k0  t fixed effects akk t
R2
Observations

(1)

(2)

(3)

.01281(.0078)2.7804**(.0996)2.4002**(.0658)2.2492**(.0040)2.1312**(.0095)Yes

2.1952**(.0126)2.9606**(.1518)2.13261(.0703)2.2629**(.0049)2.1012**(.0110)Yes
Yes

2.1391**(.0139)2.6631**(.1834)2.14421(.0872)2.2127**(.0074)2.0721**(.0137)
Yes.536
159,001.572
158,920

0

Yes
.656
134,861

Note.—Standard errors are in parentheses, clustered at the firm-industry level.
p < .10.
** p < .01.

1

3076

journal of political economy
TABLE B3
Intensive Margin of Sales
Dependent Variable: log Salesjkt

InputSimilarity0jk

InputSimilarityKL0jk
InputSimilarity-Dereservation0jkt
OutputSimilarity0jk
OutputSimilarity-Dereservation0jkt
Firm  year fixed effects ajt
Industry  year fixed effects aktk  k0  t fixed effects akkt
R2
Observations

(1)

(2)

(3)

.5261**(.0359)1.8510**(.5145)1.2502**(.2563)4.1096**(.0186)2.3806**(.0391)Yes

1.0434**(.0522)4.8912**(.7342).6725**(.2516)3.4748**(.0222)2.5480**(.0445)
Yes
Yes.5077**(.0505)4.9163**(.7247).8664**(.2438)1.5068**(.0244)2.2616**(.0406)Yes.802
251,026.832
250,963

Yes.911
220,6130Note.—Standard errors are in parentheses, clustered at the firm-industry level.
** p < .01.

B2.

Robustness of Industry Add Regressions to the Inclusion of Factors

Tables B4 and B5 include analogous measures of factor similarity (capital andlabor) in the reduced form, showing similar results.

TABLE B4
Industry Entry Correlations, with Primary Factors
Dependent Variable: Addjkt

InputSimilarity0jk

InputSimilarityKL0jk

(1)

(2)

(3)

(4)

(5)

(6)

.0543**(.0006).0543**(.0006).0032**(.0002)
Yes.0530**(.0006).0529**(.0006).0077**(.0003)Yes
Yes.0377**(.0009).0376**(.0009).0045**(.0003)
Yes

Yes
Yes
Yes
Firm  year FE ajt
Yes
Industry  year FE akt
Yes
Yesk  k0  t FE akk t
R2
.0088
.0088
.0109
.0110
.0572
.0572
Observations
46,387,505 46,387,505 46,387,505 46,387,505 46,360,567 46,360,567
0Note.—Standard errors are in parentheses, clustered at the firm-industry level. FE 5
fixed effects.
** p < .01.

comparative advantage of ﬁrms

3077

TABLE B5
Industry Entry, with Primary Factors
Dependent Variable: Addjkt

InputSimilarity0jk

InputSimilarityKL0jk
InputSimilarity-Dereservation0jkt

(1)

(2)

(3)

(4)

.0525**(.0006).00324**(.0002).0713**(.0043).0511**(.0006).00768**(.0003).0705**(.0042).0365**(.0009).0045**(.0003).0339**(.0040)

Yes

Yes
Yes

Yes

.0357**(.0009).0045**(.0003).0325**(.0040)2.0997**(.0143)Yes.0089
46,387,505.0111
46,387,505

Yes
.0573
46,360,567

Yes
.0573
46,360,567

InputSimilarity-Tariff 0jkt
Firm  year fixed effects ajt
Industry  year fixed effects aktk  k0  t fixed effects akk t
R2
Observations
0

Note.—Standard errors are in parentheses, clustered at the firm-industry level.
** p < .01.

B3.

Robustness of Industry Add Regressions to Logit

Table B6 shows the results of the logit estimation of the industry addition regressions, corresponding to the baseline specifications of table 4.

0
jkt

Logit (ML)52,691,029

Yes

6.665**(.031)(1)

Yes
Logit (ML)52,691,029

Yes
Logit (ML)52,691,029

6.585**(.032)
2.134**(.172)(3)Yes

5.209**(.070)(2)

Logit (ML)52,691,029

Yes
Yes

8.204**(.047)
2.448**(.198)(4)

Yes
Logit (ML)52,691,029

Yes

5.136**(.071)
1.455**(.247)(5)Note.—Standard errors are in parentheses, clustered at the firm-industry level. FE 5 fixed effects; ML 5 maximum likelihood.
* p < .05.
** p < .01.

0Plant  year FE ajt
Industry  year FE aktk  k0  t FE akk t
Estimator
Observations

InputSimilarity-Tariff 0jkt

InputSimilarity-Dereservation

InputSimilarity0jk

Dependent Variable: Addjkt

TABLE B6
Revealed Comparative Advantage: Robustness

Yes
Logit (ML)52,691,029

5.095**(.072)
1.388**(.247)
23.731*(.899)
Yes(6)

comparative advantage of ﬁrms
B4.

3079

Robustness of Unit Value Regressions

Table B7 shows results of a regression of log unit values of domestically sourced
intermediate inputs (by 5-digit input category i) on a dummy that takes the value 1
when input i used to be reserved and has been dereserved in the current or a past
year. The regressions include either input i fixed effects or firm-input fixed effects
and therefore show the impact that the dereservation had on average prices paid
on i. The ASI unit value data are noisy, and we correct for known problems. One
particular problem is that from 2005 onward, the magnitudes of reported quantities (and therefore unit values) jump inexplicably by a factor of 100 or 1,000
within firm-input observations. In columns 3 and 4 of table B7, we report results
for a sample of “safe” observations where we are pretty sure that this problem is
not present to begin with (more precisely, all observations that are within a factorof 90 of the median of the pre-2005 distribution of unit values for that productcode).
TABLE B7
Domestic Input Unit Values after Dereservation: Robustness
Dependent Variable: log pjitt ≥ year i was dereserved
SampleYear FE
Input product fixed effects
Firm  input product fixed effects
R2
Observations

(1)

(2)

(3)

(4)

2.0696**(.012)All
Yes
Yes

2.0617**(.013)
AllYes

2.0450**(.012)
Safe
Yes
Yes

2.0654**(.014)
Safe
Yes

.864
900,003

Yes.966
481,036.882
761,703Yes.969
418,361

Note.—Standard errors are in parentheses, clustered at the firm-industry level.
** p < .01.

B5.

Diversification Discount: Robustness

The dependent variable in the following tables is log average sales of the firmin the industry it entered over a 3-year or a 5-year horizon, where the average
is taken across all years where we observe the firm. Table B8 includes fixed effects
for the firms’ industry  year, so we are comparing entries of firms from the same
industry into different industries. We find that entry into industries with moresimilar input mixes is associated with higher sales performance. Table B9 also includes industry-year fixed effects and finds similar results. Finally, table B10 performs a stringent exercise by comparing firms that are both in the same industry
and are entering the same industry. Estimates for unweighted input similarity arecloser to zero than in the tables before, but policy-weighted input similarity is stillof a similar magnitude and statistically significant. At least for dereservationinduced entry, input similarity is positively associated with postentry performance.

3080

0

Yes
.159
55,296

Yes.159
55,296.7614**(.0841)1.8308**(.3298)220.0752**(1.3439)
Yes.164
55,296

(3)

Yes
.166
55,2961.1604**(.0831)

Yes.167
55,2961.0839**(.0836)2.2253**(.3341)(5).9493**(.0849)1.8558**(.3281)220.1344**(1.3607)Yes.172
55,296(6)(4).8957**(.0827)2.1992**(.3333)(2)(1).9713**(.0822)Note.—Dependent variable is the log average sales by firm j in industry k between t 1 1 and t 1 h for h 5 3 or 5 years. Years where the firm is notsurveyed are excluded in the calculation of the average. Standard errors are in parentheses, clustered at the firm-industry level. FE 5 fixed effects.
** p < .01.

Firm industry  year FE ak t
R2
Observations

InputSimilarity-Tariff 0jkt

InputSimilarity-Dereservation0jkt

InputSimilarity0jk

Dependent Variable: logðAvg Salest,jk ::: ,t15 Þ

Dependent Variable: logðAvg Salest,jk ::: ,t13 Þ

TABLE B8
Postentry Growth: Within Continuing Industries

3081

0

0
jkt

Yes
Yes
.259
55,1631.2924**(.0879)

Yes
Yes
.260
55,1631.2304**(.0885)1.5378**(.3355)1.0765**(.0895)1.2308**(.3301)
219.6582**(1.2664)
Yes
Yes
.264
55,163

(3)

Yes
Yes
.266
55,1631.4854**(.0890)

Yes
Yes
.267
55,1631.4227**(.0896)1.5566**(.3391)(5)

1.2684**(.0905)1.2490**(.3317)219.7009**(1.2797)
Yes
Yes
.271
55,163

(6)

(4)

(2)

(1)

Note.—Dependent variable is the log average sales by firm j in industry k between t 1 1 and t 1 h for h 5 3 or 5 years. Years where the firm is notsurveyed are excluded in the calculation of the average. Standard errors are in parentheses, clustered at the firm-industry level. FE 5 fixed effects.
** p < .01.

Industry k  year FE akt
Firm industry k0  year FE ak t
R2
Observations

InputSimilarity-Tariff 0jkt

InputSimilarity-Dereservation

InputSimilarity0jk

Dependent Variable: logðAvg Salesjkt, ::: ,t15 Þ

Dependent Variable: logðAvg Salest,jk ::: ,t13 Þ

TABLE B9
Postentry Growth: Within Continuing and Entering Industries

Yes
.445
39,695Yes.445
39,695(2).1549(.1241)1.6002**(.3937)(1).21851(.1230)(3).0125(.1261)1.4386**(.3868)217.4555**(1.4814)Yes.448
39,695Yes.450
39,695.3344**(.1253)

(4)

Yes
.450
39,695.2734*(.1264)
1.5331**(.3947)(5).1317(.1282)
1.3723**(.3877)217.3741**(1.4820)
Yes.453
39,695(6)

Dependent Variable: logðAvg Salest,jk ::: ,t15 ÞNote.—Dependent variable is the log average sales by firm j in industry k between t 1 1 and t 1 h for h 5 3 or 5 years. Years where the firm is notsurveyed are excluded in the calculation of the average. Standard errors are in parentheses, clustered at the firm-industry level. FE 5 fixed effects.
1
p < .10.
* p < .05.
** p < .01.

0k  k0  t FE akk t
R2
Observations

InputSimilarity-Tariff 0jkt

InputSimilarity-Dereservation0jkt

InputSimilarity0jk

Dependent Variable: logðAvg Salest,jk ::: ,t13 Þ

TABLE B10
Postentry Growth: Within-Industry Pairs

comparative advantage of ﬁrms

3083

Appendix C
Data
C1. Data Sources
1. Manufacturing Plant Data
Our manufacturing plant data come from the “detailed unit-level data with factory identifier” of the Indian ASI for the years 2000–2001 to 2009–10. The data
can be obtained by writing to ASI Processing and Report (Deputy Director General, CSO (IS Wing) 1, Council House Street, Kolkata; email: asidata.cc-mospi@
gov.in).
2. Tariff Data
The Indian import tariff data come from UNCTAD-TRAINS (United Nations
Conference on Trade and Development–Trade Analysis and Information System,
accessed through WITS [World Integrated Trade Solution]; http://wits.worldbank.org/).
3. Dereservation Data
Notices of dereservation of products are from the website of the Development
Commissioner, Ministry of Micro, Small, and Medium Enterprises. (http://
www.dcmsme.gov.in/publications/reserveditems/resvex.htm). We manually concord the product codes to 5-digit ASIC codes on the basis of the text descriptionof the dereserved items.
C2. Variable Definitions• Add dummies Addjkt: equal 1 if and only if j does not produce any productin 3-digit industry k at time t and does produce a product in k at time t 1 1.
We exclude outputs with zero or missing sales from the set of produced
products.
• Drop dummies Dropjkt: equal 1 if and only if j does produce a product in
3-digit industry k at time t and does not produce any product in k at timet 1 1. We exclude outputs with zero or missing sales from the set of produced products.
• Salesjkt: j’s total sales of products in 3-digit industry k at time t, including
exports.
• Plant expenditure shares vijt: expenditure on intermediate inputs in 3-digit
category i by j at time t, divided by total expenditure on individually listed
intermediate inputs of j at time t. These listed intermediate inputs include
all agricultural, mining, and manufacturing products that are being consumed in the production process (including imports) during the current
period and exclude energy and services inputs.

3084

journal of political economy• Aggregate expenditure shares vik : sum of expenditures of single-industry
plants that produce only products in 3-digit industry k on intermediate inputs from 3-digit category i, divided by total expenditure of these plants on
individually listed intermediate inputs (including imports).
• Plant sales shares jkjt, xjkt: plant j’s total gross sales revenue of products in 3-digit
category k divided by j ’s gross sales of individually listed physical outputs(which excludes revenue from services, renting out capital, interest, etc.),
both at time t, including exports.
• Aggregate sales shares jik , x
ik : total gross sales in 3-digit category i of plantsthat derive the highest fraction of their revenue from sales of products in 3-digit
category k, divided by total gross sales of individually listed physical outputs ofthese plants, including exports.
• Dereservation dummies dijt and Bijt: equal 1 if and only if there is a 5-digit input
in the 3-digit basket i that has been dereserved during or before t and shows
up at some point in j’s basket of intermediate inputs. In section IV, the reservation dummy Bijt equals 1 when there is 5-digit product in the 3-digit basket ithat the firm is using at some point and that is reserved at time t.
• Tariff change Δtijt: difference between year t Indian import tariff and year
2000 tariff on 5-digit products in 3-digit category i, weighted by j’s average
expenditure share on 5-digit imports in i. We concord tariffs from the 6-digit
Harmonized System (HS) codes reported by TRAINS to ASIC codes via the
ASIC 2009/10–NPCMS (National Product Classification for Manufacturing
Sector) concordance published by MOSPI, and the CPC (Central Product
Classification)–HS concordance published by UNStats (United Nations Statistics Division; the first five digits of NPCMS are CPC v2.0 codes). Tariffs are
effective applied tariffs where available and most-favored-nation tariffs otherwise. We focus on nonagricultural tariffs to avoid endogeneity concernswith agricultural tariffs, which often vary as a result of policy responses to domestic economic conditions that can affect firm sales directly. In section IV,
tijt is defined analogously as the level of that tariff.
• Input similarity: InputSimilarity tjk ; oNi51 vijt vik , where N is the number of 3-digit
industries.
• Output similarity: OutputSimilaritytjk ; oNi51 jijt jik .
• Input similarity weighted by policy changes:
N

InputSimilarity-Dereservationtjk ; odijt vijt vik ,i51
N

InputSimilarity-Tariff tjk ; oΔtijt vijt vik :i51• Output similarity weighted by a policy change:
N

OutputSimilarity-Dereservationtjk ; odijt jijt jik ,i51
N

OutputSimilarity-Tariff tjk ; oΔtijt jijt jik :i51

comparative advantage of ﬁrms

3085

• Upstream and downstream:
N

Upstreamtjk 5 ojijt vki ,i51

N

Downstreamtjk 5 ojjit vki :i51

C3. Sample Definition
Our sample consists of all plant-year observations between 2000–2001 and 2009–
10 that report being in operation and that report both physical intermediate inputs and outputs.
Appendix D
TheoryD1. Firm Input Choice
1. Proof of Proposition 1
Final-goods firms purchase from the lowest-price supplier. If b1 and b2 are the lowest and second-lowest supplier-cost draws, then the price siit charged to firms will
be either the monopolistically competitive markup over b1 or the limit price b2,
implying siit 5 minfjb1 =ðj 2 1Þ, b2 g. Letting G denote the cdf (cumulative distribution function) of supplier cost draws and suppressing i, j, and t subscripts, ageneral positive moment of Sijta is3086

journal of political economy

E½S  5 E½S jjb1 =ðj 2 1Þ ≤ b2  1 E½S jjb1 =ðj 2 1Þ > b2 ðð∞2lðN 22Þ lðN 22Þa ∞j
N ! b2smb1
dG ðb2 Þ dG ðb1 Þ
5
j
c
j21
ð
N
2
2
Þ!
j21b
ð ∞ ð j21j b
2lðN 22Þ lðN 22Þ
N ! b2sm
1dG ðb2 Þ dG ðb1 Þb2ac b
ðN 2 2Þ!
ð  2l21 ð∞2lðN 22Þ lðN 22Þ
a ∞
j
lb2
N ! b2sm
b1
db2 dG ðb1 Þ
5
2l
j
c
j21
ð
N
2
2
Þ!
s
b
m
j21
ð ∞ ð j21j b  2l21 2lðN 22Þ lðN 22Þ
lb2
N ! b2sm
1
db2 dG ðb1 Þ
b2a
2l
c b
ðN 2 2Þ!
smðð∞2lðN 21Þ21 lðN 21Þ
a ∞j
N ! lb2sm
b1
db2 dG ðb1 Þ
5
j
c
j21
ð
N
2
2
Þ!
b
j21
ð ∞ ð j21j b
a2lðN 21Þ21 lðN 21Þ
N ! lb2sm
1
db2 dG ðb1 Þc b
ðN 2 2Þ!
ð∞
a2lðN 21Þja2lðN 21Þ21
5 NsmlðN 21Þ
b1
dG ðb1 Þcj21ð∞a2lðN 21ÞlðN 2 1Þja2lðN 21Þ21
12
dG ðb1 Þb1
1 NsmlðN 21Þ
clðN 2 1Þ 2 a
j21


ð∞
a2lðN 21Þ
a2lðN 21ÞjlðN 2 1Þjb1a2lN 21 db1
12
1
5 lNsmlNcj21
lðN 2 1Þ 2 aj21a2lðN 21Þ
a2lðN 21ÞlN
jl ð N 2 1Þjc a2lNsmlN
12
51
lN 2 aj21l ð N 2 1Þ 2 aj212lðN 21Þ1alN
ajsmlN c 2lN 1a 1 2
125,
lN 2 alðN 2 1Þ 2 a
j21
a

a

a

1

1

1

1

1

1

1

1

1

which gives the expression above for a 5 1 2 j. The Cobb-Douglas cost index
is straightforward. QED
2. Proof of Proposition 2
What we want is the index that converts supplier revenues to profits under limit
pricing. Intuitively, supplier revenues convert to profits at a rate of price minus
cost over price, which is 1/j under monopolistic pricing, and when the lowestcost supplier has marginal cost b1 and must undercut the second-lowest-cost producer at marginal cost b2, this becomes ðb2 2 b1 Þ=b2 . The aggregate Lerner index
under monopolistic pricing for a firm with capability c jit , letting G denote the cdf
of supplier cost draws, is therefore
ð∞ ð∞
c jit



1 lsml Nit ! b22lðN 22Þ smlðN 22Þ
db2 dG ðb1 Þ
l11
j
c
j b2
ðNit 2 2Þ!
j21b

ð∞
2lðN 21Þ lðN 21Þ 2lðN 21Þ N ! b
1
j
sm
lsml
it
1
db1
5
c j j 2 1ðNit 2 1Þ!
b1l11

1 Nit ! b22lðN 22Þ smlðN 22Þ
dG ðb2 Þ dG ðb1 Þ 5jjðNit 2 2Þ!
b
j21
it

1

it

ð∞ ð∞
jit

it

it

1

it

it

jit

2lðN 21Þ
1
j
c 2lN
5
smlN :
jit
j j21
it

it

it

it

comparative advantage of ﬁrms

3087
2lðNit 21Þ

The probability of limit pricing is therefore PrðLPÞ 5 f1 2 ½j=ðj21Þg
c 2lN
smlN , while the probability of not producing (with a Lerner index of zero) isjitsmlN . The aggregate Lerner index under limit pricing is
1 2 c 2lN
jit
it

it

it

it

ð ∞ ð ½j=ðj21Þb2lðN 22Þ lðN 22Þ
Nit ! b2smb1
b221
dG ðb2 ÞdG ðb1 ÞcðNb
it 2 2Þ!
ð ∞ ð j21j b
2lðN 21Þ22 lðN 21Þ
lNit ! b2sm
db2 dG ðb1 Þ
5 PrðLPÞ 2 b1cðNit 2 2Þ!
b




ð∞
2lðN 21Þ21 lðN 21Þ
lNit ! b1sm
j 2 1 lðN 21Þ11 lb12l21db1
125 PrðLPÞ 2 b1cjðlðNit 2 1Þ 1 1ÞðNit 2 2Þ!
sm2l


ð∞
l2 Nit ! b12lN 21 smlN
j 2 1 lðN 21Þ11db1
5 PrðLPÞ 212
c ðlðNit 2 1Þ 1 1ÞðNit 2 2Þ!
j1
j 2 1 lðN 21Þ11 2lN lN
c jit sm :512lðNit 2 1Þ 1 1
jit1PrðLPÞ 2

jit

it

1

it

1

jit

it

1

it

it

it

jit

it

it

it

it

it

Adding these indexes conditional on monopolistic limit pricing and not producing gives the expression above.
We define Λ ; lðN 2 1Þ 1 1 ≥ 1 2 l > 0 and suppress the i and t subscripts
for brevity. The percentage change in the expected Lerner index with entry is
h
 
 Λ
 Λ i
1 j21 Λ21jj
l ln j21
1 Λ1 j21l ln j21
2 Λl2 1 2 j21
jj
d lnL 2 j j
h
5
:
 
j21Λ i
1 j21 Λ21
1
dN
1 12
j

j

Λ

j

The first three terms correspond to how the expected Lerner index falls,
d ln L=dN < 0, as the probability of monopoly pricing decreases (which is the highest possible markup), and while the probability of limit pricing increases, the expected Bertrand markup decreases as well. The numerator of d ln L=dN can be
written



h
2Λ
Λi 1
j
1
1
j
j
l
2
ln
1 12
2 :
j21
Λ j21
j21
j21
Λ
The first term is weakly negative for Λ ≥ j 2 1, which holds for N ≥ 1 1 ðj 2 2Þ=l; the second term is negative. The upper bound for L comes from evaluation at
N 5 1 1 ðj 2 2Þ=l. QED
3. Proof of Proposition 3
 ;We define Λ ; lðN 2 1Þ 1 1 and suppress the i and t subscripts. For RlNcoj ok rvk Rjk ðsm = j Þ =N , noting pjk 5 ð1 2 rÞRjk and holding capabilities fixed, we
have that3088

journal of political economy
c lN =dNd ln R1
j ok vk  dpjk sm = j
o
5
2

lN

dN
N
c
oj ok vk pjk sm = jc lN  dpjk =dNjk vk sm = j
5 oo



c lN
j
k vk pjk sm = joov p  d s =c
=dN
1
o
o
1
2 :


v p s =c
N
oo
lN

j

k k

jk

m

j

k k

j

lN

jk

m

j

Now considering the individual profit terms, holding capabilities fixed, these
may increase profits through increased downstream demand in response to lower
costs. Note that
d lnpjk 
r d ln cjkt 52
1 2 r dN c fixeddN c fixed
jt

jt

5

vik d lnðΩit ϑit =½Ωit 1 ðj 2 1ÞÞr
1 2 rodNj21iFor Ωit 5 lNit and Φit ; lðNit 2 1Þ 1 j 2 1, ϑit 5 1 2 ½ðj 2 1Þ=Φit f1 2½ðj 2 1Þ=jΦ g. Consider that after some rearrangement,hj21Φ i j21 j21Φlðj21Þ  11jlΩit ϑit1l ln j21
2 Φ1l
1
2
2 Φ
d ln Ωit 1
Φ1l
Φ
j
j
Φ
1
ðj21Þ
h
i
5 1
,
 Φ
N
dN
1 2 j21 1 2 j21
it

Φ

j

since lðN 2 1Þ 1 j 2 1 > 0 is assumed and implies that ½ðj 2 1Þ=jlðN 21Þ1j21 < 1,which impliesd ln pjk 
dN c

jt

8
9

 ðj21Þ hj21Φ i
 Φ
Φ
j
Φ =
ln j212 Φ1l
2 ðj 2 1Þ j21
jr
1 <1
l 1 1 Φ1l Φ 1 2 j
h
i
:
5
1
 Φ
;
1 2 r j 2 1 :NΦ
fixed
1 2 j21 1 2 j21
ΦjReturning to the sum of profits across firms and industries, we havedpjkoov dN
k

j

k

 lN
sm
cj

5 oovk pjk
j

k

8
9

 ðj21Þ hj21Φ i ΦΦjΦ = lN
ln j212 Φ1l
2 ðj 2 1Þ j21
jr
1 <1
l 1 1 Φ1l Φ 1 2 j
sm
1
 Φ
; cj
1 2 r j 2 1 :NΦ
1 2 j21 1 2 j21
8
<1



r
1
l
1
5
1 2 r j 2 1 :NΦ ðj21ÞΦ
1 1 Φ1l
Φ

h

12

Φ

j21Φ ijj21Φ

2 ðj 2 1Þ jh Φ i
1 2 j21
1
2 j21
Φ
j

We also have, from sm ≤ c j , that

h



9
j
Φ =
ln j21
2 Φ1l

v p
;oo

j

k

j

i

lN

o o v p d s =c  =dN
W ðN Þ ;o o v p s =cv p s =c
lln s =c
o
o
5
≤ 0:


o o v p s =c
j

k k

jk

j

k k

k k

jk

m

j

lN

jk

m

j

lN

j

m

j

m

lN

j

k k

jk

m

j

j

k

jk

 lN
sm
:
cj

comparative advantage of ﬁrms

3089

So we can conclude, using W ðN Þ  N ≤ 0 and the arguments above, that89
 ðj21Þ hj21Φ i
 Φ
Φ
j
Φ =
2 ðj 2 1Þ j21
ln j212 Φ1l
jd ln Rr
1 <lN 1 1 Φ1l Φ 1 2 j
h
2 1:
≤
11
 Φ i;d lnN
1 2 rj 2 1:Φ
1 2 j21 1 2 j21
Φj

In what follows, the denominator 1 2 ½ðj 2 1Þ=Φf1 2 ½ðj 2 1Þ=jΦ g is positive
so long as N ≥ 1, which is assumed. From the above equation, then, it follows that
lim

N →∞


d ln R
r 12l
r 1 1 2 j 1 jr 2 r
1 2 jð1 2 rÞ
≤
21<
5
:
d lnN
12rj 21
ð1 2 rÞðj 2 1Þ
ð1 2 rÞðj 2 1Þ

Clearly, then, jð1 2 rÞ ≥ 1 is sufficient for average weighted revenues to be decreasing and approach zero as N → ∞ because l > 0. QED
4. Proof of Proposition 4
We define Λ ; lðN 2 1Þ 1 1 and suppress the i and t subscripts for brevity. Taking logs and differentiating E½z i  with respect to N, holding input capabilities
fixed and noting that pjk 5 ð1 2 rÞRjk , we see thatlN
d lnE½z i  d lnL oj ok vk  dpjk sm =c j =dN
1
5
1
2 :

lN

dN
dN
N
c
p
s
=
v
k
jk
m
j
j
k

oo

Also, direct inspection shows thath
 j 2Λ nN j Λ i N o
N
j
ln
l
2
1
1
2
j21
Λ
j21
j21
j21
d lnL
Λ2
h
i
lim
5 lim




Λ21
l
ð
N
21
Þ11
N → ∞ d lnN
N →∞
1 j21
1 Λ1 1 2 j21jjj
5 l lnjðN =ΛÞ 2 ½N =ðj 2 1Þ
 lim
5 2∞,
j 2 1 N →∞1=ðj 2 1Þ

so from the proof of proposition 3, we have
lim

N →∞

d lnE½z i 
d lnL
r 12l
< lim
1
2 1 5 2∞,N → ∞ d lnN
dN
12rj 21

which implies limN → ∞ E½z i  5 0. We also have, from the proof of proposition 3,
thatd ln E½z i  d ln L<dNd ln N89 ðj21Þ hj21Φ i
 Φ
Φ
j
Φ =
ln j212 Φ1l
2 ðj 2 1Þ j21
jr
1 <lN 1 1 Φ1l Φ 1 2 j
h
11
2 1:
1
 Φ i;1 2 rj 2 1:Φ
1 2 j21 1 2 j21ΦjSince, from proposition 2, d lnL=d ln N < 0 for N > maxf1 1 ðj 2 2Þ=l, 1g, asufficient condition on demand for expected profits to be decreasing in entry
holding capabilities fixed is therefore ðj21Þ hj21Φ iΦjjΦ
2 ðj 2 1Þ ln j21
2 Φ1l
ð1 2 rÞðj 2 1ÞlN 1 1 Φ1l 1 Φ ln j21 Φ 1 2 jhi; B ðN Þ:
>11


Φ
r
Φ
1 2 j21 1 2 j21
Φ

j

(D1)
ðD1Þ

3090

journal of political economy

Dropping the lnðj=ðj 2 1ÞÞ terms in equation (D1) that are in sum negative andusing lN < Φ from l < j 2 1 impliesh Φ i j21 h Φ i j21 h Φ ilN
1 2 j21
1 2 j211 Φ 1 2 j21
1 Φ1l 1 2 j21
2 Φ1l
Φ
j
j
j
h
i
B ðN Þ <Φ
1 2 j21
1 2 j21
Φ
j
 
 Φ
j21
j21
j21 j21 Φ
2 2 j21Φ1l 1 Φ1lh 2 Φ1lj i
h j   io5
j21Φ 5 Φ1l n
Φj21
1 2 j2112
1
2
1 2 j21
Φ
j
j21
Φ
j
 Φ
2 2 j2122j 5 lN:5hj21Φ i < Φ1l 
l
l
Φ1l
l
2 11
12
j21 2 1 1 Φ
j21 2 lðN 21Þ1j21
j21

Φ

j

This last equation is decreasing in N where the denominator is positive, whichhappens for N > 1 as assumed, and the minimum value N can take, by assumption, is 1 1 ðj 2 2Þ=l. Substituting this into the last term, we have2
½ðl 1 j 2 2Þ=ðj 2 1Þ 2 ½l=ðj 2 2 1 j 2 1Þ
2
j21
≤
52
,
½ðl 1 j 2 2Þ=ðj 2 1Þ 2 ½l=ðj 2 1Þ
j22
where the inequality follows from j 1 2, which follows from the assumption that
(1 2 r)j ≥ 2. Therefore, 2ðj 2 1Þ=ðj 2 2Þ is an upper bound for B(N) for N ≥ 1 1
ðj 2 2Þ=l. We can conclude that ð1 2 rÞðj 2 1Þ=r ≥ 2½ðj 2 1Þ=ðj 2 2Þ implies
that expected profits are decreasing in entry, which holds for ð1 2 rÞj ≥ 2. QED
5. Proof of Proposition 5
Firms solve
ð∞
min
mijkt

siit miijkt dGit ðiÞ, subject to

c ijt

ð ∞
c ijt

ðj21Þ=jmiijktj=ðj21Þ
dGit ðiÞ

≥ Mijkt :A natural question is, Why not frame this as a free-end-point problem with achoice of input varieties ½c ijt , cijt ? The reason we have not is that for the case j >1, “love for variety” implies cijt 5 ∞, and for j < 1, the production function exhibits “hate for variety,” and allowing the producer to choose a subset of suppliers willcause them to snap to the lowest-cost supplier.
Cost minimization conditional on c ijt implies a first-order condition of 37
j siit 12jðj21Þ=jðj21Þ=jmiijkt5 Mijkt, wherej21 hðc
1=ð12jÞ
12jjsdGit ðs Þ:
hit 5 2
j21
∞
ijt

37
This is for j > 1. For j < 1, replace j=ðj 2 1Þ with j=ð1 2 jÞ, as the sign of the inequality constraint changes. The second-order condition holds for j > 0 (weakly at
j 5 1).

comparative advantage of ﬁrms

3091

Under these distributional assumptions, we have
hit 5

j
Ωit
smΩ c 12j2Ω
ijt
j 2 1 Ωit 1 ðj 2 1Þit

1=ð12jÞ

itunder the condition Ωit > 1 2 j, hit is finite, and the input choice is nondegenerate.38 Defining the cost index of input i as Sijt, we have minimum costs of SijtMijkt,
whereSijt 51=ð12jÞ
Ωit ϑit=ð12jÞ Ω =ð12jÞ
c 12Ω
sm
,
ijt
Ωit 1 ðj 2 1Þititand therefore
d lnSijt
Ωit511:
d ln c ijt
j21
Now the restriction Ωit > 1 2 j is especially informative, as if j > 1, thend lnSijt =d ln c ijt > 0, consistent with love for variety, and d lnSijt =d ln c ijt < 0 for j <1, consistent with hate for variety. Unit input costs cjkt conditional on capabilities
are then as above. QED
6. Proof of Proposition 6
Profit maximization can be considered in two steps, maximizing industry profits
conditional on unit costs and then maximizing joint profits by choosing capabilities. A firm will optimally choose a markup pjkt 5 cjkt =r in the first maximization
step, so the profit accruing from each industry is ½ð1=rÞ 2 1ðrDkt Þ1=ð12rÞ
:
pjkt 5 ½ð1=rÞ 2 1q c jt cjkt qjkt 5   r=ð12rÞ
q c jt cjkt

(D2)

Noting that for this particular profit form and common markups across industries, we have d lnq c jt
d lnpjktrd lncjkt52
1
12r
d ln c ijt
d ln c ijt
d ln c ijt


r
Ωit
52
ln c ijt 2 ln c i0 1 vik 1 2
,
12r
12j
it follows that the first-order condition for profit maximization
dpjt
pjkt d lnpjkt
5oc ijt d ln c ijt
d c ijt
k
52



r
pjkt
vik 1 2 Ωit
c
c
ln
2
ln
1
5 0:
ijt
i0
c ijt
1 2 ro
12j
k

(D3)

38
Otherwise, for j < 1 it is optimal to use all of the cheapest input, and for j > 1, input
vectors of the type ks 12j all satisfy the production constraint, so as k → 0, costs go to zero.

3092

journal of political economy

Using the fact that rpjkt =ð1 2 rÞ 5 qðc jt Þcjkt qjkt , equation (D3) implies that for firminput expenditure shares of vijt, the optimal capability choice satisfiesΩitvijt :
ln c ijt 5 ln c i0 2 1 1
j21
Substitution into equation (D2) and further expansion shows that revenues Rjkt
take the above form. QED
D2. Extensive Product Margin
Equation (9) can be modified to consider the extensive product margin choiceof firms. Assume that firms face a fixed cost ð1 2 rÞfkt to produce in an industry keach period and so produce when profits pjkt 5 ð1 2 rÞRjkt > ð1 2 rÞfkt . Fromequation (8), with identical coefficients and fixed effects similar to equation (9)and error terms with 2εjkt logistic, a firm j operates in industry k when the following equation is positive:
ln


2


2
Rjkt
5 kkt 1 kjk 2 k0 o vijt 2 vik 1 k1 o aB Bijt 1 at Δtijt vijt 2 vik 1 εjkt ,
fkt
i
i

(D4)

Equation (D4) can be estimated to recover the tariff equivalent of dereservationon the extensive margin of industry adoption.
D3. Input Similarity Equation: Proof of Proposition 7
Let {Dkt} be demand shifters in period t. Let Cjk 5 cjk q jk be the variable costs forfirm j in producing in industry k and Cj 5 ok Cjk total variable costs, so thatvik Cjk
vik Dkt1=ð12rÞ cjkt2r=ð12rÞ
vijt 5 oK
5 oK 1=ð12rÞ 2r=ð12rÞ :CjoK Dkt cjkt

(D5)

Holding c ijt fixed, for xjkt ; Cjk =Cj , the cost share of industry k for firm j (equal torevenue shares), it is the case that
 

dvijt
1
1 Cjk xjkt vik 2 vijt
vik Cjk
5
5 2
Cj 2
C
:
v
ik
jk
o
1 2 r Dkt kdDkt
1 2 r Dkt
Cj 1 2 r Dkt
It follows from the mean-value theorem that for some {djk} with each djk ∈½Dkt21 , Dkt , cost shares x*jk , and expenditure shares v*ij evaluated at {djk},

 

2
2

 * 

vik vijt 2 vijt 2 vik vijt21 2 vijt21 5
vik 2 v*ijt xjk vik 2 v*ijt Dkt 2 Dkt21 :
oi
o
2
2
12r
djk
i
Redefining djk 5 Dkt21 as common across firms yields the (feasible) approximation




2
2

2 xjkt21 Dkt 2 Dkt21
vik vijt 2 vijt ≈vik vijt21 2 vijt21 1oioioi vik 2 vijt21 1 2 r Dkt21 :22Adding v2ik and rearranging gives the result. QEDcomparative advantage of ﬁrms

3093

D4. Extensions to Primary Factors
The model can be extended on the production side to include factor services
that are not directly consumed, in particular factors such as capital, different
types of labor, and other firm balance sheet items. In this extension, to produce
a quantity qjkt in industry k at time t, firm j combines inputs from industry i, Mijkt,
and factor services from factor f, Ffjkt, using a constant-return-to-scale Cobb-Douglas
technology with industry input expenditure shares vik , vfk and idiosyncratic industry
productivity labeled Jjk. At input prices Sijtwit and factor service prices Wfjtwft, the unit
cost of firm j to produce in industry k at time t is therefore
YSijt wit v YWfjt wft v
cjkt ;
:vik Jjk
vfk Jjk
ik

fk

i

f

Thus, cjkt is a vector of unit costs that are influenced by input prices and industry
productivities. Industry-level inputs Mijk and F are again composite quantities ofvarieties through a CES aggregator with elasticity of substitution j for inputs
and jf for factor services where varieties follow a Pareto distribution, with Prðsiit ≥sÞ 5 ðs=sm Þ2Ω for inputs and Prðwift ≥ wÞ 5 ðw=wm Þ2Ω for factors with Ωft 5 lNft ,and Nft is the mass of suppliers as modeled above but for factor services. Firms
have capabilities of using inputs with prices ½c ijt , ∞Þ for inputs and ½c fjt , ∞Þ for factors, where c ijt and c fjt are chosen by the firm. The analogous version of proposition 1 goes through with corresponding and symmetric terms for factors. Lettingc jt denote the vector of acquired capabilities, the unit costs of a multiproduct firm
are given by qðc jt Þcjkt in each industry and are assumed to follow
( 


)
c 2 oi ln c ijt 2 
i ln ijtoq c jt ; exp
1
:
2
2
it

ft

A firm can use its acquired capabilities across any number of products andreoptimizes by choosing capabilities each period.
In period t, firms pay a fixed cost of fkt to operate in industry k and face inverse
demand in industry k of 
pjkt q jkt 5 Dkt qjktr21 ,as above. A firm’s profit-maximizing capability and production choices considering product markets jointly are analogous to proposition 6. In particular, forΘit ; 1 1 Ωit =ðj 2 1Þ and Θft ; 1 1 Ωft =ðjf 2 1Þ, firm revenues are given byln Rjkt 5r
1=ð12rÞ
ln Jjk 1 ln rr=ð12rÞ Dkt
12r|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}|ﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄ}
demand ðkt Þ
RCA ð jk Þ2
1=ð12jÞ sm12Θ
1=ð12j Þ wm12Θ
r
r
ð12jÞ
vik lnwit ϑ1=
vfk ln wft ϑft1=ð12jÞ 1 2 Θ21
1 2 Θ21
2
it
ft
ft
o
o

vfk
12r i
12r f
vik
|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} |ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}
ft

it

f

input supplier ðkt Þ

"

1

#

"

factor supplier ðkt Þ

#




2
vik 2 1 Θ2ft vfjt 2 vfk 2 ,
Θ
v
2
it
ijt
o
o

r
r
Θ2it v2ik 1 oΘ2ft v2fk 2
2ð1 2 rÞ o2ð1 2 rÞ ii
ff
|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} |ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}
supplier-tech ðkt Þcore competency ð jkt Þ|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}
comparative advantage ð jkt Þ3094

journal of political economy

where ϑft ; 1 1 fðj 2 1Þ=½lðNft 2 1Þ 1 j 2 1gf1 2 ½ðj 2 1Þ=jlðN 21Þ1j21 g. Line and Ωf 0 5 Ω f and letarizing Ωit and Ωft around the initial policy states Ωi0 5 Ωting kx represent a fixed effect for characteristic x yields equation (15). The IV
estimator is analogous to the one above; for ~vfjkt ; ðvfjt vfk 2 v2fjt =2Þ and x~fjkt ;
xjkt ðvfjt vfk 2 v2fjt =2Þ, we defineft

IjktM ðl, gÞ ; lo~vijkt21 2 gox~ijkt21 ,ii

IjktF ðl, gÞ ; lo~vfjkt21 2 gox~fjkt21 ,ff~ijkt21 , I ðl, gÞ ; lotijt ~vijkt21 2 gotijt x
I ðl, gÞ ; loBijt ~vijkt21 2 goBijt x~ijkt21 :
B
jkt

t
jkt

i

i

i

i

The resulting first-stage equations for our estimator are as follows for z ij ;ðlij , gij Þ:39
 11 
 12 
 13 
 14 
M
F
B
t
M
o~vijkt 5 kkt 1 kjk 1 Ijkt z 1 Ijkt z 1 Ijkt z 1 Ijkt z 1 hjkt , (D6)
i

o~v

fjkt

 
5 kkt 1 kjk 1 IjktM z 21 1 IjktF ðz 22 Þ 1 IjktB ðz 23 Þ 1 Ijktt ðz 24 Þ 1 hLjkt ,

(D7)

 
5 kkt 1 kjk 1 IjktM z 31 1 IjktF ðz 32 Þ 1 IjktB ðz 33 Þ 1 Ijktt ðz 34 Þ 1 hBjkt ,

(D8)

 
5 kkt 1 kjk 1 IjktM z 41 1 IjktF ðz 42 Þ 1 IjktB ðz 43 Þ 1 Ijktt ðz 44 Þ 1 htjkt :

(D9)

f

oB ~v

ijt ijkti

ot ~v

ijt ijktiWith our base and extended models in hand, along with an IV strategy, we next
turn to our estimate results and counterfactuals regarding the comparative advantage of firms.
Appendix E
Average Firm-Level Comparative Advantage, by Industry
Table E1 shows the average comparative advantage of single-industry firms in industry k0 , for the industry in which they enjoy the highest average CAjkt.

39
In practice, sales within a firm-industry group are unlikely to be a balanced panel, as
the extensive margin of a firm’s industries is liable to change (we in fact model and estimate this with a logit model). Consequently, our one-period-lag strategy may lose some observations, but it reduces the number of parameters that must be estimated simultaneously.

TABLE E1
Comparative Advantage of Single-Industry Firms, by Industry

Industry k

0Dairy products
Other jute and natural fiber
goods, n.e.c.
Fabrics and cloth of jute, coir,sisal, hemp, mista, etc.
Fibre of jute, coir, and other plants
Cereals (incl. rice) and pulses,
unmilled
Products of milling industries; malt
and malted milk
Ginned cotton, cotton, and raw
cotton waste
Cotton yarn and fibre, including
cotton thread
Vegetables oils and fats
Raw fibre of jute, coir, sisal, hemp,
mista, etc.
Aluminium and aluminium
alloys, unwrought
Leather apparel
Fruit juices and vegetable juices
and syrup, pickles
Craft paper and paperfor special use
Leather bags, cases, purses
and other novelty items
Boards, paper boards
Chocolate, cocoa and cocoa
preparations and sugar
Edible fruits and nuts; edible
vegetables and certain roots
Aluminium and aluminium
alloys worked
Paper (uncoated) used fornewsprint and for otherspecial purposes
Pig iron/ferroalloys, etc., inprimary form
Cotton apparel
Inorganic elements, excludingbase metals, rare gas
Miscellaneous leather manufactured items
Copper and copper alloy, refinedor not, unwrought

Highest–Average
Comparative Advantage
Industry (except k0 )Live animals, chiefly for foodFabrics and cloth of jute, coir, sisal,
hemp, mista, etc.
Other jute and natural fiber goods,
n.e.c.
Fabrics and cloth of jute, coir, sisal,
hemp, mista, etc.
Products of milling industries; malt
and malted milk
Cereals (incl. rice) and pulses,
unmilled
Cotton yarn and fibre, including
cotton thread
Ginned cotton, cotton, and raw
cotton waste
Diesel products and by-products
Fabrics and cloth of jute, coir, sisal,
hemp, mista, etc.
Aluminium and aluminium alloys
workedLeather bags, cases, purse and othernovelty items
Edible fruit and nuts; edible
vegetables and certain roots
Boards, paper boards

Comparative
Advantage
15.8*
13.1*
12.3*
11.71
11.6*
11.5*
10.2*
10.01
9.8
9.6
9.5*
9.2*
9.2
9.1*

Leather apparel

9.0*

Craft paper and paper for special use.
Sugar, molasses, khandsari, gur.

8.7
8.6

Fruit juices and vegetable juices &syrup, Pickles
Aluminium and aluminium alloys,
unwrought
Craft paper and paper for special
use

8.5*
8.2
8.0

Metro railways and tramways androlling stock
Fur skins and articles thereof
Charcoal

7.9*

Leather bags, cases, purses andother novelty items
Copper and copper alloys, worked

7.3

7.7
7.4

7.0*

Note.—Table shows the average comparative advantage CAjkt of single-industry plants inindustry k0 , for the industry k where CA jkt is the highest. n.e.c. 5 not elsewhere classified.
1
p < .10.
* p < .05.

3096

journal of political economy

Appendix F
Core-Competency Premia with Factor Complementarity
TABLE F1
Core-Competency Sales Premium, with Primary Factors
Number of Industries with Positive Sales
Industry Rank

1

2

3

4

5

6

7

8

9

101

1
2
3
4
5
6
7
8
9
101

.024

.030
.014

.030
.012
.010

.017
.009
.008
.007

.013
.009
.007
.007
.006

.011
.008
.007
.006
.006
.006

.010
.008
.006
.006
.006
.006
.005

.010
.008
.006
.005
.005
.006
.005
.005

.007
.006
.008
.006
.006
.006
.005
.005
.005

.011
.014
.009
.009
.005
.004
.004
.005
.005
.003

TABLE F2
Core-Competency Sales Premium, with Primary Factors—Weighted
Number of Industries with Positive Sales
Industry Rank

1

2

3

4

5

6

7

8

9

101

1
2
3
4
5
6
7
8
9
101

.029

.038
.003

.070
.007
.001

.085
.022
.003
.001

.076
.098
.004
.004
.002

.077
.198
.031
.025
.005
.002

.097
.166
.012
.010
.008
.004
.001

.168
.205
.023
.014
.006
.006
.004
.001

.299
.014
.144
.014
.011
.004
.003
.001
.003

1.102
2.214
.858
.116
.029
.007
.011
.004
.003
.001

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