JOHANNES BOEHM AND EZRA OBERFIELD
The strength of contract enforcement determines how firms source inputs andorganize production. Using microdata on Indian manufacturing plants, we showthat production and sourcing decisions appear systematically distorted in stateswith weaker enforcement. Specifically, we document that in industries that tend
to rely more heavily on relationship-specific intermediate inputs, plants in stateswith more-congested courts shift their expenditures away from intermediate inputs and have a greater vertical span of production. To quantify the effect of these
distortions on aggregate productivity, we construct a model in which plants haveseveral ways of producing, each with different bundles of inputs. Weak enforcement exacerbates a holdup problem that arises when using inputs that require customization, distorting both the intensive and extensive margins of input use. The
equilibrium organization of production and the network structure of input-output
linkages arise endogenously from the producers’ simultaneous cost-minimization
decisions. We identify the structural parameters that govern enforcement frictions
from cross-state variation in the first moments of producers’ cost shares. A set ofcounterfactuals show that enforcement frictions lower aggregate productivity to
an extent that is relevant on the macro scale. JEL Codes: E23, O11, F12.

I. INTRODUCTION
Weak contract enforcement hinders firm-to-firm trade anddistorts production decisions. For example, a manager who∗ We are grateful to Pol Antràs, several anonymous referees, David Baqaee,
Hugo Hopenhayn, Sam Kortum, Eduardo Morales, Jacopo Ponticelli, Steve Redding, Matt Rognlie, Meredith Startz, Felix Tintelnot, Gustavo Ventura, Chris
Woodruff, and various seminar participants for helpful suggestions. Anusha Guha,
Hélène Maghin, and Juan Manuel Castro provided excellent research assistance.
We are grateful to Daksh India for sharing data, and to CEPR/PEDL and theSciences Po/Princeton partnership for financial support. Boehm thanks the International Economics Section at Princeton and Oberfield thanks the Stanford
Institute for Economic Policy Research for hospitality during the later stages ofthe project. This document is an output from the research initiative “Private Enterprise Development in Low-Income Countries” (PEDL), a program funded jointly
by the Centre for Economic Policy Research (CEPR) and the Department for International Development (DFID), contract reference PEDL_LOA_4006_Boehm. The
views expressed are not necessarily those of CEPR or DFID. All mistakes are ourown.

C The Author(s) 2020. Published by Oxford University Press on behalf of the President

and Fellows of Harvard College. All rights reserved. For Permissions, please email:journals.permissions@oup.com
The Quarterly Journal of Economics (2020), 2007–2058. doi:10.1093/qje/qjaa020.
Advance Access publication on June 16, 2020.

2007

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MISALLOCATION IN THE MARKET FOR INPUTS:
ENFORCEMENT AND THE ORGANIZATIONOF PRODUCTION∗

THE QUARTERLY JOURNAL OF ECONOMICS

cannot rely on courts for timely and cheap enforcement may needto purchase low-quality substitutes from a family member, vertically integrate the production process, or switch to a different
technique that avoids the bottleneck input. Regardless of the chosen alternative, she will find herself producing at a higher cost.
Collectively, the micro distortions induced by weak enforcement
alter the equilibrium network structure of production and reduce
aggregate productivity.
This article studies theoretically and empirically how weaklegal institutions—more precisely, slow contract enforcement due
to congestion of the courts—shape the organization of production.
We develop a framework that allows us to use detailed micro
production data to quantify the impact of these frictions on
aggregate productivity.
We study contract enforcement frictions in the context of the
Indian manufacturing sector. India is a country with infamously
slow and congested courts: the World Bank (2016) currently ranks
India 172nd (out of 190) when it comes to the enforcement of contracts, behind countries such as the Democratic Republic of Congo(171st) and Zimbabwe (165th). Around 6 million of the 22 million
pending cases are older than five years, and while India’s Law
Commission has been advocating vast reforms for several decades,
these reforms have not been implemented, and pendency ratios
have not decreased. At the same time, India’s liberalization andgrowth has spurred demand for timely enforcement of contracts.
Using plant-level data from India’s Annual Survey of Industries, we document several facts about how court congestion alters
plants’ input choices. Although there is an enormous amountof heterogeneity in the input bundles plants use even within
narrowly defined (five-digit) industries,1 the bundles differ insystematic ways related to the quality of courts. To focus on thesedifferences, we differentiate inputs that are relatively homogeneous and standardized from those that require customizationor are relationship-specific, using the classification from Rauch(1999). Users (or potential users) of relationship-specific inputs
1. Some of this heterogeneity reflects different organizational and technological choices. As an example, a plant that produces frozen chicken may purchase
live chickens and slaughter and freeze them; or it may purchase chicken feed andraise, slaughter, and freeze the chicken at the same vertically integrated plant.
Other examples indicate horizontal technological choices, for example, aluminum
can be produced from bauxite or from aluminum scrap.

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2009

are most likely to benefit from better formal enforcement of
supplier contracts.
Our first fact is that in states where courts are morecongested, plants in industries that typically rely on relationshipspecific intermediate inputs have systematically lower cost sharesof intermediate inputs. Second, we show that where courts are
slower, the composition of plants’ intermediate-input bundles istilted toward homogeneous inputs. Third, we construct a measureof the vertical span of production of plants designed to capture
the number of sequential production steps performed by theplant. We show that where courts are more congested, plants
in industries that typically rely on relationship-specific inputs
tend to have larger vertical spans of production; that is, moresequential production steps are performed within plants.
We use a variety of strategies to alleviate concerns that thesepatterns arise from omitted factors or through reverse causality.
We control for a range of fixed effects and interactions with stateand industry characteristics to ensure that court congestion is notstanding in for other state characteristics. We also confirm theseresults using an instrumental variable strategy that exploits thehistorical origins and structure of the Indian judiciary. Newly created courts tend to be fast and accumulate backlogs over time. As aresult, the oldest High Courts, which were set up by the British in
the nineteenth century, are the most congested, and newer courts,
which have often been created because of new states being carved
out of existing ones, are typically faster. We therefore use the ageof the High Court as an instrument for its congestion and argue
that the nature of the political events surrounding the creationof new courts makes it less likely that the resulting congestion iscorrelated with unobserved determinants of plants’ input mixes.
We construct a model to interpret these facts and quantitatively evaluate the ramifications of these distortions for
aggregate productivity. Our model is written to speak to thepatterns of intermediate-input use among Indian manufacturing
plants. We see that plants use different mixes of intermediate
inputs to produce the same output. It is likely that much ofthis heterogeneity—reflecting different organizational forms,
technology, or variation in input prices—would arise even in
the absence of distortions. The model incorporates a rich set oforganizational, technological, and sourcing decisions so that we
do not conflate distortions with other sources of heterogeneity.

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Our model is a multi-industry general-equilibrium model ofheterogeneous firms and intermediate-input linkages that form
between them. Firms face a menu of technology/organizational
choices (recipes) and draw suppliers along with match-specificproductivities. Both primary inputs and relationship-specificinputs are subject to distortions that reflect weak contract
enforcement. Each firm chooses the production technique andsuppliers that minimize cost. The effective cost of an input depends on the match-specific productivity, the supplier’s marginal
cost, and the distortion. We model the enforcement distortionfor each potential supplier as randomly drawn to reflect the ideathat formal enforcement may only sometimes be relevant at themargin.2 Weak enforcement has a direct impact on producers who
use inputs that require contract enforcement, but may also leadfirms to switch to suppliers with a higher cost or to an entirely
different production technique with a different set of inputs. We
think of changing the organization of production to increase thevertical span as one such option.
To make quantitative statements, we structurally estimate
technological parameters and distributions of wedges that distortthe use of relationship-specific intermediate inputs. Our identification strategy rests on two key properties of our model. First, themodel has the implication that, among firms that in equilibrium
use the same production recipe, average cost shares of each
input among firms are invariant to factor prices but depend on
distortions.3 This is a weaker implication than the assumption
typically made in the misallocation literature, which is that eachplant’s cost share is invariant to factor prices (Cobb-Douglas)
and that all heterogeneity in cost shares is due to distortions.
This property allows identification of distortions from variationin average cost shares across regions. We also make the conservative assumption that weak contract enforcement does not
distort the use of homogeneous inputs. As a result, the structural
estimating equations take a simple form that is similar to the
2. For example, formal enforcement may not be necessary if the buyer andsupplier are engaged in a long-term relationship, are related, or share other social
ties.
3. As in Houthakker (1955), the aggregate production function among thosefirms is Cobb-Douglas even though there may be considerable cross-sectional dispersion in cost shares. While Houthakker (1955) assumed that individual production functions are Leontief, we show that this result extends to any constantreturns to scale production function in which inputs are complements.

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2011

motivating reduced-form regressions. The identified structuralwedges on relationship-specific intermediate inputs are therefore
correlated with the observed congestion in the regional courts, inline with the results from the reduced-form regressions.
One issue that arises is that we must separate the impact of
distortions from the possibility that plants in different states systematically use different recipes. This problem is closely related
to those studied by Bonhomme and Manresa (2015) and Moon
and Weidner (2015); we want to identify the effect of contract
distortions and recipe technologies, but we do not directly observe
which plants use which recipes. Like Bonhomme and Manresa(2015), we use an iterative procedure that alternates between (i)estimating recipe technologies and distortion parameters given
an assignment of plants to recipes, and (ii) a clustering procedurethat assigns plants to recipes given distortion parameters. Bothlarge- and small-sample Monte Carlo simulations show that, toa reasonable degree of accuracy, the procedure is able to recover
the distortion parameters.
Our results suggest that courts may be important in shaping
aggregate productivity. Having estimated the model parameters,
we conduct counterfactuals to investigate the role of contracting
frictions. For each state we ask how much aggregate productivityof the manufacturing sector would rise if court congestion werereduced to be in line with the least congested state. On average
across states, the boost to productivity is roughly 4%, and thegains for the states with the most congested courts are roughly
8%. Distortions on relationship-specific inputs are only imperfectly explained by our measured congestion, and if one were tohalve the distortions on relationship-specific inputs, the averagestate would see a 7.1% increase in productivity (up to more than
20% for the most distorted state).
Our model builds on recent models of firm linkages ingeneral equilibrium that include Oberfield (2018), Eaton,
Kortum, and Kramarz (2015), Lim (2018), Lu, Mariscal, and Mejia(2013), Chaney (2014), Acemoglu and Azar (2020), TaschereauDumouchel (2020), and Tintelnot et al. (2017),4 and uses aggregation techniques pioneered by Houthakker (1955) and Jones(2005). We model the technology choice and choice of organization
concurrently with the sourcing decision, motivated by evidence
4. These are also closely related to models of global value chains and global
sourcing such as Costinot, Vogel, and Wang (2012), Fally and Hillberry (2018),
Antràs and de Gortari (2017), and Antràs, Fort, and Tintelnot (2017).

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THE QUARTERLY JOURNAL OF ECONOMICS

that increased access to intermediate inputs has a productivityenhancing effect (e.g., Pavcnik 2002; Goldberg et al. 2010;
Khandelwal and Topalova 2011; Bas and Strauss-Kahn 2015).
As in Grossman and Helpman (2002), one producer’s choiceof organization depends on the industry environment and the
choices of other producers.
Our article is also closely related to the literature on
misallocation in developing countries (Restuccia and Rogerson
2008; Hsieh and Klenow 2009; Hopenhayn 2014). Several papers
have studied distortions to the use of intermediate inputs, forexample, Jones (2013), Bartelme and Gorodnichenko (2015),
Caprettini and Ciccone (2015), Fadinger, Ghiglino, andTeteryatnikova (2016), Caliendo, Parro, and Tsyvinski (2017),
Liu (2019), Osotimehin and Popov (2020), Baqaee and Farhi(2020), Bigio and La’O (2020), and Boehm (forthcoming).
These papers typically posit industry-level production functions
and use industry-level data. Our approach of identifying wedges
from factor shares (in our case, intermediate-input expenditure
shares) extends the work of Hsieh and Klenow (2009) along three
key dimensions. First, we relate the estimated wedges to thequality of Indian state-level institutions, which allows us to draw
policy conclusions from our exercise. Second, we confront thefact that firms produce in very different ways even in narrowly
defined industries by explicitly modeling this heterogeneity; weallow firms to choose among several types of technologies (recipes)
in the theory and identify these recipes in the data through theapplication of techniques from statistics/data mining.5 Third, we
identify wedges from systematic differences in first moments,
which helps alleviate concerns about mismeasurement being
interpreted as misallocation.6 In fact, our model predicts thateven in the absence of distortions, firms using the same broad
technology would use inputs with varying intensities.
The article is related to the literature on legal institutions and economic development (La Porta et al. 1997;
Djankov et al. 2003; Acemoglu and Johnson 2005; Nunn
2007; Levchenko 2007; Acemoglu, Antràs, and Helpman 2007;
Laeven and Woodruff 2007; Mukoyama and Popov 2020; among
5. Similarly, Asturias and Rossbach (2019) cluster Chilean manufacturingfirms based on their capital, labor, and intermediate-input usage and argue that
if the clusters are interpreted as representing different technologies, ignoring thisheterogeneity would lead to an overstatement of the extent of misallocation.
6. See Bils, Klenow, and Ruane (2017) and Rotemberg and White (2019).

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2013

many others). Ponticelli and Alencar (2016) and Chemin (2012)
argue that better courts reduce financial frictions. Amirapu(2017) shows that where district courts in India are morecongested, firms in industries that relied on relationship-specificinputs grew faster. Johnson, McMillan, and Woodruff (2002)
provide survey evidence that reduced trust in courts makes firmsthat rely on relationship-specific inputs less likely to switch
suppliers. By embedding a contracting friction into a generalequilibrium model, we explore its quantitative importance foraggregate outcomes. Boehm (forthcoming) characterizes theimpact of weak enforcement on aggregate productivity, using
cross-country differences in input-output tables to show thatweak legal institutions have a larger effect on industry pairs thatare more vulnerable to holdup problems.
II. INPUT USE AMONG INDIAN MANUFACTURING PLANTS
II.A. Intermediate-Input Use
We use data from the 2000/01 to 2012/13 rounds of the Annual
Survey of Industry (ASI), the official annual survey of India’s formal manufacturing sector. The ASI is a panel that covers all establishments with more than 100 employees, and every year a fifth of
all establishments with more than 20 employees (or more than 10
if they use power). The ASI’s unique feature is that it contains detailed product-level information on each plant’s intermediate inputs and outputs. Product codes are at the five-digit level, of which
there are around 5,200 codes in their classification. The productclassification remains largely unchanged during the years 2000/01
to 2009/10. The rounds 2010/11 to 2012/13 use a different (but similar) product classification, and we bring product-level data to theclassification of the earlier years using the official concordancetable published by the Ministry of Statistics. Online Appendix A
contains more details on the data and a description of our sample.
One striking feature of the data is that even in narrowly
defined industries, plants produce using very different input
bundles. Figure I shows two examples that are particularly clear.
Among producers of bleached cotton cloth and polished diamonds,
output is made using different sets of inputs. Although we believethat much of the heterogeneity in organization and input bundles
is not associated with inefficiencies and would arise naturally,
Section II.C shows that some of the differences are systematicallyrelated to court congestion.

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MISALLOCATION IN THE MARKET FOR INPUTS(A)THE QUARTERLY JOURNAL OF ECONOMICS(B)

FIGURE I
Heterogeneity in Input Mixes within Narrow Industries
The figure shows the variation in plants’ input mixes for single-product plantsthat produce only bleached cotton cloth (Panel A) or polished diamonds (Panel B).
Each dot represents a plant-year observation; the coordinates on the horizontal
and vertical axes correspond to the materials cost share of two different typesof intermediate inputs. For example, a plant on the top left of Panel B produces
polished diamonds entirely from cut diamonds (therefore doing just the polishing);
a plant on the bottom right produces polished diamonds entirely from rough diamonds (therefore doing both cutting and polishing themselves). Observations on
the bottom left mostly produce their output from unbleached cloth (Panel A) or
industrial diamonds (Panel B). Points have been jittered to improve readability.

Intermediate inputs vary in their degree to which buyers andsellers are subject to holdup problems. Producers of goods thatare tailored to a particular buyer (relationship-specific) may findthat buyers refuse to pay for the supplied good, knowing that they
are useless to anyone but themselves (Iyer and Schoar 2008). We
use the Rauch (1999) classification that divides goods into homogeneous goods (those that are traded on organized exchanges
or for which a reference price exists) and relationship-specificgoods (the remainder). Holdup problems are more likely to arise
with relationship-specific inputs. At the same time, timely andcheap enforcement of contracts in a court of justice is a way to
alleviate these holdup problems. Hence, firms rely more heavily
on judicial institutions to enforce supplier contracts when trading
goods belonging to the latter category (Johnson, McMillan, andWoodruff 2002).

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2015

II.B. Court Congestion in India
Among all the ills of the Indian judicial system, its slowness isperhaps the most apparent. As of 2017, about 9% of pending casesin district courts and 6% of pending cases in High Courts are older
than 10 years.7 Some cases make international headlines, such as
in 2010, when the Bhopal District Court convicted eight executivesof death by criminal negligence during the 1984 Bhopal gas leak,
which killed thousands of people. The conviction took place some
25 years after the disaster; one of the eight executives had alreadypassed away, and the remaining seven appealed the conviction.8
The slowness of the Indian courts is at least partly due to theuneven distribution of workload across its three tiers.9 The lowest
tier is the Subordinate (District) Courts, which have courthouses
in district capitals and major cities.10 The next tier are the High
Courts, of which there generally exists one for each state andwhich have both appellate and original jurisdiction over cases
originating from their state (and sometimes an adjacent union
territory). High Courts also administer subordinate courts intheir jurisdiction. The highest tier is the Supreme Court of India.
All three tiers are heavily congested, with district courts facing
the additional problems that judges are often inexperienced andare regarded as being less able or willing to make the rightdecision. While contract cases between firms should, in principle,
be filed at the district level, litigants typically bypass this stepby claiming an infringement of their fundamental rights orappealing to the constitution of India, in which case they are
permitted to file the claim directly at a high court.11 High Court
judges, often taking a dim view of the subordinate judiciary,
7. Figures for district courts are from the National Judicial Data Grid from2017. Figures for High Courts are based on authors’ calculations from the Dakshdata (see below).
8. James Lamont, “Painfully Slow Justice over Bhopal,” Financial Times, June
7, 2010.
9. See Robinson (2016) for an overview of the Indian judiciary. Hazra and
Debroy (2007) discuss its problems in relation to economic development.
10. Districts are the administrative divisions below states. Between 2001 and2010 there were around 620 districts and 28 states in India. Union territories are
small administrative divisions (typically cities or islands) that are under the ruleof the federal government, as opposed to states, which have their own government.
11. Some High Courts, such as the High Courts of Bombay, Calcutta, Madras,
and Delhi, even allow civil cases to be filed directly whenever the claim exceeds acertain value.

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THE QUARTERLY JOURNAL OF ECONOMICS

tend to accommodate this practice. The result is that the Indianjudiciary is relatively heavy in its upper levels, with only thesimplest cases being dealt with in the subordinate courts.12 For
better or worse, the quality of the higher judiciary determines
whether and how contracts can be enforced.
We construct a measure of court congestion from microdata
on pending civil cases in High Courts, which the Indian nongovernmental organization Daksh collects from causelists andother court records (Narasappa and Vidyasagar 2016). These
records show the status and age of pending and recently disposedcases, along with characteristics of the case, such as the act
under which the claim was filed or a case type categorization. Our
measure of high court congestion is the average age of pending
civil cases in each court, at the end of the calendar year 2016.
Whenever a high court has jurisdiction over two states and aseparate bench in each of them (such as the Bombay High Court,
which has jurisdiction over Maharashtra and Goa), we construct
the statistic by state. We prefer this measure over existingmeasures of the speed of enforcement, such as pendency ratios
published by the High Courts, which suffer from the problem
that different high courts measure pendencies in vastly different
ways (as emphasized by the Law Commission of India 2014).
The average age of pending civil cases varies substantiallyacross high courts—from less than one year in Goa and Sikkim,
to about four and a half years in Uttar Pradesh and West Bengal.
The cross-state average is two and a half years. These differences
can be seen in Figure II.
The problems of the Indian judiciary are not a recent phenomenon and have not gone unnoticed. Throughout the modern
history of India as an independent nation, the Law Commissionof India has pointed out the enormous backlogs and arrears ofcases (14th report, 1958; 79th report, 1979; 120th report, 1987;
245th report, 2014), and suggested many policies to alleviate thesituation. The vast majority of these proposals have not been
adopted, and the few exceptions seem to have had little effect.
Overall, the backlogs have slowly but continually accumulated.
12. Between 2010 and 2012, about 40% of all disposed cases in subordinate
courts were related to traffic tickets, another 7% related to bounced cheques (Law
Commission of India 2014).

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2017

FIGURE II
Age of the High Court and Speed of Enforcement

The main explanation for why court speed varies so much
across states lies in the history of India’s political subdivisions.
The first high courts (Madras, Bombay, and Calcutta) were set
up by the British in the 1861 Indian High Courts Act and served
as the precursor for India’s post-Independence high courts. Upon
Independence, India was divided into a number of federated
states, with the constitution of India (1947) mandating a highcourt for each state. Throughout the twentieth century andbeyond, India has frequently subdivided its states, often becauseof ethno-nationalist movements. These subdivisions were often
accompanied with new high courts being set up, which thenstart without any existing backlog of cases.13 The age of thehigh court is a strong determinant of its speed of enforcement(see Figure II; the F-statistic in that regression is 11.1). We
later use the age of high courts as an instrument for its level ofcongestion.
13. Table A.1 in Online Appendix A summarizes the reasons for the high court
being set up or the state being formed.

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II.C. Motivating Facts
We turn to documenting the correlation between court congestion and plants’ intermediate input use. For the sake of comparability we restrict our attention here to single-product plants.14
FACT 1. In states with more-congested courts, cost shares of intermediate inputs are relatively lower in industries that tend to
rely more on relationship-specific intermediate inputs.
Table I shows regressions of the plants’ materials costshare on an interaction of court congestion (as measured by
the average age of pending cases in the high court of the statein which the plant is located15 ) and the industry’s reliance on
relationship-specific inputs.16 The interaction term has a negativeand significant coefficient, showing that plants’ materials costshares decline more steeply with court congestion in industries
that tend to rely more heavily on relationship-specific inputs. The
magnitude in column (1) indicates that for each additional year of
court congestion, plants’ materials share of cost declines by 1.67
percentage points more in industries that rely on relationshipspecific inputs than in industries that rely on standardized inputs.
A primary concern in this specification is that court congestion is standing in for the level of development, or that the levelof development is correlated with the relative productivity ofindustries that rely on relationship-specific inputs. Column (1)includes district fixed effects. Column (2) controls for the interaction of relationship specificity with district income per capita, andcolumn (3) adds controls for the interaction of relationship specificity with a variety of state characteristics, including measuresof trust, corruption, linguistic fragmentation, and fragmentation
14. One difficulty that arises when studying multiproduct plants is that we
do not observe which inputs are used to produce each product. Nevertheless, theresults in this section are quantitatively similar when we include multiproductplants and assign the plant to the category of its highest-revenue product.
15. In principle, firms can bring their cases to any court; the court decides
whether it has jurisdiction over the case. We believe that in the case of India
this practice is limited, as state borders are often also language borders. Moregenerally, this would be a form of measurement error in the independent variable
that would bias the coefficient toward 0.
16. Following Nunn (2007), we measure an industry’s reliance on relationshipspecific inputs at the national level by computing the fraction of intermediate-input
expenditures spent on relationship-specific inputs across all plants in the industry.
See Online Appendix A.1 for details.

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2018

(0.0051)(0.0046)0.480
208,527

0.482
199,5440.484
196,748

OLS

0.480
208,527

IV

Yes
Yes

(0.0085)− 0.0156+

(4)

0.482
199,544

IV

Yes
Yes

0.00710(0.0095)(0.0082)− 0.0201∗

(5)

0.484
196,748

IV

Yes
Yes

Yes

0.00556(0.0096)− 0.0212∗∗(0.0078)

(6)

2019

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Notes. Standard errors are in parentheses, clustered at the state × industry level. + p < .10, ∗ p < .05, ∗∗ p < .01. “Rel. spec. × State controls” are interactions of trust, language
Herfindahl, caste Herfindahl, and corruption with relationship specificity. The sample consists of single-product plants only.

Observations

OLS

OLS

Estimator

R2

Yes
Yes

Yes
Yes

Yes
Yes

Five-digit industry FE
District FE

0.0102(0.0091)(0.0053)− 0.0118∗

(3)

Yes

0.0114(0.0086)− 0.0129∗− 0.0167∗∗

Rel. spec. × State controls

LogGDPC * Rel. spec.

Avg age of civil cases * Rel. spec.

(2)

(1)

Dependent variable: Materials expenditure in total cost

TABLE I
MATERIALS SHARES AND COURT CONGESTION (FACT 1)

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THE QUARTERLY JOURNAL OF ECONOMICS

by caste. While the coefficients (reported in Online Appendix C)
suggest that ethnolinguistic homogeneity facilitates the use of
relationship-specific inputs, this appears to be orthogonal to court
congestion. Finally, columns (4) to (6) employ an instrumental
variables strategy that we discuss below in Section II.D.
FACT 2. In states with more-congested courts, intermediate input
bundles are tilted toward standardized intermediate inputs.
Our first fact related court congestion to how plants divided
their expenditures between intermediate and primary inputs.
We next study how the composition of plants’ intermediate-input
baskets covaries with court congestion. Table II shows that instates where courts are faster, plants’ intermediate-input baskets
are tilted toward relationship-specific intermediate inputs. This
correlation remains statistically significant when controlling for
district income per capita and other state characteristics.
FACT 3. In states with more-congested courts, plants in industries
that tend to rely more on relationship-specific intermediate
inputs have larger vertical spans of production.
A low materials share suggests that a plant may be doing
more consecutive steps in the production process themselves.
For example, a car producer that assembles components may
also manufacture those components in the same facility. The
regressions in Table III show how court congestion is related to
the vertical span of production, that is, to how many consecutive production steps are performed within the plant. We first
construct a measure of the “vertical distance” between an output
good ω to an input ω . This is intended to capture the typicalnumber of “steps” between the use of ω and the production of ω,
where we define a step to be the activity performed by a single
plant.17 Finally, for each single-product plant, our measure ofvertical span is the expenditure-weighted average of the distance
17. We construct national input-output tables using our plant-level data. For
each output good ω and input good ω , we take a weighted average of the numberof steps along any path from ω to ω, weighted by the product of the input-output
shares along that path, excluding any path which cycles. This measure is similar
to Upstreamnessij of Alfaro et al. (2019). Online Appendix B gives the precise
mathematical definition of vertical distance.

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2020

OLS
0.446
204,031OLS
0.449
199,339

XR
j

IV
0.441
225,590Yes(0.0044)− 0.0144∗∗

(4)

H
XR
j +X jIV
0.446
204,031

Yes

IV
0.449
199,339

Yes

Yes− 0.00980+(0.0051)− 0.00912+(0.0051)(0.0044)− 0.0167∗∗(0.0045)(6)− 0.0146∗∗

(5)

2021

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Notes. The dependent variable is the share of relationship-specific inputs in total materials cost of plant j. “State controls” are trust, language Herfindahl, caste Herfindahl, andcorruption. The sample consists of single-product plants only. Standard errors are in parentheses, clustered at the state × industry level. + p < .10, ∗ p < .05, ∗∗ p < .01.

OLS
0.441
225,590

Yes

Estimator
R2
Observations

Yes
Yes

Five-digit industry FE

Yes(0.0024)− 0.00384(0.0046)(0.0023)− 0.00389(0.0045)(0.0022)− 0.00530∗− 0.00621∗∗− 0.00547∗

(3)

(2)

(1)

Dependent variable:

State controls

Log district GDP/capita

Avg age of civil HC cases

TABLE IIINPUT MIX AND COURT CONGESTION (FACT 2)MISALLOCATION IN THE MARKET FOR INPUTS

0.0288(0.024)0.0464∗(0.022)

0.443
163,334

0.451
156,1910.453
154,0210.443
163,334

IV

Yes
Yes

0.0292(0.019)(4)

0.451
156,191

IV

Yes
Yes

0.0491∗(0.023)(0.018)0.0314+(5)

0.453
154,021

IV

Yes
Yes

Yes

0.0330(0.024)0.0368∗(0.018)(6)

THE QUARTERLY JOURNAL OF ECONOMICS

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Notes. Standard errors are in parentheses, clustered at the state × industry level. + p < .10, ∗ p < .05, ∗∗ p < .01 “Rel. spec. × State controls” are interactions of trust, language
Herfindahl, caste Herfindahl, and corruption with relationship specificity. The sample consists of single-product plants only.

R2
Observations

OLS

Estimator

OLS

Yes
Yes

OLS

Yes
Yes
Yes

Five-digit industry FE
District FE

Yes
Yes

(0.012)(0.012)(0.011)

Rel. spec. × State controls

LogGDPC * Rel. spec.

Avg age of civil cases * Rel. spec.

0.0280∗0.0269∗0.0195+

(3)

(2)

(1)

Dependent variable: Vertical span

TABLE IIIVERTICAL SPAN OF PLANTS AND COURT CONGESTION (FACT 3)

2022

2023

from the plant’s output ω to its intermediate inputs:
verticalSpan j =


ω̂∈



X j ω̂
verticalDistanceωω̂ ,ω̃∈ X j ω̃where X j ω̂ is plant j’s expenditure on input ω̂ and ω is j’s output.
A longer vertical span indicates that the plant uses inputs thatare typically further upstream, and suggests that the plant isperforming more steps in-house. Table III shows that plants’vertical spans of production increase more sharply with court
congestion in industries that tend to rely more heavily on
relationship-specific inputs.18
II.D. Endogeneity and the Historical Determinants of Indian
Court Efficiency
The main caveat in the foregoing regressions is the concernthat there are unobserved covariates of court congestion that
may also affect the cost of plants’ inputs, and thereby their input
shares. The simplest version is reverse causality. In principle, thebias from reverse causality could be positive or negative. Suppose
that, for exogenous reasons, a state had many plants that produced using relationship-specific inputs. The disputes that arise
may cause the courts to be congested. Or alternatively, the state
may respond to the disputes that arise by spending resources
to reduce congestion. Either of these would be problematic forinterpreting the regressions as a causal relationship.
Although we believe reverse causality is unlikely to arise—
the fraction of cases related to firm-to-firm trade is relatively
low19 —it is difficult to rule out other factors that may influenceboth court congestion and usage of relationship-specific inputs.
18. Although the nature of our data allows us to speak to the activities ofindividual plants rather than of firms, it is likely that contracting frictions affectthe boundaries of firms as well. While we do not know whether two plants belong
to the same firm, our data contain an indicator of whether a plant is standalone orpart of a multiplant firm. In Online Appendix C.2, we repeat Tables I, II, and III
but compare standalone plants to plants that belong to multiplant firms. Note thatinterpreting these regressions is not straightforward because whether a plant ispart of a multiplant firm is itself an endogenous outcome.
19. The fraction of cases that is related to the enforcement of supplier contracts is hard to pinpoint exactly because courts classify cases very broadly andin different ways across states. We know, however, that they account for less than
5%, 14%, and 7% of the pending cases in the High Courts of Allahabad, Bombay,
and Calcutta, respectively.

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We therefore employ an instrumental variables strategy thatuses the historical determinants of congestion. As discussed in
Section II.B, courts have been continually accumulating backlogs
throughout the twentieth century. At certain points, however,states were split or reorganized, mostly in response to ethnonationalist movements. In the course of these reorganizations,
new high courts were set up, which initially started with a cleanslate but were, like existing courts, understaffed and started accumulating backlogs. The time since their founding—the court’s
age—is therefore a strong predictor for the current backlog, which
in turn determines the present-day speed of enforcement. Our
instrumental variable for the speed of enforcement is hence the(log) age of the high court, and the instrument for an interactionof an industry-level variable with court speed is the interactionof the industry-level variable with the log age of the court.
Figure II shows the strong correlation between court age andspeed of enforcement.
Columns (4) to (6) of Tables I, II, and III repeat the regressions while instrumenting for the speed of enforcement. The
point estimates of the coefficient of the interaction term is usuallyslightly larger than the OLS estimates.
There are a few reasons that the exclusion restriction may
be violated. We argue that two candidates would lead us toconclude that the true relationships are stronger than reported
in the IV regressions. First, new states tend to be relatively
poor and have low state capacity. Thus the usual concern that ahigh level of development causes firms to use more sophisticatedtechnologies that use relationship-specific inputs would cause
the newer states to have higher use of homogeneous inputs.
Alternatively, it may be that when a state splits, many firms lose
their suppliers and must switch. It may be easy to find a new
supplier of homogeneous inputs, whereas it might be harder tofind a supplier of relationship-specific inputs. This channel would
also cause newer states to be more intensive in homogeneous inputs. In either case, the true relationship would be stronger thanreported. A third reason that the exclusion restriction might beviolated is that newly formed states might be more ethnically homogeneous, so that newer courts might be correlated with better
informal enforcement. This is a particular concern here because
ethno-nationalist conflicts are a primary reason that states split.
Nevertheless, we can control for states’ ethnic fragmentation—ormore specifically the interaction of relationship specificity with

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2025

various measures of ethnic fragmentation—as we do in columns(3) and (6) of Tables I, II, and III. Controlling for these has little
impact on the main coefficients of interest.
In addition to the cross-sectional regressions shown above,
we bring evidence from time variation in the degree of court
congestion in Online Appendix C.3. We first show results from
two instances in which high courts set up new and fast benches
in remote areas during our sample period. In addition, we use
variation in court pendency ratios over time. In both cases
we include fixed effects to identify the relationship from time
variation in court congestion only. Although neither experimentis perfect—with the court expansion the sample is small andsome estimates are imprecise, whereas with pendency ratios it
is not clear what drives the variation—the results are consistent
with our baseline cross-sectional evidence.
A final concern is that an industry’s reliance on relationshipspecific inputs is correlated with other industry characteristics
such as capital intensity, skill intensity, upstreamness, or tradability. In Online Appendix C.1 we show that the estimates
are robust to controlling for the respective interactions of court
congestion with each of these industry characteristics.20

II.E. Inferring Properties of Contracting Frictions
What do these regressions tell us about the form of contracting frictions? The literature on contracting frictions (e.g.,
Antràs 2003) has emphasized that holdup problems may result intransactions in which the seller shades on the quantity or qualityof the inputs. These can be modeled in different ways that would
show up differently in the data. We explore the implications andempirical validity of these in Online Appendix D.
In particular, contracting frictions could be modeled as
resulting in an increase in the shadow cost of an input (Hsieh
and Klenow 2009). A testable implication of this formulation isthat the distortion should raise the buyer’s ratio of revenue tototal cost. In our setting, we find that plants that are subject tolarger wedges—those in industries that tend to use relationshipspecific inputs in states with congested courts—have lower
20. Online Appendix C.4 and C.5 show the correlation of distortions withother establishment characteristics, including import decisions, age, size, and thenumber of products.

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THE QUARTERLY JOURNAL OF ECONOMICS

revenue-cost ratios, in contrast to the prediction from a quantity
distortion.
Alternatively, contracting frictions could raise the effective
price of the input (i.e., an iceberg cost). To be consistent with ourevidence, such a formulation would require that the elasticity of
substitution between distorted and undistorted inputs is larger
than 1. As we discuss in Online Appendix D, this contrasts withavailable evidence, both from the existing literature and from oursetting.
Finally, it could be that distortions increase the effective
cost of an input, but that the additional cost takes the form of
additional expenditure on primary factors. For example, it may
be that the buyer needs to pay workers to repair defective inputs.
Such a formulation is consistent with the empirical evidence andwe use it in the subsequent model.
III. MODEL
The previous section showed that imperfect contract enforcement alters the production decisions of manufacturing plants in
India in systematic ways. We aim to quantify the impact of weak
enforcement on the productivity of the manufacturing sector.
A commonly used approach to quantify the role of factor market frictions, pioneered by Hsieh and Klenow (2009), is to positthat plants in the same industry use a common Cobb-Douglas production function. This allows them to use dispersion of cost shareswithin industries to infer dispersion in marginal products of inputs. What gives this approach traction is the implication that in
the absence of distortions, plants would have the same cost sharesregardless of the factor prices they face. Deviations from thiscost share would then be interpreted as the result of a distortion.
This approach, however, extends poorly to the question of finding
distortions in the use of intermediate inputs, where, as we haveseen, variation in factor use along both intensive and extensive
margins is widespread and unlikely to be driven entirely by distortions.21 At the same time, departing from Cobb-Douglas would
require reliable information on input prices that are comparable
across plants and across locations, as well as a way to disentangle
21. We attempt such an exercise in Online Appendix H.3. There are several
conceptual and practical obstacles. In any case, the observed variation in input
use would lead to enormous implied distortions.

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2027

distortions from differences in the level and factor bias of productivity. This is especially important in the context of intermediate
inputs, where such information is typically unavailable or
unreliable.
In this section we develop a model that we will use to evaluate the impact of contracting frictions. We will make two key
identifying assumptions. First, our assumptions will imply that,at a certain level of aggregation, factor shares will be invariant tofactor prices. This implication is related to but weaker than thosemade by Hsieh and Klenow (2009), which is that factor shares areinvariant to factor prices at the firm level and that all dispersion
is due to distortions. Second, we assume that imperfect contract
enforcement distorts the use of relationship-specific inputs and oflabor, but not the use of homogeneous inputs.22 These two aspectsof our model enable us to identify distortions in factor markets
from factor shares alone (in our case, average factor shares,
thereby not requiring price data), while still allowing plants
to have production functions that deviate from Cobb-Douglas,
and therefore have varying factor shares for reasons that are
unrelated to distortions. We then estimate the importanceof distortions on the use of relationship-specific intermediate
inputs using these average factor shares. This ties back to the
reduced-form evidence we have shown above: that patterns ofplants’ expenditure shares differ systematically across states, ina way that is correlated with a potential source of distortions.
The model gives a prominent role to two additional featuresthat may be important for our quantification of contracting
frictions: firm-to-firm trade and technology/organizational choice.
First, there are many ways to avoid contracting frictions. Supposea firm needed to use an input that required customization andtherefore faced a holdup problem. In the face of weak formal
contract enforcement, the firm might buy the intermediate input
from a relative or rely on the repeated interactions of a long-term
relationship. Such decisions, however, may come at a cost. A
family member may not be the optimal supplier of an intermediate input, and if a firm is in a long-term relationship, it may
pass up using new, more cost-effective inputs to remain in that
22. If contracting frictions also distorted the use of homogeneous inputs, thegains from reducing contracting friction would be larger than those we report.

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long-term relationship.23 Such a firm’s production cost is higher
than it would be with better contract enforcement, even though
there may not be a distortion associated with sourcing fromthat supplier. The higher production cost is therefore an indirectconsequence of weak formal enforcement that arises when firms
substitute away from suppliers with whom they would face aholdup problem. We can infer this indirect cost by incorporating
this type of decision in the model, and estimating how easily
firms can substitute across suppliers of the same input.
Second, as discussed in Section II.A, even in narrowly
defined industries, firms produce in qualitatively different ways.
As a simple example, consider two plants that produce polisheddiamonds, one that buys cut diamonds and another that buys
rough diamonds and cuts and polishes them. It may well be thecase that the latter’s decision to have a larger vertical span of production and do both cutting and polishing was a consequence of a
distortion. The two plants will use different production functions,and simply comparing their expenditure shares will not give a
direct measure of the size of the distortion. The empirical implementation of our model must therefore be able to account for thesedifferences when measuring the magnitude of the distortions.
III.A. The Environment
There is a set of industries . For industry ω ∈ , there
is a mass of firms with measure Jω that produce differentiatedvarieties. There is a representative household that inelasticallyprovides a mass of labor with measure L and has nested CES
preferences over all varieties in each industry, maximizing
consumption of the bundle U defined as

U =



η−1
η

1
η

υω Uω

ω∈

Uω =


Jω
0

η
 η−1

ε−1
ε

uωj djε ε−1,

23. Lim (2018) documents that in each year, firms switch roughly 40% of
suppliers, and Lu, Mariscal, and Mejia (2013) document ubiquitous switchingof imported inputs among importers, suggesting gains from taking advantage of
new opportunities that arise. Johnson, McMillan, and Woodruff (2002) show thatthose who distrust courts are less likely to switch suppliers, suggesting that weak
enforcement inhibits this.

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where uωj is consumption of variety j in industry ω, υ ω reflects
the household’s taste for goods in industry ω, η is the elasticity of
substitution across industries, and ε is the elasticity of substitution across varieties within each industry.
There are several different ways to produce a good using
different combinations of inputs. These different ways correspondto different production functions, which we call recipes. Denotethe set of recipes to produce a good ω by ω . Each recipe ρ ∈ ω
describes a production function Gωρ (·) that can be used by any
firm in industry ω to produce its good using labor l and aˆ ρ . We assume:particular bundle of inputs 
ASSUMPTION 1. For any recipe ρ ∈ ω , the production function Gωρˆ ρ ) areexhibits constant returns to scale and all inputs (l, complements.
Note that the different Gωρ may differ in their shape and theirfactor intensities and that they need not be Leontief.
Firm j in industry ω has random sets of productivity andsupplier draws jρ for each recipe ρ ∈ ω . We call these draws
techniques. Each technique φ ∈ jρ is characterized by (i) a set of
potential suppliers for each intermediate input, {Sω̂ (φ)}ω̂∈ˆ ρ ; (ii)for each of those suppliers s ∈ Sω̂ (φ) an input-augmenting productivity and a distortion (which we discuss further below); and(iii) a labor-augmenting productivity bl (φ). The input-augmenting
productivity for supplier s ∈ Sω̂ (φ) consists of a match-specificcomponent zs that is specific to the supplier and a componentbω̂ (φ) that is common to all suppliers of input ω̂ in the set Sω̂ (φ).
Suppose that j produced its good using a technique of recipeˆ ρ = {ω̂1 , . . . , ω̂n}. If
ρ which used labor and intermediate inputs 
it chose to employ l units of labor and purchase {xs1 , . . . , xsn }units of intermediate inputs from respective supplierss1 ∈ Sω̂1 , . . . , sn ∈ Sω̂n , its output would be
y j = Gωρ bl l, bω̂1 zs1 xs1 , . . . , bω̂n zsn xsn .
Each technique is specific to the firm producing the output(the “buyer”) and to the potential suppliers that might provide theintermediate inputs. In equilibrium, the firm chooses to produce
using the technique and suppliers that is most cost-effective,
which depends on the prices those suppliers charge and the
input-augmenting productivities of the technique.

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Terms of trade among firms determine their choices of inputs,
production decisions, and productivity. We also assume that salesof goods for intermediate use are priced at the supplier’s marginalcost.24 Firms engage in monopolistic competition when sellingto the representative household and remit all profits to thehousehold.
First, nature chooses the sets of techniques available to eachfirm. Then all firms simultaneously set prices and make theirproduction decisions (i.e., choices of technique φ ∈ ρ∈ω jρ ,suppliers, and inputs l, xs1 , . . . , xsn ) to minimize cost, taking into
account the decisions of others. All firms have perfect information
about the economy’s production possibilities and about otherfirms’ choices. The probability distribution governing the setof techniques with which firm j can produce ({ jρ }ρ∈ω ) will be
described below.
III.B. Contracting Enforcement
Enforcement of contracts facilitates the use of inputs that
require customization and the use of labor. Imperfect enforcement
introduces wedges between the effective cost to the buyer andthe payment to the supplier. If an input requires customization,
the supplier can shirk and provide a good that is imperfectly
customized to the buyer. If this happens, the buyer needs to use
extra labor to correct the defect. This is wasteful because the supplier has an absolute advantage in performing the customization.
For each supplier, the buyer draws a random cost of enforcing thecontract, which, by modulating the threat of enforcement, affects
the equilibrium performance of the supplier and hence the extralabor the buyer needs to use to correct the defect. We discuss thefull microfoundation in Online Appendix E.
24. One interpretation of this assumption is that in firm-to-firm trade, buyers have all of the bargaining power. For example, in a simpler environment,
Oberfield (2018) characterizes an alternative market structure in which firm-tofirm trade is governed by bilateral trading contracts specifying a buyer, a supplier,a quantity of the supplier’s good to be sold to the buyer, and a payment. Given acontracting arrangement, each entrepreneur makes her remaining production decisions to maximize profit. The economy is in equilibrium when the arrangement
is such that no countable coalition of entrepreneurs would find it mutually beneficial to deviate by altering terms of trade among members of the coalition and/or
dropping contracts with those not in the coalition. The terms of trade describedhere are one particular equilibrium in which buyers have all of the bargaining
power.

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This game has a reduced form in which, for each potential
supplier of a relationship-specific input ω̂, the buyer draws arandom input wedge tx ∈ [1, ∞), from a distribution with CDF
T(tx ).25 If the supplier’s price is ps per unit, the total cost to thebuyer is tx ps , with ps paid to the supplier and (tx − 1)ps spenton extra labor. We model wedges as random and match specificbecause, for some suppliers (e.g., family members, those withwhom the buyer is in a long-term relationship) the possibilityof informal enforcement may mitigate any holdup problem; forothers, the holdup problem may be more severe.
The distribution T(tx ) summarizes the quality of enforcement.
Perfect enforcement of contracts would imply that tx = 1 for all
suppliers. As discussed earlier, courts are not the only way to
enforce contracts; contracts could be enforced informally throughsocial punishments or reputation. tx should be interpreted as
the wedges that prevail after all forms of enforcement are
exhausted.26
For completeness, we include the possibility that imperfect
enforcement raises the cost of labor as well. If production is
subject to the labor wedge tl , then the firm needs to hire tl
workers to obtain one efficiency unit of labor, so that the effective
cost of labor to the firm is wtl . For simplicity we assume that tl is
the same across all firms.27
III.C. Production Decisions
For each technique, firm j draws a set of potential suppliers
to provide each input. Each potential supplier s ∈ Sω̂ (φ) comeswith an input-augmenting productivity draw and a wedge, sops,that the effective cost of using that supplier would be bω̂txs(φ)zswhich includes the cost of the extra labor needed to customize the25. As we show in Online Appendix E, there is a one-to-one mapping between
the enforcement cost and the equilibrium input wedge tx .
26. For example, if formal enforcement would leave the wedge txformal while
informal enforcement would leave the wedge txinformal , then the parties would use
whichever form of enforcement is better, that is, tx = min{txformal , txinformal }. The
argument extends in the obvious way if there are multiple ways of enforcing
contracts informally. Improving the quality of courts would reduce the formal
wedges and might alter the effectiveness of informal enforcement mechanisms if
it worsens the informal arrangements that can be sustained.
27. Our counterfactuals focus on changes in the distribution of distortions that
impede the use of relationship-specific intermediate inputs (T). Our identification
strategy does not recover the labor wedge tl .

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input. If j used technique φ, it would choose to use the supplierthat delivered the lowest effective cost for input ω̂, so that its
effective cost of that input would be:txs (φ) ps.
s∈Sω̂ (φ) bω̂ (φ)zs (φ)λω̂ (φ) ≡ min

Similarly, the effective cost of labor when using technique φ isw
λl (φ) = btll(φ). For the remainder, we normalize the wage to unity,
w = 1.
The unit cost delivered by a technique depends on theeffective cost of each input. Let Cωρ (·) be the unit cost functionthat is the dual of the production function Gωρ , so that j’s costof producing one unit of output using technique φ would beCωρ (λl (φ), {λω̂ (φ)}ω̂∈ˆ ρ ). Minimizing cost across all techniques, j’sunit cost is
min min Cωρ λl (φ), {λω̂ (φ)}ω̂∈ˆ ρ .

ρ∈(ω) φ∈ωjρ

In words, firm j’s unit cost equals that of the technique thatdelivers the lowest cost across all techniques of all recipes.
In this section, we specialize to particular functional-form assumptions. As we show below, with these assumptions, the model
aggregates easily and allows us to use a transparent strategy toidentify contracting frictions. The set of techniques available toeach firm is random and governed by the following assumptions
about the distributions of input-augmenting productivities.
ASSUMPTION 2. For a firm in industry ω,
i. Each supplier in the set Sω̂ (φ) is uniformly drawn fromall firms that produce ω̂.
ii. For each technique φ that uses input ω̂, the number ofsuppliers in Sω̂ (φ) for whom the match-specific component of productivity is greater than z follows a Poisson
distribution with meanz−ζω̂ , with ζω̂ =ˆρζ R, ω̂ ∈ Rˆρ ,ζ H , ω̂ ∈ Hˆ ρ and ˆ ρ are the subsets of inputs used inwhere R
H
recipe ρ that are, respectively, relationship-specific andhomogeneous.

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iii. Consider recipe ρ ∈ ω which uses labor and the inputˆ ρ = (ω̂1 , . . . , ω̂n). For each plant, the number ofbundle techniques to produce using that recipe for which thecommon components of input-augmenting productivities
strictly dominate28 bl , bω̂1 , bω̂2 , . . . , bω̂n follows a Poisson
distribution with meanρ−βlBωρ bl

ρ

−βω̂

−β

ρ

bω̂1 1 . . . bω̂n ω̂n .

iv. There is a constant γ such that for each ω and each recipeρ ∈ ω , βlρ + βω̂ρ1 + · · · + βω̂ρn = γ .
v. The following parameter restrictions hold for each ω̂: γ >ερ− 1, γ > ζω̂ > βω̂ where ζω̂ is ζ R if ω̂ is relationship-specificor ζ H if ω̂ is homogeneous.
Assumption 2.ii implies that above any threshold, the matchspecific components of productivity follow a power law.29 One
implication is that the industry-level elasticity of substitution
across groups of suppliers of the same input is ζω̂ + 1. When
there is more dispersion in these match-specific components of
28. We say that a vector (x0 , x1 , . . . , xn ) strictly dominates the vector (y0 ,y1 , . . . , yn ) if x0 > y0 , x1 > y1 , . . . , xn > yn .
29. This type of functional form assumption goes back to at least Houthakker(1955), and versions of it are also used by Kortum (1997), Jones (2005), Oberfield(2018), and Buera and Oberfield (2020). Note that the expected number of potential
suppliers for an input is unbounded. Formally, an economy satisfying Assumption
2.ii can be thought of as the limit of a sequence of economies that satisfy more
standard assumptions. Consider an economy in which firms were restricted to use
only suppliers with a match-specific productivity greater than z. Then the numberof potential suppliers for each input of a technique would be given by a Poisson
distribution with mean z−ζ and the match-specific productivity for each supplierwould be drawn from a Pareto distribution with CDF 1 − ( zz )−ζ . An economy satisfying Assumption 2.ii can be thought of as the limit of such an economy as z → 0.
In this limit, the number of suppliers for each input of a technique grows arbitrarily large, but the match-specific productivity associated with any single supplieris drawn from an arbitrarily poor distribution. The limit is well-behaved because
the probability of drawing a supplier with match-specific productivity greater thanz does not change as z → 0. In principle, we could have allowed the level of thematch-specific component of productivity draws to vary by input-output pair andrecipe, or Zωρ ω̂ z−ζω , reflecting the idea that industries are often concentrated geographically or ethnically, which may imply that a given output industry may facean unusually high number of good suppliers in the input industry relative to other
output industries. However, it turns out that Assumptions 2.ii and 2.iii imply thatany variation in {Zωρ ω̂ } would be absorbed into the constant Bωρ , so we simply
normalize each Zωρ ω̂ to unity.

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productivity (low ζω̂ ), a buyer is less likely to switch suppliers
in response to changes in the supplier’s price because it is likelythat there is a larger gap between the best and second-best
suppliers of an input. ζ R will play a role quantitatively because it
determines the likelihood that a buyer will have a close substituteif it faces a holdup problem with its best supplier of an input.
Assumption 2.iii says that the common components of inputaugmenting productivities of a technique follow independent
power laws. Bωρ summarizes the level of these productivity draws.
We take these to be primitives, although a deeper model mightmodel them as resulting endogenously from directed search orfrom the diffusion of technologies across entrepreneurs that knoweach other.
Assumption 2.iv says that for each recipe, the sum of thepower law exponents is the same, equal to γ . We will show laterthat the industry-level elasticity of substitution across techniques
is γ + 1.30 The parameter restrictions are necessary to keep
utility finite.
It will be useful to normalize the power law exponents by
their sum. For recipe ρ, define
ρ

αL =

ρ

βl
,
γ

ρ

αω̂ ≡

βω̂ρ
,
γ

ˆ ρ.
ω̂ ∈ 

ρρNote that this implies that α L + ω̂∈ˆ ρ αω̂ = 1. Furthermore,ρρfor some results, it will be useful to define α R = ω̂∈ˆ ρ αω̂ andRρρα H = ω̂∈ˆ ρ αω̂ .
HWith these assumptions in hand, we now characterize theequilibrium. All proofs are contained in Online Appendix F.31
PROPOSITION 1. Under Assumptions 1 and 2, the fraction of firms
in industry ω with unit cost greater than c is
e

−

c
Cω

γ

,

30. It would be straightforward to allow different industries to have different
values of γ . However, as we show below, our counterfactuals are insensitive to thevalue of γ . We therefore leave the γ constant across industries to reduce notational
clutter.
31. We thank Matt Rognlie and Sam Kortum for suggestions that simplified
the proof of Proposition 1.

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where
⎧
⎨

⎞−γ ⎫− γ1⎬ ∗ αρR αρL  αω̂ρCω =κωρ Bωρ ⎝ tx
tl
Cω̂ ⎠
⎩ρ∈
⎭
ρ
⎛

ˆ
ω̂∈

ω

(1)

tx∗ =

 ∞
1

tx−ζ R dT (tx )

− ζ1

R

and κ ωρ is a constant that depends on technological parameters.
Proposition 1 shows that the distribution of cost amongfirms within each industry takes the simple form of a Weibull
distribution with shape parameter γ and scale determined by Cω ,which we call the cost index for industry ω. Equation (1) relates
industry ω’s cost index to that of the industries that provide theinputs for each recipe and to tx∗ and tl , which summarize the effectof imperfect enforcement on those that produce the inputs used inrecipe ρ. tx∗ accounts for both the direct impact of the wedges—thewasted resources from holdup problems—and the indirect impact:wedges might cause firms to switch to a supplier with higher costor lower productivity, or to a different technique altogether.
Equation (1) is a system of equations that implicitly determines each industry’s cost index, {Cω }ω ∈  . Proposition 2 showsthat these are sufficient to characterize aggregate productivity.
PROPOSITION 2. Under Assumptions 1 and 2, the household’s
aggregate consumption is

U =


ω∈

η−1
ε−1

υω Jω

1
 η−1
 η−1

ε − 1 ε−1 1−η
 1−
Cω
L.
γ

We next turn to industry-level expenditure shares. The next
proposition characterizes the aggregate share of total expenditures (on both intermediate inputs and labor) that is spent oneach input among all firms that use a particular recipe.
PROPOSITION 3. Suppose that Assumptions 1 and 2 hold. Amongfirms that in equilibrium produce using recipe ρ:

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THE QUARTERLY JOURNAL OF ECONOMICS• the average and aggregate shares of expenditures spentρˆ ρ are both αω̂ ,on inputs from ω̂ ∈ Rt̄x• the average and aggregate shares of expenditures spentˆ ρ are αω̂ρ ,on inputs from ω̂ ∈ H• the average and aggregate ρ shares of expenditures spentρon labor are α L + 1 − t̄1x α R,
 tx −ζ ∞−1t R dT (t)where t̄x ≡ 1 tx−1 dT̃ (tx )and T̃ (tx ) ≡ 1∞ t−ζ R dT (t) .
1

Proposition 3 provides relatively simple expressions for the
average and aggregate cost shares of each input among those thatchoose to use a particular recipe. These properties will be central
to our identification procedure. Although there is micro-level
heterogeneity in the cost shares among those using a particular
recipe, the aggregate factor shares among those firms depend
only on technological parameters, not on the relative prices of
the inputs. Thus at the recipe level, there is a Cobb-Douglas
aggregate production function. This extends the celebrated aggregation result of Houthakker (1955), who derived a similar result
under the assumption that individual production functions are
Leontief.32 We require only that the production function exhibits
constant returns to scale and that all inputs are complements.33
32. Jones (2005) builds on Houthakker (1955) but derives a different type of
result. Jones first shows that if a single plant draws many Leontief production
functions where factor-augmenting productivities are drawn from independent
Pareto distributions, the envelope of those production functions is Cobb-Douglas.
He shows numerically that the result extends beyond Leontief to CES production
functions when the factors are complements. Note that these are not aggregation results; these results apply at the level of a single firm. Lagos (2006) andMangin (2017) also build on Houthakker (1955) incorporating labor market search,while Growiec (2013) extends Jones’s argument to microfound an aggregate CES
production function.
33. Why complements? If inputs are complements, then an increase in theprice of an input would have two offsetting effects on the aggregate cost share. The
higher price raises each firm’s cost share of that input. At the same time, firmsthat use that input more intensively are likely to shrink or switch to a techniquethat uses the input less intensively. When factor-augmenting productivities are
drawn from independent Pareto distributions, these offset exactly and aggregate
factor shares are unchanged. If inputs were substitutes, the two effects would
push in the same direction, so that if the price of an input rose, its aggregate
cost share would fall. Mathematically, if inputs were substitutes then the constantκ ωρ would diverge, as the arrival rate of techniques that deliver cost lower than cwould be infinite for any c. While the assumption of constant returns to scale keeps
the characterization of sourcing decisions tractable, the extension of Houthakker(1955) requires only homotheticity.

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Imperfect enforcement, on the other hand, reduces theexpenditure share of relationship-specific inputs. The buyer’s
production decisions depend on each input’s effective cost,whereas the expenditures reflect the actual payment to eachsupplier. Recall that imperfect enforcement means that thebuyer’s effective expenditure on a relationship-specific input isspent partly on payments to the supplier for the input and partly
on labor to customize the good.34
III.D. Counterfactuals
The quality of contract enforcement can be summarized by the
distribution of wedges T. Suppose that the quality of enforcementchanged in such a way that the distribution of wedges changed
from T to T . How would this affect aggregate productivity?
Taking Jω and Bωρ as primitives, the following proposition shows
how one can compute the impact of such a change.35
Let HHω be the share of the household’s expenditure on
goods from industry ω in the current equilibrium. Among thoseof type ω, let Rωρ be the share of total revenue of those that use
recipe ρ in the current equilibrium.
PROPOSITION 4. If the quality of enforcement changed so that the
distribution of wedges changes from T to T , the change inhousehold utility would be  1−η

U
Cω
=
H Hω
U
Cω
ω

1
η−1

and the change in industry efficiencies would satisfy thefollowing system of equations

(2)

Cω
Cω

−γ

⎤
 ∗ αρR    αω̂ρ −γ
C
t
ω̂
⎦ .
=
Rωρ ⎣ x∗
t
C
ω̂
x
ρ∈
ˆρ


ω

⎡

ω̂∈

34. The wedge due to imperfect enforcement and input-augmenting productivity affect a firm’s unit cost in the same way. It is important, however, to model
them separately because they affect expenditure shares in different ways. Larger
wedges tend to reduce the share of expenditures on that input because some of theeffective cost is paid to labor; lower input-augmenting productivities do not.
35. An interesting alternative exercise is asking what would happen if {Jω }and {Bωρ } also responded to the change in T.

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The first part of the proposition states that to know how
a change in court quality affects aggregate productivity, it isC
sufficient to know only the changes in industry cost indices, Cωω .
In turn, the change in each industry’s cost index depends on theweighted average over recipes of the change in the cost index of
the industries that supply inputs along with the change in tx∗ , thestatistic that summarizes the direct and indirect impact of thewedges that distort production using relationship-specific inputs.
Equation (2) describes a system of equations that implicitly
characterizes these changes in cost indices.
While Proposition 4 describes exactly how a change inenforcement would alter welfare, it is instructive to study aperturbation of the distribution of wedges to show which featuresof the economy are important for determining the first-order
impact of a change in the quality of enforcement.
COROLLARY 1. The marginal welfare impact of a change in court
quality is
d log U = −

H H ω d log Cω ,ω∈and the change in industry efficiencies can be summarized
by the following system of equations:d log Cω =


ρ∈ω

⎡
Rωρ ⎣α ρRd log tx∗ +⎤αω̂ρ d log Cω̂ ⎦ .

ˆρ
ω̂∈

One implication is that, to a first order, the change in utility
resulting from a change in the quality of enforcement does notdepend on γ or η.36
IV. IDENTIFICATION AND ESTIMATION
Our main counterfactual of interest is how aggregate productivity and the organization of production would change if thequality of enforcement improved. We do this in several steps.
36. This can be viewed as an application of the envelope theorem. For smallchanges T, one can compute the impact on aggregate productivity holding fixed
other choices, that is, holding fixed the technique each firm uses. Thus γ , which
regulates substitution across techniques, does not matter to a first order.

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We first parameterize the model using information from the ASI
under the assumption that the quality of enforcement varies bystate. We then project the implied quality of enforcement for eachstate on our measures of court congestion. Finally, we compute
the gains from reducing congestion to the level prevailing in theleast congested state.
Our most important identifying assumption is that weak
enforcement may introduce a wedge in the use of inputs that
require customization and in the use of labor, but not in the useof standardized inputs. Given our scheme for identification, weview this as a conservative assumption. If the use of standardized
inputs were also distorted by weak contract enforcement, thenall of the wedges would be larger than the ones we infer.
The following proposition shows a set of moments that we
can use in a GMM procedure to estimate the model parameters.
PROPOSITION 5. Let sRj , sHj , sLj be firm j’s spending on relationshipspecific inputs, homogeneous inputs, and labor, respectively,
as shares of its revenue. Under Assumptions 1 and 2, thefirst moments of revenue shares among firms that produce ωthat in equilibrium use recipe ρ satisfy:
&
%
sRj
sH j
E t̄x ρ − ρ = 0
αR
αH
%
&
sLj + sRj
sH j
E
= 0.
−
α Lρ + α ρR
α ρH
ASSUMPTION 3. We impose that the following objects are thesame across states: (i) the form of the production function
for each recipe {Gωρ }; (ii) the power law exponents for the
input-augmenting productivity draws for techniques of eachρρρ
recipe {βl , βω̂1 , . . . , βω̂n }; and (iii) the power law exponents forthe match-specific productivity draws, ζ R and ζ H .
We allow all other features of preferences and technology tovary freely across states. This includes absolute and comparativeadvantages in recipes, {Bωρ }; (ii) the measure of firms of eachtype {Jω }; (iii) the households’ tastes, {υ ω }; and most important,(iv) the quality of contract enforcement, T, and tl .
We also impose a parametric form for the stochastic wedges
that a firm draws for each supplier of a relationship-specific input.

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In particular, the wedge is drawn from a Pareto distribution,
where the shape parameter is specific to a state.37
ASSUMPTION 4. The distribution of wedges in state d isTd(tx ) = 1 − tx−τd for tx  1.
Our algorithm for identification is thus as follows:i. Identify
estimate technology parameters' ρ ρ ρ recipes,(
α L, α H , α R ρ∈ω ,ω∈ , and distortions to the cost of
relationship-specific inputs for each state, t̄xd. We use an
iterative procedure to ensure that our recipe classificationis consistent with the possibility of distortions that varyacross states.
a. Start with an initial guess of t̄xd for each state d.
b. Identify recipes from plants’ cost shares (see the next
section for details), taking out the distortion to thecost shares of relationship-specific inputs t̄xd.
c. Use Proposition 5 to estimate the production
parameters' ρ ρ ρ ( that are common across locations
α L, α H , α R ρ∈ω ,ω∈ and a new set of the state-specificvariables, {t̄xd}.
d. Go back to step i.b until the t̄xd have converged.
ii. Compute tx∗ for each state. Assumption 4 implies that
1

1
R ζR
t̄x = 1 + ζ R+τ
and tx∗ = τd +ζ
. We estimate ζ R exterτddnally, and then use this along with our estimates of t̄x tocompute tx∗ .
iii. For the counterfactual, we also need values of theindustry-level output elasticities of each input for each
recipe, {αω̂ρ }. To do this, we pool data across states toestimate the remaining production function parameters,αω̂ , by using the aggregate expenditures. For example,
if the sourced good ω̂ is relationship specific, then αω̂ρ isρ
equal to α R multiplied by the ratio of total expenditure
37. The Pareto distribution has the attractive property that it is closed underminimization. Following the discussion in Section III.B, contracts might be enforced formally or informally. If the probability that the formal wedge is greater−τ formal

than tx is tx d−τdinformal

and the probability that the informal wedge is greater than tx
−τ

is tx
, then the probability that the effective wedge is greater than tx is tx d ,where τd = τdformal + τdinformal .

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on input ω̂ by those that use recipe ρ to total expenditure
on relationship-specific inputs.
iv. For each state-recipe, directly measure the share of industry ω revenue earned by firms that in equilibrium use
recipe ρ, {Rωρ }. Similarly, directly measure for each state
the share of final demand spent on industry ω, {HHω }.
v. Calibrate η and γ externally.
In implementing this algorithm, we make several auxiliary
assumptions that in principle could be relaxed. First, we assume
that there is no trade across state borders. Although it would be
fairly straightforward to incorporate interstate trade, we lack therelevant data.38 A second assumption is that the recipes used bymultiproduct firms and the distribution of wedges facing them are
the same as those of single-product firms. This type of assumption,
while strong, is standard in the literature, as we lack the datathat indicates which inputs are used in the production of which
products. It allows us to estimate wedge distribution parameters
and the α’s using single-product plants only, while still being able
to make statements about the whole formal manufacturing sector
by including multiproduct plants when we calculate revenue andexpenditure shares Rωρ and HHω . We discuss the treatment ofmultiproduct plants in more detail in Section IV.C. Third, we
treat service inputs and energy inputs as primary inputs.
IV.A. Defining Recipes
One of the salient facts of the Indian manufacturing data isthat even within narrow industries, plants use vastly different
combinations of intermediate inputs to produce the same output.
Our model provides a natural way to think of these input-output
combinations as different recipes ρ ∈ ρ(ω) that could be used
to produce the same output ω. To estimate the model from themicrodata, we need a procedure that classifies each plant-year
observation into which recipe the plant is using.
38. To this point there is no comprehensive, publicly available data about crossstate trade in goods. The conventional wisdom has been that interstate trade isminimal, although the 2016–17 Economic Survey of India’s Ministry of Financechallenges this conventional wisdom. In Online Appendix G.4 we explore how
incorporating interstate trade might alter our counterfactuals. We make the assumption that 10% of inputs are sourced from out of state. We find that this has aminor quantitative impact on our counterfactual results.

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The idea that guides our classification is that for a given
output good, similar input mixes should belong to the same recipe.
We describe each plant j’s input mix by the vector of its input X
expenditure shares, (mj ω̂ )ω̂∈ =   jXω̂  ω̂∈ . Graphically, eachj ω̂ω̂vector corresponds to a point in the ||-dimensional hypercube
that is lying on the hyperplane where the sum of all coordinates
equals one. Our task is to find plants with similar input mixes,
that is, clouds of points that are close to each other (according tosome metric). In statistics, this task is known as cluster analysis,
and there are a large number of algorithms that classify clusters
based on distance, density, shape, and other criteria. Looking
at the input mixes of plants in many different industries (seethe examples of bleached cotton cloth and polished diamonds in
Figure I) convinced us that these clusters do exist and have ameaningful economic interpretation.
Our preferred method is due to Ward (1963) and constructs
clusters recursively, starting with the partition where every
cluster is a singleton. In each step, two clusters are merged tominimize the sum of squared errors: 2mj ω̂ − mρ ω̂ ,minρnρn−1ρ∈ρn j∈ρω̂where the ρ n are partitions of Jω , and in each step ρ n runs overall partitions that are coarser than ρ n−1 . This method constructs
a hierarchical set of partitions of Jω : one for each desired numberof clusters.
Our implementation of the clustering procedure to identify
recipes defines the vector mj as the concatenation of the vector of
j’s five-digit materials shares and its three-digit shares, to allow
for the possibility of misclassification of inputs within three-digit
baskets. We determine the number of potential recipes using theprediction strength method of Tibshirani and Walther (2005).
This procedure is similar to cross-validation. The procedure divides the sample into two subsamples (A and B) and then clusters
the data in each subsample. It then takes the cluster centroids
from A and all of the datapoints from B and assigns them toclusters based on the centroids from A. Each pair of points in B
thus can be categorized as being in the same cluster or different
clusters based on the original clustering of the B subsample andbased on the centroids in A. The procedure then tabulates thefraction of pairs of points for which the two agree. We choose a

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TABLE IVSTATISTICS ON PRODUCTS AND RECIPES
Count
Products (five-digit ASIC)
Products with  three plants
Products with  five plants

4,530
3,573
3,034

Recipes
Recipes with  three plants
Recipes with  five plants
Avg. plants per recipe
Std. dev. plants per recipe

26,776
6,280
2,574
8.2
79.4

Notes. “Products” are the five-digit product codes in our data, “recipes” are the output from our clustering
procedure. Plant counts include only single-product plants.

TABLE VSUMMARY STATISTICS ON RECIPES

Cost share of L
Cost share of XR
Cost share of XH
Number of inputs with cost share > 1%
Number of inputs with cost share > 0.1%

Mean

Std. dev.

Min

Max

0.40
0.27
0.33
4.4
6.4

0.22
0.28
0.30
4.6
12.6

0.0002
0
0
1
1

0.999
0.999
0.998
37
205

threshold parameter of 0.95, meaning that the procedure chooses
the largest number of clusters so that on average at least 95% ofpairs of points agree. Although a lower threshold allows for moreclusters—for example, a threshold of 1.00 is typically consistent
with a single cluster—the relative number of clusters for eachindustry is driven by the shape of the point clouds in the data.39
Table IV shows statistics on the number and size of clusters(recipes) that result from using this procedure, and Table V shows
statistics on cost shares across recipes. We find that among plants
we classify as using the same recipe, most of the expenditures
are on the same set of inputs.40 Figure III shows the resulting
39. In Online Appendix G.2 we show results for alternative values of thethreshold parameter, which varies the degree of recipe fineness.
40. Our model imposes that all firms using the same recipe use the same
bundle of inputs, but our classification algorithm does not. Formally, this can beunderstood in the context of our model as imposing that all plants that we classify
as using the same empirical recipe actually use different recipes that share thesame α R , α H , and α L . We believe that this is a relatively innocuous assumption,

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THE QUARTERLY JOURNAL OF ECONOMICSFIGURE III
Recipe Classification Example: Polished Diamonds (92104)
The figure shows the result from the recipe classification procedure (after correcting for wedged) for “polished diamonds” (92104). Observations that are classified
as belonging to different recipes are tagged with different markers.

classification for the example of the producers of PolishedDiamonds.
Once we have defined recipes, we assign plants to belong
to a recipe with a probability that is proportional to the inverse
Euclidean distance to the recipe center:√(3)

P ( j ∈ ρ) = ρ  ∈ρ(ω)

12ω (mjω −mρω )

√

1

.

2
ω (mjω −mρ  ω )because inputs that are not being used by a plant but are used by some other plants
using the same empirical recipe account for very low cost shares: on average (acrossrecipes, firms, and inputs) for around 0.32% of the recipe’s materials expenditure. It
is likely that some of the differences in input bundles, especially those arising from
inputs with very small cost shares, are due to respondents occasionally omitting
unimportant inputs.

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FIGURE IV
Correlation between t̄x and Court Congestion
The figure shows the correlation between t̄xd and the average age of pending civil
cases in the state’s high court. The solid line is the OLS regression line; the dashedline is the fit of an IV regression where the age of pending cases is instrumented
using the log age of the high court.

We use these assigned probabilities as weights in the estimation
below.
IV.B. Estimation
We estimate the t̄xd, α ρR, α ρH , and α Lρ from the moment conditions in Proposition 5 using our algorithm described above. To
identify the level of t̄x , we set the smallest t̄x to 1, thereby making
the assumption that the least distorted state is undistorted.41
We also exclude state-recipe pairs where the average share of
relationship-specific inputs in sales exceeds that of homogeneous
inputs by a factor of 100 (and vice versa).
Figure IV shows the estimated t̄xd and their correlation withhigh court congestion as measured by the average age of pending
civil cases. Frictions are large: t̄x exceeds 1.75 in the most heavily
41. We view this as conservative. Given the expenditure shares we see in thedata, more severe distortions (larger t̄x ) would raise the estimated output elasticρ
ities of relationship-specific inputs (higher α R ). This would amplify the responses
to changes in enforcement.

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distorted state, and is close to 1.5 in several others. Some ofthat variation is explained by the congestion of courts. In stateswith slower courts, firms face larger distortions (higher t̄x ) whensourcing relationship-specific intermediate inputs. The solid lineis the fit of an OLS regression of t̄x on court congestion; the dashedline is the fit of an IV regression where we instrument court
congestion using the log age of the high court. The estimated IV
slope coefficient is similar to the one in the OLS. This relationshipbetween t̄x and the age of pending court cases is closely related
to the fact that intermediate-input bundles are tilted towards
homogeneous inputs in states where enforcement is weak (Fact
2). The main difference here (beyond the fact that the t̄x arecoming from a nonlinear regression) is that the t̄x are identified
from within-recipe variation in the input mix, whereas Fact 2 isabout within-product variation.
Before proceeding, it is worth discussing how we separate
heterogeneity in production technology (i.e., recipes) from distortions. Given a set of recipes and a classification of plants into
which recipes they use, identification of the α’s and t̄x ’s fundamentally comes from the assumption that the parameters that govern
contracting frictions (the t̄x ’s) vary by state, whereas the recipe
technology parameters (the α’s) are the same across states butvary across recipes.42 Similar to the problem of estimation withgrouped fixed effects studied by Bonhomme and Manresa (2015),
we face the problem of estimating these parameters jointly with
the number of recipes and the assignment of plant observations
into recipes, that is, jointly with the clustering procedure with achoice of the number of clusters. Like Bonhomme and Manresa(2015), we do this by iterating between a clustering procedureand parameter estimation, so that, in our context, the recipeclassification accounts for the possibility of distortions.
The theoretical results in Bonhomme and Manresa (2015)
and Moon and Weidner (2015), who study similar estimation
procedures in closely related models, suggest that our estimation
procedure has the following properties. First, if we choose
the right number of recipes, the estimated distortions will be
42. This is analogous to a nonlinear panel regression. In a panel regression,
one might estimate individual fixed effects and time fixed effects. Here we are
estimating state fixed effects (the distortions) and recipe fixed effects (technology
parameters). The fact that the moment conditions are nonlinear does not change
the basic logic.

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consistent as the number of plants grows large. Second, if wechoose too few recipes, the estimated distortions may be biased,
as the difference in recipe usage across states might be misinterpreted as distortions. Third, if we choose too many recipes, theestimated distortions will be consistent, as the additional recipes
act like irrelevant extra regressors in a least squares regressions.
Although our model is not nested by either of those, we confirm
these large sample properties, and study the small-sample behavior of our estimator, using Monte Carlo simulations in Online
Appendix G.3.
IV.C. Estimating and Calibrating the Remaining Parameters
To perform a counterfactual where we assess the aggregate
effect of a change in the wedge distribution T, Proposition 4
tells us that we need to know the change in the moment tx∗ ofthe wedge distribution that is relevant for the industry’s cost
distribution, which depends on the parameter ζ R and, under ourparameterization of the wedge distribution, on its Pareto tail τ d .
We also need to know the parameters αω̂ρ , the within-industry
sales shares Rωρ of each recipe, the household’s expenditure
shares HHω , and the elasticities γ and η.
1. Estimating ζ . The parameter ζ R , which allows us to backout τ d from t̄x , also governs the elasticity of substitution across setsof suppliers of the same input. Although our data do not indicate
the identity of the supplier of an input, it does indicate whether it
was purchased from a foreign or domestic supplier. We can thus
estimate ζ R using these two groups for each input-output pair:

log

XωDOM
ω̂t
P
XωI M
ω̂t

= ζ log(1 + ιω̂t ) + λt + λωω̂ + ηωω̂t ,where ιω̂t is the import tariff on ω̂ at time t, and the λ’s are fixed
effects. Table VI shows the results for this regression. We use thepoint estimate of 0.218 for ζ R .43
2. Calculating the αω̂ from α R and α H . The elasticities ρ αω̂ canρ 
be recovered as the product of the input-type elasticity α R or α H
43. Choosing a low ζ R is conservative; see the discussion in Section IV.E. We
conduct sensitivity checks in Online Appendix G.1.

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MISALLOCATION IN THE MARKET FOR INPUTS

THE QUARTERLY JOURNAL OF ECONOMICSTABLE VI
ESTIMATING ζ
Dependent variable: log

XωDOM
ω̂t



P
XωI M
ω̂t

(1)

(2)

(3)

log(1 + ιω̂t )0.617(0.44)

0.218(0.77)

1.209∗(0.52)

Industry × Input FE
Year FE

Yes
Yes

Yes
Yes

Yes
Yes

Level

Five-digit

Five-digit

Five-digit

SampleAll inputs

R onlyH only0.601
23,6920.580
12,002

0.623
11,690R2
Observations

Notes. Robust errors are in parentheses, clustered at the state × industry level. + p < .10, ∗ p < .05,∗∗ p < .01. Dependent variable is the log ratio of total expenditure on domestically sourced to total imported

intermediate inputs of type ω̂ among producers of ω at time t. We only use census plants (which are surveyed
every year) to reduce artificial fluctuations that result from sampling.

and the average cost share of plants that produce using recipe ρ:
ρ

ρ

mρ ω̂
if ω̂ relationship specific,ω ∈ R mρ ω̂αω̂ = α R 

αω̂ρ = α ρH mρ ω̂if ω̂ homogeneous.
mρ ω̂ω ∈ H

3. Accounting for Multiproduct Plants. We target the demand aggregator’s expenditure shares HHω and the recipe revenue shares Rωρ to represent the aggregate of India’s formal manufacturing sector, which includes single- and multiproduct plants.
We calculate HHω separately for each state as total sales of ω (fromboth single-product and multiproduct plants) minus total intermediate consumption (less imports) of ω (or 0, if this difference isnegative), divided by the sum of this difference over all products.
To calculate the recipe revenue shares Rωρ , we need toassign the revenue of multiproduct plants to a particular recipe.
We assume that multiproduct plants produce each of theirproducts ω using one or more recipes ρ ∈ ρ ω , with each of themaccounting for a fraction rjωρ of sales of ω. We estimate the rjωρ byminimizing the Euclidean distance between the firm’s observed
vector of materials cost shares mjω and expected cost shares

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(which depend on the rjωρ as well as on t̄xd). We then construct
the recipe sales shares Rωρ using the output of single-productplants and the estimated output of multiproduct plants. This
strategy is model consistent but requires that all recipes usedby multiproduct firms are in the support of recipes used bysingle-product firms (otherwise we would not be able to detect
them in the estimation/clustering procedure). Moreover, whencalculating Rωρ , we pool observations across states and years but
weight each plant-year observation by the inverse of the numberof times the plant shows up in the ASI. This weighting allows us
to construct parameters that better represent the aggregate ofIndia’s formal manufacturing sector.
Finally, we calibrate η = 1 and γ = 1; we show in Online
Appendix G.1 that our counterfactuals are insensitive to theseparameters. Inputs that do not show up in our data as outputs(predominantly agricultural and mineral commodities) are
assumed to have unchanged productivity distributions in the
counterfactual simulation.
IV.D. Counterfactuals
We then perform two counterfactuals. In the first one, we
reduce t̄xd for each state by the amount that is implied by the IV
regression in Figure IV, down to a point where the average age ofpending cases is one year (which is roughly the level of congestion
enjoyed by the best state, Goa). Using our estimate for ζ R , weback out τ d at the original and counterfactual level and compute
1

R ζR
the change in the welfare-relevant moment tx∗ = τd +ζ. We
τdthen compute the corresponding change in the household’s utility
aggregate as given by Proposition 4.
Figure V, Panel A shows the corresponding counterfactual
increase in the household’s consumption aggregate U. The numbers are in the range of 0% to 7%, suggesting that the gains from
improving court speed can be large. That said, there are several
sources of uncertainty around these estimates. The correlation
between court congestion and identified wedges t̄x is a correlation
at the state level and is therefore not very precisely estimated.
Furthermore, the wedges t̄x are estimates themselves, and thismoment will be less precisely estimated in states where we havefewer plant observations.
In the second counterfactual, we reduce the magnitude of
distortions in such a way that the wedges t̄x are half as large

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MISALLOCATION IN THE MARKET FOR INPUTS

THE QUARTERLY JOURNAL OF ECONOMICSFIGURE VCounterfactural Increases in Aggregate Productivity
The figure shows the counterfactual increase in C when the wedges on
relationship-specific inputs are reduced. In Panel A we reduce t̄x according to
the fraction of t̄x that is explained by court congestion in a linear IV regression(Figure IV); in Panel B we cut the t̄x in half.

as in the estimates. This counterfactual is independent from thecorrelation of wedges with the measured congestion in the highcourts, and would thus reflect an improvement in the overall
quality of contract enforcement. Figure V, Panel B shows thecounterfactual increase in U for each state. U would increase by
7.1% on average and by more than 10% in the most distorted
states. These welfare gains are more precisely estimated thanthose for the first counterfactual; however, they are still subject torandom variation in the estimated wedge moments t̄x that comesfrom the fact that we do not observe the universe of smaller
plants, just a random sample of them.
IV.E. Direct and Indirect Costs of Distortions
The model captures the idea that buyer–supplier relationships differ in their susceptibility to imperfect contract enforcement. Some buyer–supplier pairs are able to enforce contracts
informally or transact in a way that avoids holdup problems. To
capture this in a parsimonious way, we assume that the buyer
draws a distortion for each potential supplier from a distributionthat deteriorates when formal enforcement is less reliable.
Our estimation procedure identifies t̄x for each state, whichis the (harmonic) average of the realized distortions. Thissummarizes the direct cost of weak enforcement on users ofrelationship-specific inputs. tx∗ captures the direct and indirect
cost of the distortions. We infer the indirect cost by estimating

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ζ R , which indexes the probability that a firm has a comparable
alternative supplier. Jensen’s inequality implies that t̄x  tx∗ ,which implies that the t̄x is a lower bound for the total impact, andthis lower bound is attained only if the distribution of distortions
T is degenerate. In that case, a firm faces the same wedge for all
suppliers and could not avoid a distortion by substituting to analternative supplier; as a result, there would be no indirect cost.
The respective contributions of the direct and indirect effects
depend on both the value of ζ R and the levels of the distortion.
Given our estimates and the range of t̄x we observe, the direct
effect comprises much more of the effect of weak enforcement, but
the indirect effects are nontrivial. For the average state, the indit∗ −t̄rect impact accounts for x t∗ x = 6% of the total impact, and for thexmost distorted state the indirect impact accounts for about 23%.
IV.F. The Role of Heterogeneity
An alternative approach that is common in studies thatmeasure misallocation using input-output tables is to posit
industry-level Cobb-Douglas production functions and backout distortions from differences across states (or countries) inindustry-level cost shares.44 In our view, our approach has several
advantages over this alternative.
First, a cursory look at the data indicates that plants areproducing using different technologies (i.e., some appear to
be more vertically integrated than others). We believe thatallowing for several recipes facilitates making apples-to-apples
comparisons when measuring the effect impact of distortions. Our
identification strategy relies on comparing input expenditures
among plants that, in equilibrium, use the same recipe. With theindustry-level approach, differences in recipe composition acrossstates could lead researchers to infer spurious distortions.
Second, the industry-level approach would miss the indirect
effect of the distortions. Given our identification strategy andconditioning on the data, the fact that wedges differ across
suppliers implies indirect productivity losses due to plants
switching to alternative suppliers to avoid a distorted input. This
raises the implied productivity loss from imperfect enforcement.
44. Our model nests such a model as a special case when there is a single
recipe per industry and the distribution of wedges T is degenerate so that all
suppliers of relationship-specific inputs face the same wedge.

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Our identification strategy consists of measuring {t̄x } and then using these along with our functional-form assumptions to computetx∗ . In the industry-level approach, there is typically only a direct
effect.
Third, as discussed earlier, there is quite a bit of heterogeneity in cost shares across plants. This leads to the following
situation: there are occasionally state-industry pairs that are
dominated by a small number of plants, and the aggregate costshares among these plants happen to deviate quite a bit from theindustry average. If we used the industry-level cost shares to backout a wedge for that state-industry, we would conclude that thestate-industry is severely distorted. In contrast, our estimating
equations treat each individual plant as an observation, and themodel has a structural error term for the cost share of each plant,
which stems from different productivity and cost draws. Thus ourapproach allows for the possibility that such a state-industry has
an extreme cost share because of its draw of a technique; we are
not forced to conclude that the distortion for the state-industry is
severe.
IV.G. Entry and Exit
In our benchmark model, we assumed that the numberof producers of each product is given exogenously. Of course
we would expect that if the formal enforcement improved,
profitability would increase more in industries that rely moreheavily on relationship-specific inputs. We do in fact observethat as formal enforcement deteriorates, the number of firms
decreases relatively more in the industries that rely more heavily
on relationship-specific inputs (see Table D.3 in Online Appendix
D.3). Thus it is likely that the quality of enforcement affects
firms’ entry and exit decisions.
How would our estimates differ if firms could endogenously
enter and exit? Our estimates of contracting frictions andtechnology would be unchanged because the strategy places norestrictions on the determinants of the set of firms. Nevertheless,entry and exit may be important for the counterfactuals we conduct. Exactly how depends on the specifics of entry and exit andthe particular counterfactual. Consider the following two possibilities. First suppose firms were committed to enter but could choose
which industry to enter. Then the additional adjustment after
formal enforcement improved could raise aggregate productivity

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even more than a benchmark model suggests.45 Second, supposethat firms were committed to producing in a particular industry
but choose which state to locate in. Here, if formal enforcement
improves in one state, aggregate productivity in that state would
rise as firms for other states moved in. However, aggregate productivity in other states would fall as firms moved out. This suggeststhat the response to nationwide improvement in formal enforcement would differ from the response to a single state improving
enforcement. Furthermore, cross-sectional evidence about how
the number of firms responds to changes in enforcement may
not be informative about the economy’s response to a nationwide
improvement.
IV.H. Interpretation of Our Estimates
Our estimates suggest that lowering the degree of congestionin high courts to the level enjoyed by the most efficient states
would bring about productivity increases of on average 4%. For
several reasons this estimate is likely to be a lower bound for theoverall productivity loss arising from poor contract enforcement.
First, even the least congested Indian courts suffer from otherproblems that constitute imperfections in the enforcement of contracts that are not captured by our court quality measure (such as
objectivity and incorruptibility). Second, if contracting frictions
are also present for homogeneous intermediate inputs, our estimates of the productivity gains from improving courts are biased
downward.46 Third, holdup problems are particularly severe forservices inputs, which account for a substantial fraction of cost insome industries; hence court improvement could lead to substantial additional cost reductions (Boehm forthcoming). Formal enforcement is also likely to be important for the smallest firms that
may be less able to rely on reputation. Moreover, courts matter for
economic outcomes beyond their role in mitigating holdups with
suppliers, notably by improving contracting between managers
45. In Online Appendix G.5, we posit such a model and study how our counterfactual exercises might change. We show that if the household’s elasticity of
substitution across industries (η) is one, as we have assumed in our calibration,then the improvement in aggregate productivity is the same as in our baseline.
46. That said, Johnson, McMillan, and Woodruff (2002) bring survey evidence
that the role of courts in determining supplier switching is about five times as large
for relationship-specific inputs than for standardized inputs, suggesting that mostof the productivity gains are correctly accounted for.

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THE QUARTERLY JOURNAL OF ECONOMICS

and workers (Besley and Burgess 2004; Bloom, Sadun, andReenen 2012), and improving access to financing (Visaria 2009).
V. CONCLUSION
This article studies the organization of production in the Indian manufacturing sector and how it relates to the quality of formal contract enforcement institutions. We make two main points:
one about the within-industry heterogeneity and measurement of
the organization of production, and a second one about how institutions shape intermediate-input use and aggregate productivity.
First, we show that there is considerable heterogeneity
in technology and organization even within narrowly definedindustries. These differences should be reflected in the level ofaggregation at which researchers assume a homogeneous shapeof the production function. We argue that information on input
use can be helpful in understanding differences in organizationand technology within industries: a plant that produces cotton
cloth from raw cotton has a long vertical span of production
and performs both spinning and weaving, whereas a plant that
produces cotton cloth from cotton yarn will only perform theweaving and might therefore have different factor intensities. We
provide a simple and flexible way of finding groups of firms that
use the same production function (which we call recipes) using astatistical clustering algorithm.
Second, we find that the organization of production is shapedby the contracting environment. We find that slow enforcementof contracts impedes the use of relationship-specific materials.
As a result, firms tilt their input basket toward the use of
more standardized inputs, for which spot markets exist, andfor which enforcement by courts is not necessary. We develop
a multi-industry general-equilibrium model where firms source
multiple inputs and choose the organizational form optimallyto minimize the cost of production. We estimate the relative
distortions associated with the use of relationship-specific inputs
from first moments of cost shares, which, compared with thestandard approaches of estimating input wedges, is more robust
to potentially imprecise measurement of input use. Our results
suggest that distortions associated with poor courts are sizable
and that improving courts would increase welfare: reducing
the average age of pending cases by a year would, on average,
increase a state’s aggregate productivity by about 2%.

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SCIENCES PO
PRINCETON UNIVERSITY
SUPPLEMENTARY MATERIAL
An Online Appendix for this article can be found at The
Quarterly Journal of Economics online.
DATA AVAILABILITY
Data and code replicating tables and figures in this article
can be found in Boehm and Oberfield (2020), in the Harvard
Dataverse, doi: 10.7910/DVN/OGP2EK.
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