The Impact of Contract Enforcement Costs on Value
Chains and Aggregate Productivity
Johannes Boehm∗
April 19, 2020
Abstract
Contracting frictions affect the organization of firms, but how much does thismatter on the aggregate level? This paper studies how costly supplier contract enforcement shapes the patterns of intermediate input use and quantifies the impactof these distortions on aggregate productivity and welfare. Using the frequency of
litigation between US firms as a novel measure to capture the potential for hold-up
problems and therefore the need for formal enforcement, I find a robust relationshipbetween countries’ input-output structure and their quality of legal institutions: incountries with high enforcement costs, firms have lower expenditure shares on intermediate inputs in sector pairs where US firms litigate frequently for breach ofcontract. I adapt a Ricardian trade model to the study of intersectoral trade, andshow that the variation in intermediate input shares that is explained by contracting frictions is large enough to generate sizeable welfare increases when enforcement
institutions are improved.

Countries differ vastly in the speed and cost of formal contract enforcement: while
Icelandic courts often resolve commercial disputes within a few months, cases in India
that are decades old are commonplace.1 A large and prominent literature has argued thatthese institutional frictions constitute transaction costs between firms, which affect theirorganizational choice and intermediate input sourcing decision (Williamson, 1985), andpotentially even the pattern of development (North, 1990). The logic goes as follows: if
enforcement of supplier contracts is costly or impossible, firms will perform a larger partof the production process in-house, instead of outsourcing it, thereby avoiding having tocontract with an external supplier. Compared to a world with good enforcement, firms
will have a lower expenditure on externally sourced intermediate inputs, and a higher cost∗

Boehm: Department of Economics, Sciences Po, 28 Rue des Saints-Peres, 75007 Paris, France. Email:johannes.boehm@sciencespo.fr. I thank Francesco Caselli, Lorenzo Caliendo, Thomas Chaney, DavinChor, Swati Dhingra, Ben Faber, Teresa Fort, Luis Garicano, Jason Garred, Sergei Guriev, Beata Javorcik,
Danial Lashkari, Kalina Manova, Thierry Mayer, Michael Peters, Veronica Rappoport, Markus Riegler,
John Sutton, Silvana Tenreyro, Catherine Thomas, John Van Reenen, and audiences at many seminars
and conferences for helpful comments. I am grateful to Andreas Moxnes for sharing data, and to the ESRC
and a LSE Bagri Fellowship for financial support.
1
Council of Europe (2005), Supreme Court of India (2009)1

of production. Higher production costs then feed into higher input prices in downstream
sectors, thus amplifying the distortions on the macroeconomic scale.2 While these Coasiantransaction costs are widely acknowledged to determine firm-level outcomes such as the organization of production, we know little about whether they really matter for the aggregate
economy and the level of development.
This paper studies the quantitative importance of legal institutions and imperfect contract enforcement for aggregate outcomes using tools from quantitative trade theory, together with data on contract enforcement costs and intermediate input expenditure sharesacross countries. I start by showing a set of correlations between industries’ bilateral intermediate input expenditure shares, as observed in Input-Output tables, and the degreeof contracting frictions between them— which I measure, similar to Rajan and Zingales(1998), as the product of the country’s quality of contract enforcement in courts, and theindustries’ bilateral dependence on formal contract enforcement. To measure this dependence on formal enforcement, I construct an index of observed litigation between firms fromtwo sectors using microdata on US case law: firms will only go to court when there is noother way to resolve hold-up problems, and this is when the quality of courts matters.3 The
stylized fact that emerges is that in countries where the enforcement of supplier contracts incourts is more costly, intermediate input expenditure shares are lower in sector-pairs where
litigation (in the US) is more prevalent: enforcement institutions are not only correlatedwith the sectoral specialization of countries, but also with the input mix used to produce
in each of them. Since my novel measure of firm’s dependence on enforcement is a bilateral(sector-pair-specific) measure, I can include fixed effects for upstream sectors × countries,
and thereby control for a vast amount of industry characteristics that may be confounding
the role of frictions in buyer-supplier relationships. This strategy allows me to separate
the role of legal institutions in the enforcement of buyer-supplier contracts from its role in
the provision of financing, and get stable and robust results. The resulting patterns canbe explained by theories where buyers of relationship-specific goods can hold up their suppliers, and where enforcement of contracts in a court is a solution to the hold-up problem
as long as courts are sufficiently good.
In order to interpret these observed correlation and to perform counterfactuals, I construct a general-equilibrium model of domestic intersectoral trade. For each step in the
production process, firms face the decision between performing it in-house using labor,
which is frictionless, or sourcing it from a plant belonging to an upstream sector, in whichcase they may benefit from a lower cost draw but are subject to contracting frictions that
distort the cost of sourcing. These frictions are transaction costs in the spirit of Coase2

Nunn (2007) and Levchenko (2007) show that institutional quality affects comparative advantage ofa country through this channel; see also the handbook chapter by Nunn and Trefler (2014). The ideaof a ’multiplier effect’ of intermediate input linkages goes back to Hirschman (1958), with more recent
applications to development patterns by Ciccone (2002), and Jones (2011, 2013).
3
Similarly to the argument in Rajan and Zingales (1998), the cross-industry variation in litigation for acountry with good institution will capture the technological factors underlying the propensity to litigate,
such as the degree of relationship-specificity.

2and Williamson. Hence, intermediate input shares are determined by the relative productivity under in-house production and under outsourcing, and by bilateral contracting
frictions. This relationship resembles a gravity equation in international trade: contracting frictions reduce intermediate input shares in a similar way to how iceberg trade costs
reduce international trade shares. The resulting equation is hence the structural (nonlinear) counterpart to the reduced-form regressions from before: when frictions are large,
firms perform a larger range of tasks in-house, resulting in lower expenditure shares on
externally sourced intermediate inputs.4 Using results from theories of hold-up in bilateralbuyer-supplier relationships and using the data on litigation between US firms, I identify
the role of contract enforcement costs in shaping contracting frictions. The key idea behind the identification is that for a given level of institutional quality, litigation will only
be observed when formal contracts (where parties have the option to enforce it in a court)
are preferable over informal ones (where product-specific attributes such as the degree ofrelationship-specificity entirely determine incentives in the relationship). This allows me
to invert the mapping between the product-specific attributes and litigation and use thelitigation data to estimate the distortions under formal and informal contracting, and inturn to estimate the parameters of the gravity equation for intersectoral trade. I then study
the importance of contract enforcement institutions for aggregate welfare by simulating themodel under counterfactually low enforcement costs.
The exercise reveals that supplier contracting frictions distort intermediate input use
to an extent that makes them relevant on the macroeconomic scale: even under the mostconservative specifications, many countries would see their output grow by between two andeight percent if they had access to the enforcement institutions of the United States. The
sectors that would benefit the most are those where intangible inputs and relationshipspecific components are an important part of the production process: improvements incontracting institutions would allow firms to outsource these tasks and components tospecialized suppliers. These improvements, however, need to be large enough to push firms
to adopt formal contracting relationships: as long as firms prefer informal “gentlemen’s
agreements” over formally enforceable contracts, a marginal improvement in court quality
will have no effect. The effects that I estimate are due to the improved contracting between
buyers and sellers alone; they are not due to better access to financing or due to otherbenefits from improved legal institutions.
4

Strictly speaking, input-output tables are constructed at the plant level, and within-firm across-planttransactions are part of the observed cost shares (through recent work by Atalay et al. (2014) using US
data shows that most vertical flows are across-firm rather than within-firm). The estimated welfare gains
in this paper depend on the difference in frictions in the plants’ use of primary factors and the use ofintermediate inputs that is explained by the quality of enforcement institutions. If both are distorted,
then our estimates would underestimate the true importance of enforcement costs. If some intermediate
input use is not subject to hold-ups (perhaps because the transactions are intra-firm), that decreases thewelfare gains from reducing enforcement costs that we estimate through the decrease in explanatory powerof enforcement costs. Hence, for the estimation of the counterfactual welfare gains, we can be agnostic
about how much of the intermediate inputs are sourced from within the firm. Section 3.3.1 discusses thispoint in more detail.

3

This paper is related to several different literatures. The first is the literature on legal institutions and trade, and includes, among others, contributions by Nunn (2007),
Levchenko (2007), Costinot (2009), and Chor (2010), who show that legal institutions determine countries’ industry mix and comparative advantage. In contrast, I provide direct
evidence that each industry’s mix of inputs is distorted by poor enforcement; these distortions then increase the cost of production. The distinction is not only of interest by
itself, but also has implications for countries’ exposure to trade shocks and for the verticalpropagation of shocks – in short, whenever the network structure of production matters for
economic outcomes.5 It also yields a powerful new way to identify and quantify the role ofenforcement institutions in shaping development.
The paper also links to the theoretical and empirical literature on the determinantsof the fragmentation of production along the value chain – both in the sense of spatial
fragmentation, i.e. the value chain spanning several countries, and in the sense of the value
chain being broken up into work done by different firms (the question of the firm boundary).
Some parts of that literature view both geographic and firm borders as transaction costs(see, for example, Fort (2017) on communication costs and human capital, Kee and Tang
(2016) on trade costs, Acemoglu et al. (2010) on technology, and, most recently, Atalay
et al. (2019) on the role of the firm border). Parts of this literature, in particular those that
discuss the firm border6 , build on the property rights approach pioneered by Grossman andHart (1986) and Hart and Moore (1990) and integrated into the literature on global sourcing
by Antràs (2003) and Antràs and Helpman (2004). My paper is most closely related to workthat emphasizes the role of contractibility of inputs (Antràs and Chor, 2013, Alfaro et al.,2019) but deviates from the standard incomplete contracts setup to allow for institutional
characteristics to affect equilibrium performance on the margin. This feature allows for ameaningful interpretation of the systematic patterns of litigation that we observe in thedata, and for a tighter integration of quantitative measures of institutional quality in thequantification exercise. Another point of departure from the global value chains literatureis that I focus entirely on domestic value chains. This has the advantage that the role oflegal institutions is easier to identify in a domestic setting (international trade contracts
are often written to be enforced in a third-party country). Compared to the internationalsetting, I can also cover services trade, which not only accounts for a large fraction of
economic activity, but is also particularly prone to hold-ups due to services being intangible
by nature. This aspect also distinguishes the magnitude of results in this paper from thosein the literature on quantitative trade models with multinational production.7
The paper is also related to the recent literature on the importance of intermediate
inputs and linkages for aggregate productivity (Jones, 2011, 2013, Caliendo and Parro,
2015, Caprettini and Ciccone, 2015, Oberfield, 2018). This literature typically takes the5

See recent work by Baqaee and Farhi (2019, 2020) on this topic.
Bresnahan and Levin (2013) give an overview of the literature on vertical firm boundaries.
7
See recent contributions by, among others, Garetto (2013), Tintelnot (2016), Irarrazabal et al. (2013),
Fally and Hillberry (2018), and Ramondo and Rodriguez-Clare (2013).
6

4

structure of intersectoral linkages as exogenous, or even uses the US input-output table todescribe the industry structure in other countries. In contrast, I show that input-output
tables differ substantially and systematically across countries and exploit the systematiccomponent of the variation in the empirical analysis. In this sense, the most closely related
papers are by Bartelme and Gorodnichenko (2015), Caliendo et al. (2017), and Liu (2017),
who also document the cross-country dispersion in intermediate input shares and link it toaggregate productivity. The contribution of this paper differs from those by pointing to aparticular source of these frictions and showing that they are quantitatively significant.
Finally, the paper is related to the literature on legal institutions and their macroeconomic effects (Rajan and Zingales, 1998, La Porta et al., 1997, Djankov et al., 2003,
Acemoglu and Johnson, 2005, Acemoglu et al., 2009, and many others). These papers use
reduced-form regressions to evaluate the overall importance of institutions for growth anddevelopment. This paper contributes to this literature by providing reduced-form evidenceof one particular channel – the role of legal institutions in enforcing supplier contracts –and by quantifying its importance through structural econometric modelling. Most importantly, my setup accounts for the possibility to use informal ways of enforcing contracts,
which lessen the dependence on formal enforcement institutions. The channel I study is
independent of other functions of legal institutions, such as the protection of financial investors8 , the enforcement of employment contracts9 , or the provision of incentives to invest
in better technology10 .

1

Reduced-form Empirical Evidence

1.1

Empirical Strategy

My approach to identifying the importance of legal institutions relies on the differencesin the degree to which buyers and sellers require formal enforcement of contracts. Sometransactions will be unaffected by the quality of legal institutions, such as when the presenceof spot markets or relational contracts guarantee the efficient outcome. The literature
on incomplete contracts, following Klein et al. (1978), has given various justifications forcontracts being incomplete: either the terms of the contract are not describable (in whichcase the incompleteness stems from the nature of the good or service being transacted),or judges do not understand them, or the costs of enforcement are prohibitively high. In
the latter two cases the incompleteness originates from the quality of the judicial or legal
institutions. In the former case, however, the quality of institutions will not matter for
performance in the bilateral buyer-seller relationship.
8

See Ponticelli and Alencar (2016) on the quantitative effects of bankruptcy reform in Brazil, and Laevenand Woodruff (2007) and Chemin (2012) on judicial efficiency and firm size and productivity in Mexico
and, respectively, India.
9
See recent work by Grobovsek (2020).
10
In related theoretical work, Acemoglu et al. (2007) show that supplier contracting frictions in thesourcing of intermediate inputs may lead firms to adopt inferior technologies.

5

I study the correlation between the input-output structure of an economy, which captures the inter-sectoral flows of goods and services, and the quality of its legal institutions.
More specifically, I estimate the following reduced-form regression:
(1)

c
Xni
= βδ c × zni + αni + αic + αnc + εcni
Xnccwhere Xni
is the total expenditure of sector n in country c on intermediate inputs fromsector i, both domestically and internationally sourced; Xnc is the gross output of industry
n in country c; δ c is a country-level measure of the cost of enforcing contracts (and hence
inversely related to the quality of legal institutions); zni is a bilateral measure of how much
sectors n and i depend on formal enforcement of contracts; αni are sector-pair fixed effects;
αic are upstream sector times country fixed effects, and αnc are downstream sector times
country fixed effects. The intermediate input expenditure shares on the left-hand sideof equation (1) are directly observed in input-output tables. In the field of input-output
analysis they are called the “empirical technical input coefficients”, and are typically seen as
exogenous parameters that describe the technical requirements of the production process.
In equation (1), country- and sector-pair-specific expenditure shares are explained by aninteraction of a country characteristic (the quality of legal institutions) with a sector-paircharacteristic (the dependence on formal enforcement) and sector-pair fixed effects. Hence,the coefficient β captures the correlation of interaction term and left-hand side within sector
pairs and across countries. If β is negative, countries that have worse legal institutions havelower intermediate input shares in sector-pairs that rely heavily on formal enforcement.
Additional fixed effects, along the upstream sector × country and downstream sector ×
country dimensions, further condition this correlation on attributes that vary along these
dimensions.
Equation (1) is similar to the functional form used by Rajan and Zingales (1998) andmany subsequent papers, who explain country-sector-level variables using an interaction ofa country-specific variable (often institutions or, as in the original paper, access to financial
markets) with a sector-specific variable, while controlling for country- and sector-attributes
using fixed effects. In order to interpret a significant coefficient on the interaction term as a
causal effect, this literature typically goes to great lengths to try to control for the plethoraof confounding factors that co-vary with the interaction term. Equation (1) improveson this by exploiting variation across three different dimensions (country, upstream, anddownstream sector). Hence, I can include fixed effects at the sector × country level, thereby
controlling for unobserved heterogeneity in the upstream and downstream sectors.
Equation (1) also decomposes the variation of intermediate input shares into variation
along different dimensions. In order to find any significant conditional correlation β, there
must be cross-country variation in the left-hand side, and hence in input-output tables ingeneral. If input-output tables are either the same across countries, or if the differences arevery small (as a large number of papers tacitly assumes), then the sector-pair fixed effect6

should explain most of the variation in the left-hand side. The conditional correlation with
the interaction term will likewise be zero if the variation in input-output tables is purenoise. We will see that neither of that is the case.
The regression equation is also similar to the ones proposed by Nunn (2007) and
Levchenko (2007), who show that in countries with bad institutions, sectors that rely
heavily on legal institutions trade relatively less with foreign countries. International tradecontracts, however, may in principle be governed by the law of any trading partner, oreven a third-party country. The advantage of using input-output relationships to study
the importance of institutions is that one can be almost certain that the vast majorityof transactions are governed by the local law and institutions. In addition, there is anadditional dimension of variation in the data, which will help to distinguish contracting
frictions from productivity differences across countries and sectors.

1.2

Data

Intermediate Input Expenditure Shares My data on intermediate input expenditure
shares comes from the GTAP 8 database, (Narayanan et al., 2012). GTAP contains tablesfrom 109 countries, from varying years ranging from the 1990’s to mid-2000 (see Appendix
A), but all based on the 1993 System of National Accounts. These tables typically originate from national statistical sources and have been harmonized by GTAP to make theminternationally comparable. A notable feature of this dataset is that it includes many
developing countries, for which industry-level data is typically scarce. The tables coverdomestic and import expenditure for 56 sectors, which I aggregate up to 35 sectors thatroughly correspond to two-digit sectors in ISIC Revision 3. My main variable of interest
is Xni /Xn — the share of expenditure of sector n on intermediate inputs from sector i, ingross output of sector n. Whenever not mentioned explicitly, these intermediate input purchases include imported inputs. All results are robust to excluding imported intermediate
inputs (see Appendix D).
Quality of legal institutions / enforcement costs My measure of institutional quality δ c is the “cost of contract enforcement” from the World Bank Doing Business survey.
This variable measures the monetary cost necessary to enforce a standardized fictional supplier contract in a court, and is collected through surveys of local law firms. The monetary
cost is the total cost that the plaintiff (who is assumed to be the seller) must advance toenforce the contract in a court, and is measured as a fraction of the value of the claim. It
includes court fees, fees for expert witnesses, attorney fees, and any costs that the seller
must advance to enforce the judgment through a sale of the buyer’s assets.
The cost of enforcement from Doing Business has been widely used to proxy for thequality of contract enforcement (e.g. Acemoglu et al., 2009, Nunn, 2007). While no measureof institutional quality is without drawbacks, there are two reasons why this particularmeasure lends itself well to my purposes: first, it is not based on observed litigation, and7hence does not suffer from a potential bias due to firms switching to informal contracts
when enforcement costs are too high. Second, unlike indices that aggregate over different
dimensions of institutional quality, it has a direct quantitative interpretation. This will be
useful when studying the quantitative importance of enforcement institutions in Section 3.
Dependence on Enforcement I construct a novel measure of dependence on formal
enforcement from data on observed litigation between firms. My measure is the frequency
with which firms from a particular sector-pair resolve conflicts in court, or more specifically,
the number of court cases between two sectors over a fixed period of time, per buyer-seller
relationship. I collect this data for one particular country where legal institutions are good(the United States), so that institutional quality itself is not censoring the prevalence of
litigation in an asymmetric way across sectors.
My data come from the LexisLibrary database provided by LexisNexis, which covers
cases from US federal and state courts. I take all cases between January 1990 and December
2012 that are related to contract law, ignoring appeal and higher courts, and match theplaintiff and defendant’s names to the Orbis database of firms, provided by Bureau Van
Dijk. Orbis contains the 4-digit SIC industry classification of firms; I thus know in which
sectors the plaintiffs and defendants are active in. I count the cases by (unordered) pairof sectors, and assign the plaintiffs and defendants to the two sectors in proportion to theexpenditure flows in the US input-output table.11 To obtain the likelihood of litigation
between the two sectors, I divide the observed number of cases by a proxy for the numberof buyer-seller relationships between firms from each pair of sectors. My first proxy for thisvariable is the geometric mean of the number of firms in each sector, which reflects thatthe number of trading relationships will generally be increasing in the number of firms in(1)each sector. This yields a measure zni .12 As an alternative, I use data from Japan, where
the number of buyer-seller relationships by sector-pair can be constructed from microdata,
to fit a linear model describing the number of relationships with the number of firms ineach sector and the input-output expenditure shares, and then use the predicted value for(2)
the US to normalize the number of cases, yielding a measure zni .13 These two measures
are capturing the likelihood of litigation, and hence enforcement-intensity, in each pairof sectors. Appendix A provides detailed information on the construction procedure ofnumerator and denominator in both measures, discusses the content of cases for particular11

If sales from the petroleum to the chemicals industry account for 80% of the total sales between
petroleum and chemicals, then I assume that 80% of the cases between petroleum and chemicals are
related to sales of petroleum to chemicals. Appendix D shows results using a measure where the plaintiff
is the seller, which is by far the most common case. All results also hold using these measures.
12
Results are robust to (1) using the number of cases divided by the number of upstream sector firms(or downstream sector firms) as a measure of enforcement-intensity; (2) using the number of firms fromthe Census Bureau’s Statistics on U.S. Businesses instead of the number of firms in Orbis.
13
The exact procedure, as well as results on the goodness of fit, are in Appendix A.3.2. I am gratefulto Andreas Moxnes for sharing the statistics on the number of Japanese buyer-seller pairs. See Bernard
et al. (2019) for more detailed information on the data source.

8

sector pairs, and compares the measures to existing measures of dependence on institutions.
(2)(3)(# cases between sectors i and n)(1)
zni = p(# firms in sector i) (# firms in sector n)(# cases between sectors i and n)
(2)
zni =
\ between i and n)(# buyer-seller relationships

Table 1 shows the ranking of upstream sectors by the average degree of enforcement(1)(2)
intensity, as measured by zni (the ranking for zni is similar). Services sectors are on
average more enforcement-intensive than manufacturing sectors, which are in turn more
enforcement-intensive than raw materials-producing sectors. Once a service has been performed, it cannot be sold to a third party, thus the scope for hold-up should be high. On
the other end of the spectrum, raw materials have low depreciability and may be readily
obtained through organized markets, thus there is relatively little scope for hold-up. A
similar ranking is usually regarded to apply to the degree of relationship-specificity of inputs. Hence, my measure is consistent with the view that relationship-specific investment
leads to an increased dependence on formal enforcement.

Figure 1: Enforcement-intensity z (1)Note: Figure shows the enforcement-intensity measure z (1) by sector pair. Selling sector is on the xaxis, buying sector on the y-axis. Darker shades indicate higher values. Values have been monotonicallytransformed to improve readability.

Figure 1 shows the within-sector variation in z (1) in more detail. There is much litigation
between firms belonging to the same sector, as the diagonal in the matrix demonstrates.
9

(1)Table 1—: Average enforcement-intensity of upstream sectors, zni measure.
(1)

(1)

Upstream sector

zni · 104

Upstream sector

zni · 104

Insurance
Business services nec
Financial services nec
TradeElectricity
Chemical,rubber,plastic prods
Transport nec
Machinery and equipment nec
Air transport
Communication
Ferrous metals
Construction
Sea transport
Metal products
Metals nec
Agriculture, Forestry, Fishing
Motor vehicles and parts
PubAdmin/Defence/Health/Educat

1.515
1.307
0.863
0.483
0.399
0.371
0.337
0.225
0.211
0.205
0.205
0.199
0.194
0.176
0.147
0.130
0.130
0.121

Paper products, publishing
Manufactures nec
Transport equipment nec
Recreation and other services
Mineral products nec
Electronic equipment
Petroleum, coal products
Water
Coal
Minerals nec
Food products and beverages
Oil and Gas
Wearing apparel
Wood products
Gas manufacture, distribution
Leather products
Textiles

0.103
0.097
0.095
0.090
0.082
0.082
0.080
0.072
0.069
0.049
0.048
0.036
0.031
0.028
0.027
0.023
0.021

(1)

Note: The table shows the enforcement-intensity zni of an upstream sector i, averaged across downstream
sectors.

Many of these disputes arise in the licensing of intellectual property, which, due to its
intangible nature, relies heavily on enforcement by courts. But even apart from the diagonal, the firms’ propensity to litigate seems to vary considerably across different buyer
sectors: transport equipment sales, for example, are more likely to be associated with litigation when the buyer is from the ocean shipping industry, than when she belongs to
the land transport industry (“transport n.e.c.”). Sometimes, as in this case, the different
litigation rates arise because goods and services supplied to different sectors have different
characteristics, which then lead to different likelihoods of disputes; in other cases it is due
to particular market structures or regulation. Appendix A.3.3 documents some of thesedifferences based on the case descriptions in LexisLibrary.
Comparison to existing measures The above measures are related to existing measures of dependence on legal institutions, such as the ones of Nunn (2007) and Levchenko(2007)14 , but differ in three important ways. First, the existing measures are only available
for physical goods, whereas my measures cover services sectors as well. This extension
is important because services contracts seem to rely heavily on formal enforcement — atleast in the United States — and they account for a large share of intermediate inputs andof overall economic activity. Second, the existing measures rely heavily on each sector’s
14

Nunn (2007) uses the fraction of a sector’s inputs that are traded on an organized exchange to describe relationship-specificity, arguing that legal institutions will matter only when relationship-specificinvestment lead to hold-ups. Levchenko (2007) uses the Herfindahl index of input shares to measure product complexity, with more complex products relying more heavily on institutions. Bernard et al. (2010)
measure contractability as the weighted share of wholesalers in overall importers.

10intermediate input mix, which, as I will show further below, varies sharply across countries and is likely to depend on the country’s quality of institutions. Third, my measurevaries across bilateral sector-pairs, instead of being associated with the upstream sector.
Given that the sectors in the input-output table dataset are fairly broad, it is likely thatthe products being sold to one sector are quite different to the ones sold to other sectors,
and that the form of interaction varies with the trading partner. Despite these conceptual
differences, Table 2 shows that the enforcement-intensity measures are mildly positively
correlated with the measures of Nunn (2007) and Levchenko (2007).
Table 2—: Pairwise correlations, dependence on institutions
(1)

(1)

z̃n
(2)
z̃n
NunnconnNunnlibn
Levchenkon

(2)

z̃n

z̃n

NunnconnNunnlibn

Levchenkon

1.00
0.93
0.20
0.22
0.13

1.00
0.03
0.03
0.14

1.00
0.99
0.68

1.00
0.61

1.00

Note: The table shows the pairwise correlation coefficient between the average z (by downstream sectorn, weighted across upstream sectors i using the US intermediate input shares), as well as Nunn (2007)’sand Levchenko (2007)’s measures of dependence on institutions. The latter is defined here as one minus
the Herfindahl of cost shares. See Appendix A.3.4 for details on the construction.

Using observed litigation to measure the dependence on formal enforcement has advantages and drawbacks. One advantage is that it allows me to ignore the many different
possible solutions to the hold-up problem that the microeconomic literature has pointed
out: if we observe firms going to court, it must mean that the other solutions are notapplicable or have failed. The main disadvantage of using observed litigation is that firms
may rely on it even if we do not observe it: if payoffs under enforcement are deterministic
and common knowledge and enforcement is costly, then parties will settle in advance. Herelies the main difference between observed litigation and relationship-specificity: only when
the investment is relationship-specific, legal institutions may matter; the reverse is not necessarily true. Hence, relationship-specificity is necessary for institutions to matter in thecontracting, whereas observing litigation is sufficient. I will return to these considerations
when interpreting the correlations.

1.3

Cross-country Dispersion in Input-Output Tables

Before turning to the regression results, I show some moments of the intermediate input
shares to dispel the myth that input-output tables are the same across countries. Table 3
shows the dispersion of intermediate input shares at the two-digit level from their respective
cross-country means. To obtain the numbers in the first part of the table, I first calculated
the standard deviation of the intermediate input shares for each sector-pair, and thentook averages of these standard deviations. The average dispersion of expenditure shares

11

across all sector-pairs is 2.3 percentage points. For services-producing upstream sectors,
the dispersion is significantly higher (at the 1% level) than for sectors that produce physicalgoods. For the average sector pair, the cross-country dispersion in materials shares equals
2.3 times the mean. Most striking, however, is that there is a sizeable number of sectorpairs for which the cross-country dispersion in input expenditure shares is high: for five
percent of sector pairs, the standard deviation is greater than 10 percentage points, andfor ten percent of sector pairs, the standard deviation is more than four times as high as
the mean. Hence, input-output tables are not the same across countries.15
For which inputs is the cross-country dispersion in expenditure shares particularly large?
Figure 2 shows for every upstream sector the expenditure share on this sector, averaged (inan unweighted way) across downstream sectors. The left panel shows that the dispersion
is higher for inputs with higher average expenditure shares. Still, even in log-deviations
there is considerable heterogeneity across inputs. Among the inputs with high average
expenditure shares, the (wholesale and retail) trade, business services, electricity, transport,
and financial services sectors show particularly high dispersion across countries. Notethat these sectors are also particularly enforcement-intensive (Table 1 above), whereas thepercentage-wise cross-country dispersion in input shares on the (not very enforcementintensive) oil and gas and petroleum and coal products sectors is relatively low. Thissuggests that contracting frictions may play a role for external intermediate input use. In
the remainder of this section I will try to rule out alternative explanations.

1.4

Results

Table 4 presents the results of estimating equation (1) using ordinary least squares (coefficient estimates are standardized betas). The first two columns include only sector-pair
fixed effects, and do not correct for sectoral productivity differences across countries. Nevertheless, the estimates of the interaction term’s coefficient, β, are negative. Columns (3)and (4) correct for the presence of unobserved heterogeneity in the upstream sectors by including fixed effect for each upstream sector-country pair. The estimates of the coefficientincrease in magnitude. In columns (5) and (6) the regression also includes downstream
sector-country fixed effects to control for differences in the size of the downstream sectors
across countries. The interaction coefficients increase slightly as a result, and remain statistically significant. Overall, Table 4 shows that in countries where enforcement costs are
high, firms use less intermediate inputs in sector-pairs where litigation is more prevalent in
the United States. The estimates in columns (5) and (6), my preferred specifications, imply
that a one-standard deviation increase in each of the interacted variables is associated witha decrease in the input share by 0.3 and 0.2 percentage points, respectively.
Table 5 shows results when controlling for additional variables. As a large literaturepoints out, contracting institutions are correlated with financial development. In order to15

Appendix A.1 shows the variation in Input-Output tables in more detail.

12Gas manufacture, distribution
Water
Coal
Wearing apparelSea transport
Manufactures nec
Air transport
PubAdmin/Defence/Health/Educat
Leather products
Insurance
Recreation and other services
Minerals nec
Construction
Transport equipment nec
Mineral products nec
Communication
Motor vehicles and parts
Electronic equipment
Wood products
Food products and beverages
Metal products
Metals nec
Paper products, publishing
TextilesFinancial services nec
Ferrous metals
Agriculture, Forestry, Fishing
Machinery and equipment nec
Oil and Gas
Transport nec
Electricity
Chemical,rubber,plastic prods
Petroleum, coal products
Business services nec
Trade

Gas manufacture, distribution
Water
Coal
Wearing apparelSea transport
Manufactures nec
Air transport
PubAdmin/Defence/Health/Educat
Leather products
Insurance
Recreation and other services
Minerals nec
Construction
Transport equipment nec
Mineral products nec
Communication
Motor vehicles and parts
Electronic equipment
Wood products
Food products and beverages
Metal products
Metals nec
Paper products, publishing
TextilesFinancial services nec
Ferrous metals
Agriculture, Forestry, Fishing
Machinery and equipment nec
Oil and Gas
Transport nec
Electricity
Chemical,rubber,plastic prods
Petroleum, coal products
Business services nec
Trade

0
.05
.1
.15
Average expenditure share on sector-12 -10 -8 -6 -4 -2
Log average expenditure share on sector

Figure 2: Cross-country distribution of input shares by upstream sector
Note: Figure shows the cross-country distribution of average intermediate input expenditure shares, by
upstream sector. Averages are unweighted, and are taken within each country across downstream sectors.

Table 3—: Cross-country dispersion in two-digit intermediate input shares
I. Average standard deviations and coefficient of variation of intermediate input shares

All sector pairs
Goods-producing upstream sectors only
Services-producing upstream sectors only

σ

σ/µ

.023
.020
.028

2.3
3.5
1.9

II. Frequency distribution of standard deviations and coefficient of variation
Standard deviation
Category# sector pairs

Coefficient of variation% of total

Category# sector pairs% of total

All
1225
100
σni < .02
838
68.4 σ/µ < 1119
9.7.02 < σni < .04
194
15.8 1 < σ/µ < 2536
43.6.04 < σni < .06
68
5.6 2 < σ/µ < 3309
25.2.06 < σni < .08
46
3.8 3 < σ/µ < 4135
11.0.08 < σni < .1
18
1.5 4 < σ/µ < 693
7.6.1 < σni < .15
34
2.8 6 < σ/µ < 8221.8σni > .15
27
2.2 σ/µ > 8110.9
Note: The table presents statistics regarding the cross-country dispersion of intermediate input expenditure shares, at the two-digit sector-pair level. Part I shows means of the standard deviations, Part II
shows the frequency distribution of standard deviations and coefficients of variation. All intermediate
input shares cover both domestically and internationally sourced inputs.

13

Table 4—: The Correlation of Intermediate Input Shares and Contracting frictions
Dependent variable: Xni /Xn(1)(1)
δ c × zni

-0.035∗∗∗(0.0069)

(2)

(3)

Yes
Yes

(4)

-0.040∗∗∗(0.0091)-0.028∗∗∗(0.0046)

δ c × zni

Country FE
Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs

(2)

Yes
Yes

(5)
-0.043∗∗∗(0.0095)-0.034∗∗∗(0.0071)
Yes
Yes

(6)

Yes
Yes

-0.037∗∗∗(0.0074)
Yes
Yes
Yes

Yes
Yes
Yes

R2
0.449
0.449
0.531
0.531
0.537
0.537
Observations
133525133525133525133525133525133525
Note: The dependent variable is the expenditure of sector n in country c on domestically and internationally sourced intermediate inputs from sector i, divided by the total gross output of sector n in country(1)(2)
c. δ c is the cost of enforcement a contract, as a fraction of the value of the claim. zni and zni are themeasures of enforcement-intensity. The table shows standardized betas, with standard errors clustered at
the country level. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

make sure that the observed correlation is indeed coming from contracting institutions,and not from financial development, columns (1) and (2) control for interactions of financial development (as measured by the ratio of private debt to GDP) with enforcementintensity. The coefficient of interest remains negative and significant, suggesting that priorspecifications were not confounding the two. Interestingly, countries that are financiallywell-developed do seem to use more intermediate inputs in sector pairs where litigation
is frequent. There are many possible explanations for this: credit market imperfections
may lead to production being concentrated among larger firms, which may find it easierto produce inputs that are tailored to their production process. Alternatively, better access to financing may build trust between firms, and may allow them to overcome hold-up
problems through relational contracts. Without firm-level data these explanations are hardto distinguish. Columns (3) to (6) of Table 5 also control for interactions of enforcementintensity with per-capita income. Again the coefficient of interest remains negative andsignificant.
Table 6 turns to regressions on subsamples. Columns (1) and (2) include only pairsof sectors that produce physical goods (i.e. agriculture, mining, and manufacturing; thetop left square of the input-output table), and columns (3) and (4) include only pairs ofservices sectors (the bottom right square). Notice two things: firstly, the coefficients arelarger than in the benchmark. Perhaps firms are more willing to produce an input in-house
if they are in a related business. Secondly, the coefficient in the services-only subsample issubstantially larger than in manufacturing. A plausible explanation would be that firms
face more discretion over their choice of services tasks in the production process. Managers
in developing countries may not see accounting or R&D as vital to their production, and14

Table 5—: Contracing Institutions vs. Financial Development vs. Overall Development
Dependent variable: Xni /Xn(1)(1)
δ c × zni

(2)-0.029∗∗(0.0099)(2)(3)-0.019∗(0.0094)-0.026∗∗(0.0078)δ c × zni

(1)

F IN DEV c × zni

(2)

(5)

-0.018∗(0.0077)-0.020∗(0.0084)0.041∗∗∗(0.012)0.040∗∗∗(0.0082)(1)0.032∗∗∗(0.0094)0.22∗∗(0.068)log GDP C c × zni

(2)

0.093
(0.076)0.18∗∗∗(0.049)log GDP C c × zni

Yes
Yes
Yes

(6)

-0.021∗(0.011)0.050∗∗∗(0.010)F IN DEV c × zni

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs

(4)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

0.074
(0.054)
Yes
Yes
Yes

Yes
Yes
Yes

R2
0.54
0.54
0.54
0.54
0.54
0.54
Observations
132300132300133525133525132300132300Note: The dependent variable is the expenditure of sector n in country c on domestically and internationally sourced intermediate inputs from sector i, divided by the total gross output of sector n in country c. δ c(1)(2)
is the cost of enforcement a contract, as a fraction of the value of the claim; zni and zni are the measurescof enforcement-intensity. F IN DEV is the ratio of private debt to GDP; log GDP C c is log per-capita
GDP. The table shows standardized betas, with standard errors clustered at the country level. ∗ p < 0.05,∗∗
p < 0.01, ∗∗∗ p < 0.001.

neglect those activities when expecting difficulties in sourcing them.
Let us take a closer look at how δ c and zni interact. Table 7 shows the results of aregression of intermediate input shares on interactions of the enforcement-intensity measures with dummies for whether enforcement costs are in each of the five quintiles of thecross-country distribution of enforcement costs (the first quintile being the base category):
5
c
X
Xni
=
βj 1 (δ c ∈ Quintile j) × zni + αni + αic + αnc + εcni
Xnc
j=2

and likewise with interactions of quintile dummies for enforcement-intensity z with δ. We
see that the correlation with the interaction term is only significant when enforcement
costs (respectively, z) are in the highest quintile. This is in line with the view that whenenforcement costs are sufficiently low, parties use formal contracts that are enforceable incourts. In such cases, product-specific attributes that determine the scope for hold-ups
do not affect performance in the bilateral relationship: once you can cheaply enforce yourcontract in the court, how relationship-specific your good is does not matter anymore.
When you get held up, you either threaten to enforce the contract, or to sell the goods to a15

Table 6—: Within Manufacturing & Within Services
Dependent variable: Xni /Xn(1)(1)
δ c × zni

-0.047∗∗(0.015)(2)

Sample(3)(4)-0.11∗∗∗(0.023)-0.040∗∗∗(0.010)δ c × zni

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs(2)-0.10∗∗∗(0.020)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

M onlyM onlyS onlyS only

2

R
0.64
0.64
0.47
0.47
Observations
48069
48069
21364
21364
Note: The dependent variable is the expenditure of sector n in country c on domestically and internationally sourced intermediate inputs from sector i, divided by the total gross output of sector n in country(1)(2)
c. δ c is the cost of enforcement a contract, as a fraction of the value of the claim. zni and zni are themeasures of enforcement-intensity. The table shows standardized betas, with standard errors clustered at
the country level. For columns (1) and (2), the sample consists of all sector pairs where both sectors areproducing physical goods (agriculture, mining, and manufacturing); for columns (3) and (4) the sample
consists of all sector pairs where both sectors are services sectors.

third party — but not both. I will return to these considerations when writing the modelin Sections 2 and 3.

1.5

Discussion

The results above show that input output table cost shares are lower in countries withhigh enforcement costs for sector-pairs that see relatively more litigation in the UnitedStates. While the amount of litigation will of course depend on the quality of enforcement,
and enforcement costs in particular, note that the enforcement-intensity variable measuresthe variation across sector-pairs holding fixed institutions, i.e. for the enforcement institutions in the United States. The variation in litigation across input output links therefore
captures the industry-pair-specific attributes that determine whether formal enforcement isrequired to solve contracting problems, including the degree of relationship-specificity. Thisis analogous to Rajan and Zingales (1998), who also use a market outcome (the observed
external capital use of firms) across industries, holding fixed the institutional characteristic (the supply of credit in the United States), to measure an industry characteristic (thedependence on external financing).
When can we interpret these estimates as causal? There are two main threats: reverse
causality, and omission of variables that are correlated with the interaction term and are
affecting input-output shares. Reverse causality could arise if some countries are, for otherreasons, more or less intensive in the use of certain intermediate inputs, which affects theirdecision to invest in the quality of enforcement institutions. Given that changes in judicial
16

Table 7—: Conditional correlations for different degrees of enforcement costs
Dependent variable: Xni /Xn
(1)

(2)

(1)

(2)

Using zni

Using zni

Using zni

Using zni

(1)

(2)

(3)

(4)

1 (δ ∈ 2nd Quintile ) × zni

0.0076(0.010)0.0017(0.0081)1 (δ c ∈ 3rd Quintile ) × zni-0.0070(0.0087)-0.010(0.0071)

1 (δ c ∈ 4th Quintile ) × zni-0.0074(0.011)-0.011(0.0083)

1 (δ c ∈ 5th Quintile ) × zni-0.024∗(0.010)-0.024∗∗(0.0082)

1 (zni ∈ 3rd Quintile ) × δ c-0.0042(0.0032)-0.0018(0.0037)

1 (zni ∈ 4th Quintile ) × δ c-0.0058(0.0061)-0.0033(0.0059)

1 (zni ∈ 5th Quintile ) × δ c-0.029∗∗(0.011)-0.028∗∗(0.0096)

Yes
Yes
Yes

Yes
Yes
Yes

c

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs

Yes
Yes
Yes

Yes
Yes
Yes

R2
0.537
0.537
0.537
0.537
Observations
133525133525133525133525
Note: The dependent variable is the expenditure of sector n in country c on domestically and internationally sourced intermediate inputs from sector i, divided by the total gross output of sector n in country(1)(2)
c. δ c is the cost of enforcement a contract, as a fraction of the value of the claim. zni and zni are themeasures of enforcement-intensity. 1 denotes the indicator function. The table shows standardized betas,with standard errors clustered at the country level. In columns (3) and (4), the base category for the interactions are the observations where z is zero, which account for the first two quintiles of the z distribution.
∗p < 0.05, ∗∗ p < 0.01.

budgets are uncorrelated with changes in judicial performance and given that many countries have tried but failed to improve case clearance rates (Buscaglia and Dakolias, 1999),
this explanation is unlikely to drive the results. Unobserved heterogeneity across sectors
and countries is a more serious threat, but the presence of a full set of fixed effects meansthat such unobserved determinants of input-output shares would need to be varying at thelevel of both sectors and country, in a way that is correlated with the interaction term. An
upstream industry × country characteristic, for example, would need to be affecting downstream sectors to different degrees in a way that is correlated with enforcement-intensity.
The most plausible of such explanations, that hold-up problems could be transferred tobanks through financial intermediation, is one that is explicitly controlled for in Table 5
above.
So what do these results tell us? First of all, they are consistent with the view that
good formal enforcement helps with overcoming holdup problems when sourcing interme-17diate inputs, in line with the empirical results of Nunn (2007) and Levchenko (2007) at
the industry level, and the results of Johnson et al. (2002) at the firm level. Secondly,
while there may be alternative ways to get around holdup problems (relational contracts,
hostages, option contracts — ways that do not depend on the characteristics of the productbeing traded), these do not seem to be a perfect substitute for formal enforcement in courts:
if they were, the correlation would disappear. Thirdly, for some sector-pairs formal andinformal enforcement are indeed substitutes: when a product is not relationship-specific,
firms will use informal contracts and never litigate; for these sector-pairs the quality oflegal institutions is not correlated with intermediate input use. Likewise, when formal
enforcement costs are low, the degree of relationship-specificity does not matter (Table 7).
Stronger contracting frictions are associated with lower intermediate input use. But
is that because the firm vertically integrates, or because it decides to use a production
technology that omits certain inputs? Both interpretations are consistent with the above
results. Input-Output tables are typically constructed at the plant level, and are therefore
not fully conclusive about the extent of vertical integration.16 Even though the SNA 1993,
which underlies the construction of the Input-Output tables, mandates the recording of all
types of intermediate inputs that come from outside the unit of observation (the plant),
it is a fact of the data collection process that services inputs that come from within thefirm are typically not priced, and therefore have no expenditure associated with it. Hence,services inputs would typically only show up in input-output tables if they are comingfrom outside the firm. Hence, at least for services inputs variation in the input shares will
come from variation in the use of services sourced from other firms (cf. columns (3) and(4) of Table 6). Ferguson and Formai (2013) extend the work of Nunn (2007) to showthat contracting institutions shape comparative advantage less for industries that havethe ability to vertically integrate, suggesting that integration alleviates (at least to someextent) the hold-up problem. Perhaps the most conclusive evidence about how firms react
to imperfect formal enforcement can be found by studying the precise mix of intermediate
inputs at the plant level: Boehm and Oberfield (2020) study detailed microdata on the
input mix of Indian manufacturing plants and show that when judicial institutions arepoor, plants respond by performing a larger range of production steps within the plant or
switch to a different set of inputs that omits certain relationship-specific components.
Finally, I mention some additional results and robustness checks. The correlations between contracting frictions and the intermediate input shares are not smaller for homogeneousgood-producing sectors, suggesting that firms producing lower quality products when contracting frictions are large is not the main driver of the correlation reported above. Furthermore, the negative correlation remains statistically significant (a) when having the16

There is, however, a large literature that measures the degree of vertical integration as the fraction ofvalue added in gross output (for more recent examples see Holmes, 1999 and Macchiavello, 2012). Ramondo
et al. (2016) and Atalay et al. (2014) present evidence on input flows between vertically integrated plants.
A recent paper by Atalay et al. (2019) is able to separate within-firm sourcing frictions from across-firm
frictions.

18

input-output share with domestically source intermediate inputs only on the left hand side;(b) when excluding the top three most litigious sectors — insurance, business services, andfinancial services; (c) when controlling for interactions of δ c with the US input-output
shares; (d) when replacing zni by a measure of relationship-specificity using Rauch’s classification of goods, in the spirit of Nunn (2007); (e) when controlling for interactions of avariable that is constructed similarly to z (i) but uses the US input output table instead of
the pairwise litigation count; (f) results with the US input output table as a “placebo”; (g)PPML instead of OLS estimates of (1). The interested reader can find all this (and more)in Appendix D.

2A Quantitative Model of Input Sourcing

This section presents a simple macroeconomic model where firms face the decision between
producing in-house and outsourcing. The purpose of the model is twofold: to explain
how differences in input-output shares emerge from differences in productivity patterns
and from frictions, and to present a framework for empirical work, in which productivity
differences and contracting frictions can be identified and their importance for aggregate
outcomes evaluated. The model explains the correlations from the preceding section, andallows me to link them to welfare.

2.1

Technology

The model economy is closed.17 There are N sectors in the economy, each consisting of aunit measure of firms. Sector n firms convert inputs {(qni (j), j ∈ [0, 1]}i=1,...,N into output
yn according to the production function.18
(4)

yn =

N Z 1Yi=1

qni (j)(σn −1)/σn dj

 σnσn−1 γni,

n = 1, . . . , N.

0P
where i γni = 1 for all n = 1, . . . , N . The sets {(n, i, j), j ∈ [0, 1]}i=1,...,N are the setsof inputs that sector n may source from a firm belonging to sector i, or, alternatively,
produce itself using labor.19 The index j denotes the individual activities/varieties withineach basket.20 The technological parameters γni capture the weight of the broad set of17

It would be straightforward to extend the model to include international sourcing, but difficult toempirically operationalize it: trading partners would have to choose a jurisdiction to govern contracts, andthis jurisdiction may even be a third country. In the data we do not observe which jurisdiction governs
contracts. However, as I will show, most of the gains from improving formal enforcement institutions arise
from the lower cost of using services inputs, which are typically not traded across country borders.
18
Appendix E generalizes the production function to a CES function in input bundles i.
19This is a model where every sector buys from every other sector, but apart from parameters, they are
all ex-ante identical. In a bilateral trade between two sectors, I always denote the downstream (buying)sector by n and the upstream (selling) sector by i.
20
As an example, consider a car manufacturing plant.
Then, n = car and i ∈{metal, electricity, R&D, . . . } are the different broad sets of activities, corresponding to the different up-

19

inputs i in the production process of sector n: γcars,steel will be high, whereas γcars,agriculture
will be low.
For each activity (n, i, j), the sector n firms have to decide whether to produce theactivity themselves using labor, or to source it from the upstream sector i. I will refer tothe first option as “in-house production” and the second option as “outsourcing to sectori” even though in the latter case the transaction may not be crossing the firm boundary,such as when the activity is sourced from a plant that belongs to a different sector but
to the same firm. The manager of this input-supplying plant may incentives that are notcompletely aligned with those of the headquarter, giving rise to a hold-up problem. For
the sake of brevity I refer to the supplier as the “upstream firm”.
Both the downstream firm and the upstream firm draw an activity-specific productivity realization, which determine the cost of each option. The downstream firm decides onwhether to outsource by comparing them. Outsourcing is subject to contracting frictions,which increase its cost and thus lead to too much in-house production compared to a frictionless world. Once the decision of whether to outsource has been taken, it is irreversible.
I discuss each of the two options in turn.
In-house Production. The sector n firm can produce activity (n, i, j) itself by employing labor. One unit of labor generates sni (j) units of activity (n, i, j), thus the production
function is qni (j) = sni (j)l(n, i, j), where l(n, i, j) is labor used and sni (j) is a stochastic
productivity realization that follows a Fréchet distribution,−θP (sni (j) < z) = e−Sn z .
The productivity draws sni (j) are independent across i, j, and n. The parameter Sn captures the overall productivity of in-house production by sector n firms: higher Sn will, on
average, lead to higher realizations of the productivity parameters sni (j). The parameterθ is inversely related to the variance of the distribution.
The labor market is perfectly competitive. Denote the wage by w, and the cost of one
unit of activity (n, i, j) under on in-house production by plni (j). Then, plni (j) = w/sni (j).
Outsourcing to the upstream sector. Alternatively to in-house production, sector nfirms can source activity (n, i, j) from the upstream sector i. For each activity (n, i, j),there is one sector i firm that can produce it, and firms compete monopolistically. Eachsector i firms can transform one unit of sector i output (produced using the production
function (4)) into tni (j) units of its activity (n, i, j), thus the production function is qni (j) =tni (j)yi (n, i, j), with yi (n, i, j) being the amount of sector i goods used as inputs.21 Again
stream (roughly 2-digit) sectors, that need to be performed during the production process. The index jcorresponds to the individual varieties of inputs (in the case of physical inputs) or tasks (in the case ofintangible inputs) in each basket (n, i).
21
The assumption that variety (n, i, j) is produced using sector i goods in the case of outsourcing meansthat the model exhibits input-output linkages across sectors. Ultimately, the whole production process is20

I assume that the tni (j) follow a Fréchet distribution,
P (tni (j) < z) = e−Ti z−θand that they are independent across i, j, and n. The average productivity realization isincreasing in the parameter Ti , which captures the upstream sector’s overall capabilities(productivity, endowments, etc.). Importantly, the shape parameter θ is assumed to be
identical to the one for in-house production. The supplier’s cost of producing one unit ofvariety (n, i, j) is then cni (j) = pi /tni (j), where pi is the price index of sector i’s output
good, (4).
Institutions. Assume further that sourcing from the upstream sector is subject to contracting frictions that take the form of a multiplicative wedge dni ≥ 1 on the cost of
the activity (but that it is not a resource cost). One should think of dni as being determined by the efficiency loss associated with a hold-up problem: when the traded good
is relationship-specific, the buyer has an incentive to hold up the seller by withholding
payment. The parties then bargain over the surplus. The seller’s outside options are to
enforce the contract in a court (and the benefit of doing so depends on the enforcementcost) or to revert the production process, yielding a scrap value that depends on the degreeof relationship-specificity. The only relevant outside option will be the better one of thetwo. Going back in time, the seller will provide effort depending on her ex-post outcomes.
The overall distortion dni is therefore a minimum of an expression that depends on theenforcement cost, and one that depends on the degree of relationship-specificity. Equilibrium distortions dni are shaped both by institutions and by product-specific attributes:
when institutions are such that enforcement is not possible, the outcome will be below
the first-best, with the degree of efficiency loss being determined by the scrap value of the
produced goods, i.e. the degree of relationship-specificity. Formal enforcement improveson this outcome if the enforcement cost is sufficiently low. Appendix B formalizes this intuition and provides a microfoundation. For the purpose of explaining the macro-structureof the model, it is sufficient to treat it as a black box. In Section 3 I will place a structure consistent with this intuition on dni , and use it to evaluate the role of institutions inshaping frictions and aggregate outcomes.
Taking the contracting friction into account, the overall cost of sourcing one unit ofactivity (n, i, j) isµn pi dni
pxni (j) =tni (j)where µn = σn / (σn − 1) is the markup due to monopolistic competition. Going back intime, the downstream sector firms decide on whether to produce in-house or to outsourceby comparing the cost of the activity under the two regimes, plni (j) and pxni (j). Given thedone using labor and a constant returns to scale production technology; the distinction between labor andintermediate inputs simply draws the sector boundaries and allows for better comparison with the data.

21

perfect substitutability between the two options, the realized cost of activity (n, i, j) ispni (j) = min plni (j), pxni (j) .

2.2

Households’ Preferences and Endowments

There is a representative household with Cobb-Douglas preferences over the consumptionof goods from each sector,
(5)

U=

N
Y
cηi i ,
i=1

P
where Ni=1 ηi = 1 and ci is the quantity of units of output yi demanded by households.
Sector i firms are perfectly competitive in serving households. The output of each sector,
yi , is hence being used both for final consumption by households, and as intermediate input
in the production of outsourced activities. Households have a fixed labor endowment L
and receive labor income wL and the profits of the monopolistically competitive suppliers,P
Π. Their budget constraint is N
i=1 pi ci ≤ wL + Π, and thus pi ci = ηi (wL + Π).

2.3

Equilibrium Prices and Allocations

To describe sectoral price levels and expenditure shares, some definitions are helpful. Let
R1
Xni ≡ 0 pni (j)qni (j)1{j:pxni (j)<plni (j)} dj be the expenditure of sector n firms on activities
P R1
that are sourced from sector i, and Xn = i 0 pni (j)qni (j)dj the total expenditure (andgross output) of sector n. We then have
Proposition 1 (Sectoral price levels and expenditure shares) Under cost minimization by the downstream sector firms, the following statements hold:
1. The cost of producing one unit of output yn in sector n satisfies
(6)

pn =

N 
Y
αn
i=1

γni

where w is the wage, and αn ≡ Γ

Sn w

−θ

+ Ti (µn pi dni )

1−σn
+1
θ

1
 1−σn 1−θ − θ

γni, with Γ being the gamma function.

2. The input expenditure shares Xni /Xn are decreasing in dni and satisfy(7)

Xni
Ti (µn pi dni )−θ
= γniXn
Sn w−θ + Ti (µn pi dni )−θProposition 1 gives expressions for the sectoral price levels and intermediate input
expenditure shares. The sectoral price levels solve the system of equations (6), and dependon the cost of production under outsourcing and under in-house production, and therefore
on the productivity parameters Ti and Sn , as well as on the contracting frictions dni .
22Suppliers may themselves outsource part of their production process, which gives rise to
input-output linkages between sectors; the sectoral price levels are thus a weighted harmonicmean of the price levels of the other sectors. This mechanism strengthens the impact of theprice distortions: an increase in the price of coal increases the prices of steel and, throughsteel, machines, which in turn increases the cost of producing steel further due to the steel
industry’s dependence on machines.
The expenditure shares on intermediate inputs, equation (7), are then determined by
the relative effective cost of outsourcing versus in-house production. Higher effective costof outsourcing will lead downstream firms to produce more activities in-house instead ofoutsourcing them. Thus, the expenditure share of sector n on inputs from sector i isincreasing in sector i’s productivity, Ti , and the importance of sector i products for sectorn, γni , and decreasing in sector i’s input cost pi and contracting frictions dni .
Proposition 1 yields the key qualitative prediction of the model, namely that contracting
frictions, captured by dni ≥ 1, negatively affect the downstream sector’s fraction of expenditure on intermediate inputs from the upstream sector i. The elasticity θ determines themagnitude of this effect.
Firms make profits in inter-sectoral relationships due to them having monopoly powerPP
for their variety. Aggregate profits are Π = n,i Πni = n,i 1/(σ − 1)Xni and the markets
for sectoral output clear:(8)

p i ci +X(Xni − Πni ) = Xi ,i = 1, . . . , N.

nAn equilibrium is a vector of sectoral price functions (pn (w))n=1,...,N that satisfies (6).
Given sectoral prices, all other endogenous variables can be directly calculated from thepreceding equations. Standard contraction mapping arguments imply that an equilibrium
exists and is unique.

2.4

The welfare gains from eliminating enforcement frictions

My measure of welfare is real income per capita. Since households receive both labor
income and the profits of intermediaries, and the wage is the numeraire, welfare is
1 + Π/L
Y
=
.
PL
P

(9)

Welfare gains therefore arise from a decrease in consumer prices P , and from an increase inprofits per capita Π/L, as more tasks become outsourced. Taking the total differential of
the sectoral price levels pn in equation (6), and holding constant the T and S parameters,
we obtain(10)

d log pn =

X Xni
i

Xn

(d log pi + d log dni ) .

23

Enforcement costs affect the sector’s price index both directly through the multiplicative
distortion dni , and indirectly through the price level of its upstream sectors. The strengthof the input-output linkages is given by the expenditure
shares Xni /Xn . Writing (10) in−1matrix notation yields d log p = (I − Ξ) diag Ξ (d log dni )0n,i , where Ξ = (Xni /Xn )n,i
denotes the matrix of expenditure shares. We see that the impact of distortions on sectoral
price levels is determined by the Leontief inverse (I − Ξ)−1 . Here the Leontief inverse isendogenously determined by the cost of in-house production versus outsourcing. Hence,equation (10) is only a first-order approximation which holds exactly only for small changes
in log dni . Note, in particular, that the first-order effects of reducing dni on prices do notdepend on the elasticity θ; it matters only for the change in the multiplier (i.e. the secondorder effects).

3

Evaluating the Importance of Enforcement Costs

If, as shown in Section 1, some of the variation in Input-Output tables is explained bycontracting frictions, then how much do these distortions matter for welfare? In this section,
I apply the model to address this question. The strategy is to identify and estimate theparameters in the gravity-like expression for the input-output share, equation (7).
I start by taking the closed-economy model to a cross-country setting. Assume eachcountry is described by the closed-economy model of Section 2, with country-specific cost
parameter vectors T and S. The γni capture the country-invariant technical aspects ofthe production process. Furthermore, the demand elasticities σ and the trade elasticity θ
are assumed to be constant across countries. Denoting country-specific parameters by asuperscript c, the expression for the input-output shares becomesc
Tic (µn pci dcni )−θ
Xni
= γni
.
Xnc
Snc + Tic (µn pci dcni )−θ

3.1

Putting Structure on the Contracting Frictions

In the setup of the model in Section 2, contracting frictions are described by a multiplicative
wedge dcni on the cost of sourcing. Guided by the extensive literature on the hold-up problem
and by the empirical findings in Section 1, I will now put enough structure on this wedge
to be able to identify and quantitatively evaluate the importance of formal enforcement
institutions. Readers who are interested in a more explicit microfoundation for these adhoc assumptions are referred to Appendix B, which describes a bilateral contracting gamethat yields a special case of the expressions below.
The literature on the hold-up problem, following Klein et al. (1978), emphasizes efficiency losses in buyer-seller relationships when assets are specific to the relationship. In
empirical applications, the degree of specificity is typically seen as a characteristic of the
product or the market (Nunn, 2007, Levchenko, 2007). Denote by dI the distortion under24

an informal contract, i.e. the efficiency loss in a situation where enforcement of a contract
in a court was not possible at all. If parties always have access to such a contracting
environment (e.g. through the use of a “gentlemen’s agreement”), then the availability offormal enforcement can only act to reduce the overall amount of efficiency loss:
dcni = min (dF )cni , (dI )cni

where (dF )cni denotes the efficiency loss in a “formal” contracting environment, where parties have access to formal legal recourse. Assume now that the distortion in a formal
contracting environment depends on the quality of the legal institutions, and that the
distortions under an informal contract only depend on sector-pair-specific (and therefore
country-invariant) attributes such as the degree of relationship-specificity of the produced
goods22 , i.e. (dF )cni = dF (δ c ) and (dI )cni = (dI )ni , then the expression above becomes(11)dcni = min dF (δ c ), dIni .

Equation (11) captures the intuition that whenever the formal legal institutions are goodenough to make them preferable over an informal contract, then agents will write a contract
in such a way that in a hold-up situation, the outside option is to enforce the contract in acourt. In such a case, the equilibrium performance of agents will depend on the quality of
the legal system, including the cost of enforcement, and the degree of relationship-specificity
of assets will not matter. If, however, formal enforcement is expensive, unpredictable, or
generally unavailable, or if asset specificity is sufficiently low (more precisely, wheneverdF > dI ), then agents will use an informal arrangement for exchange, and then—on themargin—the quality of formal enforcement institutions will not matter. The equilibrium
performance, and hence the wedge, will then depend entirely on the degree of relationshipspecificity of the produced goods.
From the above considerations, it should be clear that litigation will only be observed
when parties use a formal contract, i.e. when dF < dI . Hence, for a given country c,
the prevalence of litigation tells us something about how likely it is that the distortions
from informal arrangements exceed the distortions from formal contracts: sector-pairs withfrequent litigation will on average have high dIni ; the scope for hold-up is high. Hence, one
can write dIni = dI (zni ), where zni is the empirical prevalence of litigation between firms fromsectors n and i in one country, as captured by the measure of dependence on enforcementin Section 1, and dI is an increasing function. To be conservative, I assume dI (0) = 1,
which means that enforcement frictions are not present when we do not observe litigation.
Violations of this assumption would mean that the importance of institutions would belarger than what I estimate them to be. Finally, I normalize dF (0) = 1: if enforcement is
22This assumption corresponds to the assumption in Nunn (2007) that relationship-specificity is a sector
characteristic only.

25

completely costless, there is no distortion either.23
The above functional form, equation (11), is consistent with the correlations in Section
1: Table 7 showed that litigiosity zni is only correlated with intermediate input sharesfor the countries where enforcement costs are sufficiently high, supporting the view thatthe overall distortion is a minimum of the distortion under formal contracting (which isa increasing in the country-wide enforcement costs) and the distortion under informal
contracting (which is decreasing in the degree of litigation in each pair of sectors).

3.2

Identification and Estimation

My estimating equation is the model’s expression for intermediate input expenditure shares,
with an additive error term with zero conditional mean,
(12)

c
Xni
Tic (µn pci dcni )−θ=γ+ εcninicc c −θc
Xnc
Sn + Ti (µn pi dni )where the parameter restrictions for constant returns to scale,
imposed. One can re-write this equation in the form
(13)P

i γni = 1 for all n, arec1Xni+ εcni= γniccXn
1 + exp(αn − αic + θ log dcni )cc c −θ
where, in a slight abuse of notation, αnc = log(Snc /µ−θ. Markupsn ) and αi = log Ti (pi )cµn are not identified separately from Sn . I let µn → 1, which interprets any markup aspart of Snc . This assumption leads to lower bounds for the welfare gains from reducing
dcni .24 This assumption renders the above mapping invertible; the Tic and Snc parameters
are therefore exactly identified.
To structurally identify contracting frictions, I follow two different strategies. In thefirst, I follow the motivation from above and set(14)
dcni = min dF (δ c ), dI (zni )and estimate dI and dF semiparametrically as quadratic polynomials with intercept equal
to one. Since the curvature of these polynomials is hard to distringuish from θ, I calibrate
θ directly by setting it to the consensus estimate for the trade elasticity, θ = 4 (see Headand Mayer, 2013): like the trade elasticity in standard Ricardian models, the elasticity θ
emerges from the tail parameter of the Fréchet productivity draw distributions.
23

This assumption may seem counterfactual: even when enforcement is costless, limits to e.g. verifiability
may mean that contracting frictions are present. It does not, however, impose a strong loss of generality
on the estimation: in the estimation approach below where dF is estimated nonparametrically (the “firststrategy”), the estimated function values for the countries with the best courts (around δ c = 10%) would
capture the distortion in these countries. Mathematically, the dF curve is restricted to go through the point(0, 1), but only the function values for δ c ∈ [0.1; ∞) matter for the estimation and welfare counterfactual.
24
Reducing dcni leads to more outsourcing, which, in the presence of markups, would lead to larger profits.
These profits get redistributed to households. With zero markups, this channel is absent.

26

In the second strategy I set dcni equal to the distortion as it would arise when microfounding it using the contracting game of Appendix B,
dcni = min




1
I
, d (zni ) ,1 − 12 δ cand again estimate dI as a quadratic polynomial. This approach makes use of the fact thatmy measure for institutional quality (the cost of enforcement, as a fraction of the value ofthe claim) has a direct quantitative interpretation as a model parameter. If plaintiffs are notcompensated for costs incurred during enforcement (such as, for instance, in the UnitedStates), suppliers may underperform because they know that they will be held up andthat subsequent enforcement is costly, with the cost being increasing in their performancelevel. The parameter 12 is the assumed bargaining power of the supplier in the out-of-court
settlement. This choice of parameters implies, for example, that the distortion under formal
contracting is 3.7 times higher in India, a country with notoriously slow and ineffective
courts, than in the United States. In the countries with the best courts (δ c ≈ 0.1), theassumption implies that frictions are bounded above by around 5%. This second approach
places stronger assumptions on the distortion under formal contracting, but allows me toestimate the elasticity θ myself. As we will see, both approaches lead to similar results.
I only use the measure z (2) for the quantitative empirical implementation of the model.
z (2) is preferable over z (1) , since the latter does not take into account that, conditional on
the scale of upstream and downstream sectors, the number of firm-to-firm relationships ishigher in sector pairs where the I-O table expenditure shares are larger. Using z (1) would
therefore understate dI in sector pairs with larger I-O table shares, and hence overestimate
the welfare benefits from reducing the distortions under formal enforcement dF .
Compare the nonlinear estimating equation (13) to the linear expressions in the regressions in Section 1, equation (1). In both expressions the input-output share is a functionof enforcement costs. Here, however, the sector × country fixed effects have a structuralinterpretation as parameters governing the cost of sourcing or producing inputs. The multiplicative interaction of δ and z has been replaced by the minimum: when enforcement
costs are prohibitively high, firms use arrangements that do not rely on the quality ofcourts — and then, on the margin, enforcement costs do not matter. Finally, the elasticity
θ governs how strongly frictions decrease intermediate input shares.25
Turning to the estimation, the problem of choosing a suitable estimator for the parameters in equation (13) shares many similarities with the choice of an estimator for gravity
equations in international trade (see Head and Mayer, 2013, for a summary). The nonlinear least squares estimator would place much weight on large observations and suffersfrom numerical problems due to nonconvexities. These difficulties would be resolved whenestimating the equation in logs. However, a NLS estimator on the log of (13) would place
25

Appendix C.2.1 shows a formal result on the relationship between the estimating equations in Sections
1 and 3.

27

much weight on the many intermediate input share observations that are close to zero inlevels, and deeply negative in the log. Instead, I use a Poisson pseudo-maximum likelihood(PPML) estimator, which emerges as a compromise between placing weight on large andsmall observations, while still being numerically feasible. The PPML has been widely used
to estimate gravity-type equations since being recommended by Santos Silva and Tenreyro(2006). Mathematically, the estimator is defined as(15)β̂ = arg maxβ

X Xc
n,i,c



ni
log g (β) − g (β)
Xncwhere β is the vector of estimands, g (β) = γni /(1 + exp(αnc − αic + θ log dcni )), and thePmaximization is subject to the constraints i γni = 1 for every n = 1, . . . , N . The PPML
is consistent if the conditional mean of the intermediate input shares is as described by themodel equation. Numerically, the estimator turns out to be friendly for the above functional
form: for given country- and sector-invariant parameters, the maximization converges to aunique solution, hence it is easy to find a global maximum by searching over the space ofthe country- and sector-invariant parameters.
Table 8—: Structural estimation results
Calibrated θ,
Estimated dF

Estimated θ,
Calibrated dF

(1)

(2)

θ

4

4.76
(0.02)

z measure used

z (2)

z (2)

-8550.45
0.65-8549.02
0.65

Pseudo-loglikelihood
Pseudo-R2

Note: Table shows calibrated (columns (1) and (2)) and estimated (columns (3) and (4)) values for θ, andstatistics on the model fit. The pseudo-R2 is defined as the squared correlation coefficient between fitted
input-output shares and the data. Table 23 in the Appendix shows the estimates of dI and dF .

Table 8 shows the results from estimating the model under the two approaches. The R2(defined as the square of the correlation coefficient between observed and fitted intermediate
input shares) is around 0.65, substantially larger than in the linear regressions of Section
1, where it is around 0.54. In the strategy where θ is estimated, the estimate for θ is 4.76,
close to the calibrated value in the other approach, and close to structural estimates of the
trade elasticity.

3.3

Welfare Analysis

With the model estimated, I am now able to evaluate the importance of enforcement
frictions. I take the estimated values for the model parameters and simulate welfare (real28theta estimated, z^(2) used
Counterfactual welfare increase, in percent

Counterfactual welfare increase, in percent

theta calibrated, z^(2) used
15
UKR

GEO

10

PAN
LAO
MYS

5

MDG
IND

ISR
ALB
NGA

0

QAT

IDN

BGD

KHM
MWI

VEN
COL
CMR

MOZ

ARE

LUX
-5
0.25

0.50

0.75

1.00

Enforcement cost

10
KHM

UKR
GEO
LAO

5
MYS
ISR
ARM

ZWE

IDN

PAN
MDG
VEN
COL

MWI

BGD
MOZ

ALBCMR
0QAT

ARE NGA

LUX

-5
0.25

0.50

0.75

1.00

Enforcement cost

Figure 3: Counterfactual welfare gains from setting enforcement costs to US levels
Note: Enforcement costs are top-coded at one to help exposition. Enforcement-intensity measure is z (2) .

per-capita income).26 Subsequently, I set each country’s enforcement costs to the level of
the United States (14%), a level that is low in international comparison but still possible
to achieve for most countries through judicial reform, and see how much welfare changes.
Figure 3 visualizes the results of these exercises in a scatter plot.27 Each dot corresponds
to a country; the location on the x-axis is the contract enforcement cost prior to the change,
δ c ; the location on the y-axis is the counterfactual increase in real per-capita income Y /P , inpercent. The main message of the figure is that in all specifications, the effects of reducing
enforcement costs to US levels can be large, ranging up to eight percentage points of real
income for some countries. But even under the more conservative specifications, shown in
the right panel, half of all countries would experience an increase of more than 1.5 percent,and a third would experience an increase of more than 2.4 percent in real income. Hence,
the welfare loss from poor enforcement institutions is relevant on the macroeconomic scale.
Figure 3 also shows the concave relationship between enforcement costs and the gains
from reducing them. When enforcement costs are high (such as for the four countries
where they exceed 100 percent), firms use informal contracts, and then a marginal change
in enforcement costs would not matter. Only when they are sufficiently low and firms
use formal contracting relationships, a reduction in enforcement costs will start having aneffect on performance in bilateral relationships.
3.3.1

Sources of the welfare gains

To understand the sources of the welfare gains above, it is helpful to draw parallels to theliterature on the gains from international trade. Like in Arkolakis et al. (2012), changes
in real income are a function of changes in trade shares (here, intermediate input shares)
26

In order to evaluate welfare, I need to calibrate the households’ consumption shares ηic . I set them tothe values reported in GTAP.
27
Appendix D shows the results separately for each country, and performs a robustness check where
broad input baskets are more substitutable than implied by the Cobb-Douglas production function.

29

and the elasticity θ.28 For a given variation of intermediate input shares that is explainedby contracting frictions, a lower θ would imply that the underlying price distortions arelarger, and lead to larger gains from eliminating frictions. In the case where θ is fixed, thewelfare gains are determined by the fraction of the variation in intermediate input sharesthat is explained by enforcement costs.
This analogy provides an intuition for what does (and what does not) matter for ourestimated welfare gains from reducing enforcement costs. If the functional form for contracting frictions dcni was misspecified, then enforcement cost could explain a larger – orsmaller – fraction of input cost shares.29 In particular, if some of the transactions that show
up in input-output tables are within-firm transactions where either hold-up problems do
not arise or court enforcement is not an option, then the correlation between enforcement
costs and input shares that we observe is weaker than what it would otherwise be.30 Since
our welfare counterfactual uses only the explained variation in input cost shares, we canbe agnostic about whether intermediate input use crosses the firm border or not – whatmatters is the degree to which intermediate input cost shares are explained by enforcement
costs, as captured by d = d(δ). At the same time, if the use of primary factors was also
˜ the regression would only identify the net of theassociated with contracting frictions d,
˜ If d˜ was also increasing in enforcement costs, our reported welfare countwo frictions, d/d.
terfactual would understate the welfare increases from reducing enforcement costs; likewise
if the productivity parameters T or S were decreasing in enforcement costs.
Note also that the results shown above are a lower bound for the welfare gains because
markups have been calibrated to zero: the cost difference between in-house and outsourced
activities comes either from productivity draws or from contracting frictions. If increased
outsourcing is associated with higher profits, which are ultimately rebated to households,
then the welfare increases would be higher than reported in Figure 3.

3.4

Discussion

What do these results tell us about the importance of legal institutions? Note that in themodel, legal institutions affect economic outcomes only through one particular mechanism,
namely the enforcement of supplier contracts. As such, the above welfare estimates do notinclude other channels of how legal institutions may matter, such as in the protection of
investors: Ponticelli and Alencar (2016) find that a one-standard deviation improvement
28
The “sufficient statistic” approach cannot be used here because the expenditure on in-house production
is not observed separately for each triple (n, i, c)— only as value added for each sector-country pair.
29
Note that the min functional form for dcni is supported both by theoretical considerations (substitutability of formal and informal enforcement; see Appendix B) and by empirical evidence (Table 7).
Approximating dcni itself by a polynomial in δ c and zni (and other robustness checks on the functional
form of dcni ) would be computationally challenging – each specification takes several days to estimate, andone needs to check that the local minima are global minima – but not impossible.
30
The lower correlation between I-O shares and dni would lead to an understatement of the welfare
effects of reducing enforcement costs. Appendix F.3 shows this on the example of measurement error in
zni .

30

in the quality of Brazilian district courts is associated with firms having 0.5% higher investment over assets and 2.3% higher output; this is on the same order of magnitude as theresults above. Furthermore, the results above should not be read as saying that the qualityof legal institutions matters more than other types of institutions. In a highly influential
paper, Acemoglu and Johnson (2005) argue that contracting institutions matter less fordevelopment than property rights institutions because agents can substitute for the former
using informal arrangements. This paper takes this substitutability seriously, and while
settling the question of which aspects of institutions are more important is outside of its
scope, the role of legal institutions in the enforcement of supplier contracts and in shaping
development turns out to be significant.
In the above quantification exercise, we have focused on the monetary cost of enforcement as a measure of the quality of judicial institutions, and abstracted from other dimensions that might also affect the firm’s ability to use courts to enforce contracts. The speedof enforcement, which is also measured by the World Bank, could be included in the costmeasure, but when priced at reasonable interest rates the time cost is only a relatively
small fraction of total cost.
As we have seen, the benefits of improving legal institutions can be large — but do theyoutweigh the costs? The literature on the determinants of court performance generally finds
no correlation between spending on the judiciary and the efficiency of courts (Buscaglia
and Dakolias, 1999, Cross and Donelson, 2010, Palumbo et al., 2013), and suggests thatincentivizing judges and improving case management are more important. But even if theamount of spending mattered, it is unlikely that the cost of court reform would outweighthe benefits, since the counterfactual welfare gains are an order of magnitude larger thancountries’ total spending on the judiciary: the US spends around 0.38 percent of GDP on
the judiciary; European countries on average 0.19 percent. India, a country whose judiciaryand industry structure are symptomatic of the problems discussed here spends 0.12 percent
of GDP on the judiciary — but would grow by at least 4%, and possibly much more, if it
had US enforcement institutions.31 In light of these numbers, it would be hard to deny theneed for judicial reform in India.

4

Conclusion

This paper studies the importance of contracting frictions for the firm’s sourcing of intermediate inputs. In countries where the cost of enforcing supplier contracts is high, firms
use less externally sourced intermediate inputs in sector pairs where US firms litigate a lot
for breach of contract. The amount of litigation correlates with measures of relationshipspecificity of the intermediate inputs. Hence, this fact is consistent with the view that31

Data on Indian expenditure on the judiciary from India’s Department of Justice (2015) and the Government of India (2015) for the fiscal year 2014/15, on US expenditures from the Bureau of Justice Statistics(2014) for the year 2010. European data is from Palumbo et al. (2013) and refer to the year 2010.

31

when legal institutions are good, firms manage to overcome hold-up problems caused byasset specificity through the possibility of enforcing formal supplier contracts. The paper
quantifies the importance of courts by estimating how much of the distortions in intermediate input use are explained by contracting frictions. These results confirm North’s points
about transaction costs shaping macroeconomic development through the organization of
production.
Another lesson is that input-output tables differ systematically and significantly acrosscountries. They differ systematically across countries in the sense that they are correlatedwith institutions and patterns of dependence on formal enforcement, and significantly,
because the fraction of the variation that is explained by these frictions suggests thatthe welfare gains from removing them are large. Hence, intermediate input expenditure
shares are not mere ’technical coefficients’, but are instead the endogenous outcome offirm’s sourcing decisions. In particular, economists should be cautious of using the UnitedStates’ input-output table to describe input use patterns in other countries.
The last lesson is one for policy. The paper’s findings highlight the importance of
judicial reform: the welfare costs from costly contract enforcement are substantial, andmust not be ignored. In countries with poor courts, improvements in court quality mustbe sufficiently large to induce firms to adopt formal contracting practices. Judicial reforms
must weigh the benefits against the costs. They may be targeted to reduce the costs oflegal representation, or attempt to clear the backlog of cases and speed up the litigationand enforcement process.

References
Acemoglu, Daron, and Simon Johnson. 2005. “Unbundling Institutions.” Journal of
Political Economy, 113: 5.
Acemoglu, Daron, Pol Antràs, and Elhanan Helpman. 2007. “Contracts and Technology Adoption.” American Economic Review, 97(3): 916–943.
Acemoglu, Daron, Rachel Griffith, Philippe Aghion, and Fabrizio Zilibotti. 2010.
“Vertical integration and technology: theory and evidence.” Journal of the european
economic Association, 8(5): 989–1033.
Acemoglu, Daron, Simon Johnson, and Todd Mitton. 2009. “Determinants of vertical integration: financial development and contracting costs.” The Journal of Finance,
64(3): 1251–1290.
Alfaro, Laura, Davin Chor, Pol Antras, and Paola Conconi. 2019. “Internalizing
global value chains: A firm-level analysis.” Journal of Political Economy, 127(2): 508–
559.

32

Antràs, Pol. 2003. “Firms, Contracts, and Trade Structure.” Quarterly Journal of Economics, 118(4): 1375–1418.
Antràs, Pol, and Davin Chor. 2013. “Organizing the global value chain.” Econometrica,
81(6): 2127–2204.
Antràs, Pol, and Elhanan Helpman. 2004. “Global sourcing.” Journal of political
Economy, 112(3): 552–580.
Arkolakis, Costas, Arnaud Costinot, and Andrés Rodrı́guez-Clare. 2012. “Newtrade models, same old gains?” The American Economic Review, 102(1): 94–130.
Atalay, Enghin, Ali Hortaçsu, and Chad Syverson. 2014. “Vertical integration andinput flows.” The American Economic Review, 104(4): 1120–1148.
Atalay, Enghin, Ali Hortaçsu, Mary Jialin Li, and Chad Syverson. 2019. “Howwide is the firm border?” The Quarterly Journal of Economics, 134(4): 1845–1882.
Baqaee, David Rezza, and Emmanuel Farhi. 2019. “The macroeconomic impact of
microeconomic shocks: beyond Hulten’s Theorem.” Econometrica, 87(4): 1155–1203.
Baqaee, David Rezza, and Emmanuel Farhi. 2020. “Productivity and misallocationin general equilibrium.” The Quarterly Journal of Economics, 135(1): 105–163.
Bartelme, Dominick, and Yuriy Gorodnichenko. 2015. “Linkages and Economic
Development.” Mimeo, UC Berkeley.
Bernard, Andrew B, Andreas Moxnes, and Yukiko U Saito. 2019. “Production
networks, geography, and firm performance.” Journal of Political Economy, 127(2): 639–
688.
Bernard, Andrew B., J. Bradford Jensen, Stephen J. Redding, and Peter K.
Schott. 2010. “Intrafirm Trade and Product Contractibility.” American Economic Review, 100(2): 444–48.
Boehm, Johannes, and Ezra Oberfield. 2020. “Misallocation in the Market for Inputs:
Enforcement and the Organization of Production.” Princeton University Mimeo.
Bresnahan, Timothy F., and Jonathan D. Levin. 2013. “Vertical Integration andMarket Structure.” In Handbook of Organizational Economics. , ed. Robert Gibbons andJohn Roberts. Princeton University Press.
Buscaglia, Edgardo, and Maria Dakolias. 1999. “Comparative International Studyof Court Performance Indicators: A Descriptive and Analytical Account. 1999.” World
Bank.

33

Caliendo, Lorenzo, and Fernando Parro. 2015. “Estimates of the Trade and Welfare
Effects of NAFTA.” The Review of Economic Studies, 82(1): 1–44.
Caliendo, Lorenzo, Fernando Parro, and Aleh Tsyvinski. 2017. “Distortions andthe Structure of the World Economy.” Yale University Mimeo.
Caprettini, Bruno, and Antonio Ciccone. 2015. “Turnover Taxes and Productivity:
Evidence from a Brazilian Tax Reform.”
Chemin, Matthieu. 2012. “Does court speed shape economic activity? Evidence from a
court reform in India.” Journal of Law, Economics, and Organization, 28(3): 460–485.
Chor, Davin. 2010. “Unpacking sources of comparative advantage: A quantitative approach.” Journal of International Economics, 82(2): 152–167.
Ciccone, Antonio. 2002. “Input chains and industrialization.” The Review of Economic
Studies, 69(3): 565–587.
Costinot, Arnaud. 2009. “On the origins of comparative advantage.” Journal of International Economics, 77(2): 255–264.
Council of Europe. 2005. “European Judicial Systems 2002.” Report of the European
Commission for the Efficiency of Justice.
Cross, Frank B., and Dain C. Donelson. 2010. “Creating Quality Courts.” Journal of
Empirical Legal Studies, 7(3): 490–510.
Djankov, Simeon, Rafael La Porta, Florencio Lopez de Silanes, and Andrei
Shleifer. 2003. “Courts.” The Quarterly Journal of Economics, 118(2): 453–517.
Fally, Thibault, and Russell Hillberry. 2018. “A Coasian model of international production chains.” Journal of International Economics, 114: 299–315.
Ferguson, Shon, and Sara Formai. 2013. “Institution-driven comparative advantage
and organizational choice.” Journal of International Economics, 90(1): 193–200.
Fort, Teresa C. 2017. “Technology and production fragmentation: Domestic versus foreign sourcing.” The Review of Economic Studies, 84(2): 650–687.
Garetto, Stefania. 2013. “Input sourcing and multinational production.” American Economic Journal: Macroeconomics, 5(2): 118–151.
Grobovsek, Jan. 2020. “Managerial Delegation, Law Enforcement, and Aggregate Productivity.” University of Edinburgh Mimeo.
Grossman, Sanford J., and Oliver D. Hart. 1986. “The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration.” The Journal of Political Economy,
94(4): 691–719.
34

Hart, Oliver, and John Moore. 1990. “Property Rights and the Nature of the Firm.”
Journal of Political Economy, 98(6): 1119–58.
Head, Keith, and Thierry Mayer. 2013. “Gravity Equations: Workhorse, Toolkit,
and Cookbook.” In Handbook of International Economics Vol. 4. , ed. Gita Gopinath,
Elhanan Helpman and Kenneth Rogoff. Elsevier.
Hirschman, Albert O. 1958. The Strategy of Economic Development. Yale University
Press.
Holmes, Thomas J. 1999. “Localization of industry and vertical disintegration.” Review
of Economics and Statistics, 81(2): 314–325.
Irarrazabal, Alfonso, Andreas Moxnes, and Luca David Opromolla. 2013. “Themargins of multinational production and the role of intrafirm trade.” Journal of Political
Economy, 121(1): 74–126.
Johnson, Simon, John McMillan, and Christopher Woodruff. 2002. “Courts andrelational contracts.” Journal of Law, Economics, and organization, 18(1): 221–277.
Jones, Charles I. 2011. “Intermediate goods and weak links in the theory of economic
development.” American Economic Journal: Macroeconomics, 3(2): 1–28.
Jones, Charles I. 2013. “Misallocation, Economic Growth, and Input-Output Economics.” Advances in Economics and Econometrics: Tenth World Congress Vol. II, 419.
Kee, Hiau Looi, and Heiwai Tang. 2016. “Domestic value added in exports: Theory
and firm evidence from China.” American Economic Review, 106(6): 1402–1436.
Klein, Benjamin, Robert G. Crawford, and Armen A. Alchian. 1978. “Vertical
integration, appropriable rents, and the competitive contracting process.” Journal of
Law and Economics, 21(2): 297–326.
Laeven, Luc, and Christopher Woodruff. 2007. “The quality of the legal system, firmownership, and firm size.” The Review of Economics and Statistics, 89(4): 601–614.
La Porta, Rafael, Florencio Lopez-de-Silanes, Andrei Shleifer, and Robert W.
Vishny. 1997. “Legal Determinants of External Finance.” The Journal of Finance,
52(3): 1131–50.
Levchenko, Andrei A. 2007. “Institutional quality and international trade.” The Review
of Economic Studies, 74(3): 791–819.
Liu, Ernest. 2017. “Industrial Policies in Production Networks.” Princeton University
Mimeo.

35

Macchiavello, Rocco. 2012. “Financial development and vertical integration: theory andevidence.” Journal of the European Economic Association, 10(2): 255–289.
Narayanan, Badri, Angel Aguiar, and Robert McDougall. 2012. “The GTAP 8
Data Base.” Center for Global Trade Analysis, Purdue University.
North, Douglass C. 1990. Institutions, Institutional Change and Economic Performance.
Cambridge University Press.
Nunn, Nathan. 2007. “Relationship-specificity, incomplete contracts, and the pattern oftrade.” The Quarterly Journal of Economics, 122(2): 569–600.
Nunn, Nathan, and Daniel Trefler. 2014. “Domestic Institutions as a Source of Comparative Advanage.” In Handbook of International Economics. Vol. 4. , ed. G. Gopinath,
E. Helpman and K. Rogoff, 263–315. North Holland.
Oberfield, Ezra. 2018. “A theory of input–output architecture.” Econometrica,
86(2): 559–589.
Palumbo, Giuliana, Giulia Giupponi, Luca Nunziata, and Juan MoraSanguinetti. 2013. “The Economics of Civil Justice: New Cross-Country Data andEmpirics.” Organization for Economic Cooperation and Development Working Paper
1060.
Ponticelli, Jacopo, and Leonardo S. Alencar. 2016. “Court Enforcement, Bank Loans,and Firm Investment: Evidence from a Bankruptcy Reform in Brazil.” The Quarterly
Journal of Economics, 131(3): 1365–1413.
Rajan, Raghuram G., and Luigi Zingales. 1998. “Financial Dependence and Growth.”
The American Economic Review, 88(3): 559–586.
Ramondo, Natalia, and Andres Rodriguez-Clare. 2013. “Trade, Multinational Production, and the Gains from Openness.” Journal of Political Economy, 121(2): 273–322.
Ramondo, Natalia, Veronica Rappoport, and Kim J. Ruhl. 2016. “Intrafirm tradeand vertical fragmentation in US multinational corporations.” Journal of International
Economics, 98: 51–59.
Rauch, James E. 1999. “Networks versus markets in international trade.” Journal ofInternational Economics, 48(1): 7–35.
Santos Silva, Joao, and Silvana Tenreyro. 2006. “The log of gravity.” The Review of
Economics and Statistics, 88(4): 641–658.
Supreme Court of India. 2009. “Notes on Agenda Items, Chief Justices’ Conference.”
Supreme Court of India.
36

Tintelnot, Felix. 2016. “Global production with export platforms.” Quarterly Journal of
Economics.
Williamson, Oliver E. 1985. The economic institutions of capitalism. Simon and Schuster.

37

A

Data Description (Online Appendix)

A.1

Input-Output data

A.1.1

Definition and Sources

My input-output tables are from GTAP, Version 8. GTAP harmonizes the tables fromdifferent sources and years; Table 9 shows which tables are from which year. I aggregate
sectors in such a way that they correspond to ISIC two-digit sectors (all agricultural goods
into one sector, all food products into one sector, and oil and gas into the same sector).
The shares Xni /Xn are the “Value of Firms’ purchases of i, by sector n, in region c at
Agents’ prices”, divided by the sector’s “Value of Firms’ Output at Agents’ prices”. The
former is the sum of “Value of Firms’ Domestic Purchases at Agents’ prices” and “Value ofFirms’ Imports at Agents’ prices”. Both values (and hence the shares) originate from thecontributed IO table and are harmonized across countries; the import data is also crosschecked for consistency with Comtrade (see Chapter 7 of the GTAP Documentation).
Table 9—: Source years for the GTAP 8 Input-Output tables
Year

Countries

1988
1991
1992
1994
1995
1996
1997
1998
1999
2000

Hong Kong
Zimbabwe
Tanzania
Bangladesh, Botswana, Malawi, Paraguay
Croatia, Mozambique, Tunisia, Zambia
New Zealand, Panama, Senegal, Singapore
Mauritius, Uruguay, Venezuela
Cote D’Ivoire, Turkey
Madagascar, Nigeria, Taiwan
Albania, Argentina, Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark,El Salvador, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Nicaragua, Philippines, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sri Lanka, Sweden, United Kingdom
Azerbaijan, Georgia, Guatemala, Iran, Kenya
Armenia, Costa Rica, Ethiopia, Laos, Pakistan, Uganda, USA
Cambodia, Cameroon, Canada, Chile, Colombia, Egypt, India, Kyrgyzstan, Mexico,
Russia, South Korea
Belarus, Bolivia, Ecuador, Honduras, Indonesia, Israel, Kazakhstan, Morocco, Namibia,
Peru, Ukraine
Australia, Bahrain, Brazil, Ghana, Kuwait, Malaysia, Mongolia, Oman, Qatar,
Saudi Arabia, South Africa, Thailand, United Arab Emirates, Vietnam
China, Nepal, Norway
Switzerland

2001
2002
2003
2004
2005
2007
2008

Note: Source: GTAP 8.

A.1.2

Comparing domestic input shares and total input shares

Broadly speaking, the expenditure shares on domestically sourced intermediate inputs only
dom
(henceforth denoted Xni/Xn ) are similar to the shares that include both imported anddomestically sourced intermediates: the unconditional correlation across all country andsector-pair observation is 0.83. The sectors for which total and domestic input shares differ
most asymmetrically across countries (as measured by the average standard deviation oflog-differences of domestic and total input shares, see Table 10) are those whose production38

depends to a large extent on natural resouces: oil and gas, coal, petroleum and coal products, and gas manufacture and distribution. For these inputs, whether they are sourced
domestically or imported depends mostly on the country’s endowment in the respective
natural resource. Note that the most litigation-intensive inputs (Insurance, Business services, and Financial services) do not differ a lot across countries in their import intensity.
Table 10—: Cross-country Dispersion in Differences between Domestic and Total Input Shares
SectorDispersion

Oil and Gas
Coal
Petroleum, coal products
Gas manufacture, distribution
Motor vehicles and parts
PubAdmin/Defence/Health/Educat
Ferrous metals
Minerals nec
Electronic equipment
Transport equipment nec
Machinery and equipment nec
Metals nec
Mineral products nec
Leather products
Recreation and other services
Agriculture, Forestry, Fishing
Wearing apparelTextiles

3.86
2.68
2.15
1.66
1.61
1.60
1.50
1.49
1.48
1.47
1.43
1.36
1.26
1.23
1.22
1.22
1.13
1.09

SectorDispersion

Chemical,rubber,plastic prods
Manufactures nec
Metal products
Wood products
Sea transport
Insurance
Air transport
Food products and beverages
Construction
Business services nec
Paper products, publishing
Trade
Financial services nec
Communication
Transport nec
Electricity
Water

1.07
1.06
0.99
0.97
0.94
0.93
0.74
0.73
0.68
0.68
0.61
0.45
0.45
0.41
0.24
0.19
0.16

Note:

Dispersion is the average standard deviation of within-sector-pair log difference of total and
 
2
 c
dom,c dom,c c
PN
P
Xni
Xni Xni
Xni
1
log
/
−
log
/
domestic input expenditure shares: N1 n=1 |C|−1
.
c∈C
Xc
Xc
Xc
Xc
n

A.1.3

n

n

n

Similarity of Input-Output tables across countriescFigure 4 shows the distribution of pairwise correlations of input shares Xni/Xnc . The mean
correlation is .48. Input-output tables are much more similar in OECD countries (lightgrey bars); there, the mean correlation is .70.

A.2

Enforcement Cost

The enforcement cost δ c is the “Cost (% of claim)” from the World Bank’s Doing Business
Survey, as reported on their website in December 2011. For each country, I use the value
for 2005, or, if missing, for the year closest to 2005. Table ?? in Appendix D shows thevalues for each country.

A.3

Enforcement-Intensity

A.3.1

Construction of the number of court cases by pair of sectors

I start off with all cases in the ’Federal and State court cases’ repository from LexisLibrarythat are between January 1990 and December 2012 and include ’contract’ as one of the

39

600
Frequency
400
200
0
0

.2
.4
.6
Country-pair-wise correlation coefficient
All countries.8OECD only

Figure 4: Pairwise correlation of IO-table expenditure sharescore terms in the court opinion document.32 I then exclude all cases that are filed in acourt of appeals, or a higher court. If there have been any counterclaims, I treat themas separate cases. This leaves me with 23,261 cases that span 34,219 plaintiffs and 50,599
defendants.
I match the plaintiffs and defendants to the universe of US firms that are contained in
the Orbis database of firms, based on the name strings.33 I use a Fellegi-Sunter matchingalgorithm that compares the occurence of bigrams in each possible pairing. The first fourcharacters are weighted more heavily. If the score is above a threshold (0.92), I consider
the match to be successful. I then match the SIC classifications from Orbis to GTAP
sectors, using a hand-written concordance table, which is partly based on the definition of
the GTAP sectors in terms of CPC or ISIC codes34 , and partly on the description of thesectors. Since I am only interested in the industry of the plaintiff and defendant firms,
if both firm names in a candidate pair contain the same trade name (’bank’,’architects’,etc.), I also regard the pair as matched even if their matching score is below the threshold.
Table 11 summarizes the results of the matching process. I manage to associate 50.5
percent of all parties to firms in Orbis. In order to see whether the fraction of matched
entries is close to the number of possible matches, one needs to know the fraction of businesses (or at least non-individuals) among the plaintiffs and defendants. This information
is not available in LexisLibrary. However, I compare the matching rates with the fraction ofbusiness plaintiffs and defendants in an auxiliary dataset, the Civil Justice Survey of State
Courts 1992, which covers (among other things) a sample of 6,802 contract cases in state32

I thank Jinesh Patel and the legal team at LexisNexis UK for permission to automatically retrieve andprocess the LexisLibrary data.
33
This includes many US subsidiaries of foreign firms. The total number of US firms in my version of
Orbis is 21,014,945.
34
See https://www.gtap.agecon.purdue.edu/databases/contribute/concordinfo.asp

40

courts.35 In that dataset, 53.9 percent of all parties are non-individuals, and 49.6 percent
are businesses. Even though it is likely that parties in federal courts are more likely to bebusinesses and organizations rather than individuals, this comparison supports the viewthat I am able to match most of the relevant parties.
Table 11—: Matching Plaintiffs and Defendants to Orbis Firms: Statistics
Plaintiffs
numberin pctHandmatched:
Population:
Matches:

perfect matches
above thresholdbased on trade name

Total matches:
Civil Justice Survey:

A.3.2

Defendants
numberin pctAll
numberin pct

169
34388

100.0

223
50822

100.0

392
85210

100.0

1609
12778
808

4.7
37.2
2.3

1551
25838
1325

3.1
49.2
2.6

3160
37779
2133

3.7
44.3
2.5

15195

44.2

27877

54.9

43072

50.5

non-individuals
businesses

53.9
49.6

Construction of the proxy for US buyer-seller relationships from Japanesedata

I construct a proxy for the number of buyer-seller relationships by sector pair in the UnitedStates using data on Japanese buyer-supplier linkages from Tokyo Shoko Research (TSR).
The TSR data covers more than 950,000 firms from all sectors of the economy, which is
close to the population of Japanese firms with more than four employees (see Bernard etal., 2015, for a more detailed description). Its underlying industry classification is basedon JSIC, which I map to the GTAP sectors using a JSIC–NACE concordance provided byEurostat. I then project the number of buyer-supplier relationships by pair of GTAP sectors
on the number of firms in upstream and downstream sectors (from the 2004 Establishment
and Enterprise Census of the Japanese Statistics Bureau, again concorded from JSIC) andthe IO table expenditure shares (from GTAP):
(16)
JP N

Xni
JP N
JP N
JP N
+ε̂ni
log(#links)ni = −4.15+0.70 log(#firms)n +0.57 log(#firms)i +0.13 log(0.02)(0.02)(0.01)
Xn(0.29)The R2 in this regression is 0.69. I then use this linear model together with data on thenumber of US enterprises by sector (from the US Census Bureau, mapped to GTAP using
the NAICS–ISIC concordance) to construct an estimate of the number of buyer-supplierlinkages in the US:

U S
U S
X
ni
U
S
U
S
\
log #links≡ −4.15 + 0.70 log(#firms)n + 0.57 log(#firms)i + 0.13 log
Xn
ni


35

See US Department of Justice (1996) for a description. In calculating the figures in Table 11 I exclude
cases that pertain to mortgage foreclosure, rental agreements, fraud, and employment.

41

(a) z (1)(b) z (2)Figure 5: Enforcement-intensity z (1) and z (2)Note: Figure shows the enforcement-intensity measures z (1) and z (2) by sector pair. Selling sector is on thex-axis, buying sector on the y-axis. Darker shades indicate higher values. Values have been monotonicallytransformed to improve readability.

The alternative enforcement-intensity measure is then(2)zni = (# cases between sectors i and n)

A.3.3

U S
\
#links
.
ni

(1)

(2)

The resulting enforcement-intensity measures zni and zni

The resulting measures z (1) and z (2) are very similar, with a correlation of 0.85. Most of
the variation is driven by characteristics of the selling sector: 18.5% of the overall variation(1)(2)
in zni is explained by upstream sector dummies (18.7% for zni ), and only 8.4% (6.8%) by
downstream sector dummies.
Figure 5 shows the values of z (1) by sector pair, with higher values marked in a darker
shade of grey. Observe that the measures vary considerably across buying sectors within
selling sectors: columns are not uniformly of the same shade. Reading through Lexis’ casesummaries yields a sense for why the litigiosity measures look the way they do.
The first observation is that contracts with firms from the same sector are, on average,
more litigious than with other buyers (i.e. the diagonal is darker in Figure 9a). This is
not only because there are disproportionally many vertical relationships within the same
sector (a fact known from input output tables themselves), but particularly because manyof the within-sector disputes arise from horizontal licensing of patents, trademarks, and42

intellectual property more generally (examples are, among many others, Verson Corp. vs.
Verson International PLC et al., 93 C 2996 (N.D. Ill. 1993), Zaro Licensing Inc. et al.
vs. Cinmar Inc. et al., 779 F. Supp. 276 (N.D. NY 1991)), sometimes in conjunction
with antitrust considerations (e.g. Advanced Micro Devices, Inc. vs. Intel Corp., C 91
20541 JW (N.D. Cal. 1991)). Such agreements are at the heart of firms’ organizational
and technological choices. The Economist (2017)36 documents a prominent example: theinvention of small-scale steel mills and their subsequent licensing and adoption by othersteel producers. Collard-Wexler and De Loecker (2015) study the associated productivity
gains and organizational changes. From an economic point of view, many (though not all)licensing contracts are highly prone to hold-ups: once technological knowledge has beenshared, it cannot be withdrawn, and may enable the licensee to build new technologies
on top of the licensed ones; similarly, a licensor cannot physically prevent a licensee fromusing a copyrighted trademark. In such situations the availability of formal legal recourse
is often indespensable to the establishment of market transactions.
The second observation is that services sectors, in particular Insurance, Business Services, and Finance, are more litigious than the other sectors. Insurance contracts, by
nature, are subject to the problem of default on the side of insurer, and if the insurance
contract cannot be enforced, it is worthless. Similarly to licensing agreements, businessservices and financial services are prone to hold-ups due to the intangibility of the product.
While the enforcement-intensity of insurance contracts do not vary as much across downstream sectors as other sectors, it is apparent that litigation is more frequent with heavy
industry sectors (ferrous metals, machinery, chemicals, minerals), construction, transportation, and public services (chiefly, healthcare). Reading the case narratives, one gets theimpression that litigation is particularly prevalent whenever the insurance claims are large.
In such cases, the insurer has a stronger incentive to ex-post renege on the contract.
Figure 5 also shows that litigation is surprisingly high for particular off-diagonal sector
pairs. These pairs are not alike, and there are often particular circumstances associatedwith trade between certain sectors that give rise to litigation. In the following discussion I attempt, based on my reading of the case backgrounds in each industry’s cases inLexisLibrary, an interpretation why in some sector pairs litigation is particularly prevalent.
In cases between coal suppliers to electricity producers, disputes arise mostly because
these markets use formal contracts that tie trading partners together for a long time,
under very specific (and often strongly regulated) conditions. In Teco Coal Corp. et al. vs.
Orlando Utilities Commission (6:07-CV-444-KKC, E.D. Kent. 2008) the supplier finds
these terms to make its business commercially unviable. In Central Lousiana Electric Co.
et al. vs. Dolet Hills Mining Venture (116 F. Supp. 2d 710 (W.D. Louis. 1999)), parties
are in disagreement on whether the specific clauses of their long-term contract have beensatisfied. In each case, the existence of long-term contracts that strongly ties buyers andsuppliers together destroys the generic nature of a good that might otherwise be traded on
36“New technologies could slash the cost of steel production”, The Economist, 9 March 2017.

43

a spot market (coal/lignite) with little litigation arising.
Cases between manufacturers of ferrous metals and metal products, machinery, andtransport equipment arise mainly due to disputes about the quality and specifications of
the specific metals. A typical case is Alloys International vs. Aeronca (1:10-cv-293 S.D.
Ohio 2012), in which the plaintiff, a manufacturer of specialized metals, seeks damages
for the sunk production cost of custom-made metal coils after the defendant cancels theorder and refuses payment. A similar debt recovery case is Eliott Brothers Steel Co. vs.
Michigan Metals et al. (07-15520, E.D. Mich. 2008). These cases are close to the stylized
hold-up problem in Klein et al. (1978).
Cases between manufacturers of transport equipment and transportation companies
often revolve around claims related to construction, maintenance and repair of maritime
vessels (the latter typically taking place in the shipyards where the ships were built).
Examples are United Rentals North America vs. Maritrend Inc. et al. (OO-3600 T 4,
E.D. Louis. 2002) and Susquehanna Santee Boatworks vs. River Street Ferry (01-4229,
E.D. Penn. 2005). Note that cases related to maritime vessels are more frequent than cases
related to aircraft; this is in line with aircraft being more homogeneous and standardized
than ships (see Benmelech and Bergman’s papers on aircraft as collateral).
Cases where the seller belongs to the machinery and equipment industry are relatively
most frequent in transactions with motor vehicles industry. These contracts typicallyinvolve relationship-specific investments on the side of the supplier, and sometimes also on
the side of the buyer — indeed, they were Monteverde and Teece’s (1982) classic example ofrelationship-specific investment. Examples include Techsys Chassis Inc. vs. Sullair Corp.
(4:08-cv-203, E.D. Tex. 20XX), where plaintiff and defendent worked together on a new
chassis for one of defendant’s products, under the agreement that plaintiff would be theexclusive supplier for these components. This agreement was alleged to have been violated.
In Arens Controls Co. vs. Enova Systems Inc. (08 CV 6994, N.D. Ill. 2012), the plaintiff
designed and produced custom-made power inverters for the defendant; the defendant wasalleged to have reneged on the purchase of some of the power inverters. Similar situations
are found in disputes with firms from the coal, mining, and construction industries.
Cases between electricity companies and heavy industry often revolve around the installation of electricity-related equipment (transformers, compensators). An example is
Structural Metals vs. S&C Electric Company (SA-09-CV-984-XR, W.D. Tex. 2012). As
the power infrastructure of these factories is typically custom-made and site-specific, holdups may arise.
Cases where the supplier is providing an ocean shipping service seem to be more prevalent when the transported good is a basic raw material (e.g. iron ore) than when it’s afinished good (toys from China). Cases related to the former often feature problems during
the delivery (contamination of chemicals in Sterling Chemicals Inc. et al. vs. Stolt-Nielsen
Inc et al. (97 Civ. 8018, S.D. NY 2004), disappearance of the cargo in Luvata Buffalo
Inc. et al. vs. Mol Mitsui Lines et al. (08-CV-0701(A)(M), W.D. NY 2010). A plausible
44explanation would be that in such cases the recipient’s revenue elasticity of the shipped
products is higher, therefore the value of the claim is higher, which is more likely to lead tolitigation. In other words, when Walmart does not receives a shipment of toys from China
it is harmed less than when a steel company cannot produce because it did not receive its
shipment of iron ore. (Normally these shipments are insured, and often the insurer is aninterested party in the case.)
Finally, cases between firms in the PubAdmin/Defence/Health/Education sector andInsurance companies are varied. In some cases they are about regulation of insurers, inothers about contracts between health providers and insurers, as in Shady Grove Orthopedic
Assoc. et al. vs. Allstate Insurance Co. (466 F. Supp. 2d 467, E.D. NY 2006).
A.3.4

Comparing my enforcement-intensity measures to existing measures

In this section I compare the z measures to the measures of dependence on institutions
used by Levchenko (2007) and Nunn (2007). Levchenko’s measure is the Herfindahl index
of US intermediate input expenditures:

ln =

N
X

US
Xni

!2

PN
i=1

US
i0 =1 Xni0

Since this measure depends crucially on the level of disaggregation of input industries, I
use Levchenko’s original measure (which is constructed from finer I-O tables than what
GTAP uses), and aggregate it to the 35-sector level by taking unweighted averages.
Nunn (2007)’s measure of dependence on contracting institutions builds on Rauch’s(1999) classification of SITC goods into whether they are traded on an organized exchange,
whether there exists a reference price in a trade publication, or whether neither of the two is
the case. Using these measures, I construct for each sector i the fraction of output in the US
that is neither traded on an organized exchange, nor for which there is a reference price.
This yields measures ricon and rilib , using Rauch’s conservative and liberal classification,
respectively. Rauch’s classifications are only available for physical goods, so I set r equal
to one for services industries. Analogously to Nunn (2007), I construct the fraction of asector n’s inputs that is relationship-specific:
Nunnn =

N
X

US
Xni

PN

US
i0 =1 Xni0

i=1

!
ri

The resulting measures are positively correlated with the averages of z (1) and z (2) .
Table 2 in the main text shows correlations by downstream sector n; Table 12 below shows
correlations by upstream sector i with ricon and rilib .

45

Table 12—: Spearman rank correlations between institutional dependency measures(1)

NunnconnNunnlib
n
ricon
rilib
ln

(2)

z̄i

z̄i

0.14
0.14
0.21
0.22
0.08

0.12
0.12
0.20
0.21
0.07

Note: The table presents Spearman rank correlations between the average z measures (for each upstream
sector i, averaged across downstream sectors) and the conservative and liberal measures of Nunn (2007),the conservative and liberal measures of Rauch (1999), and the measure of Levchenko (2007).

A.4

Other data

Data for the number of firms by US sector come from Census Bureau Statistics on US
Businesses (for the year 2000; concorded using the official NAICS-SIC concordance and the
SIC-GTAP concordance). Financial development, F IN DEV c , is the amount of domestic
credit to private sector as fraction of GDP, in the year 2000, from the World Bank’s
World Development Indicators. Data for GDP C c (GDP per capita, PPP adjusted, inconstant USD, for the year 2000) are also from the World Bank’s World Development
Indicators. Finally, Rauch’s classification of goods was downloaded from James Rauch’s
website and concorded to GTAP sectors via Feenstra’s SITC-HS concordance and the HSGTAP concordance.
Table 13—: Summary statistics
VariableIntermediate Input Share
Domestic Intermediate Input Share
Enforcement Costs δ(1)
Enforcement-Intensity zni(2)
Enforcement-Intensity zni

Mean

Std. Dev

Min

Max

N

0.53
0.37
0.29
2.36·10−5
1.13·10−4

0.08
0.08
0.22
7.73 ·10−5
4.11 ·10−4

0.25
0.12
.088
0
0

0.69
0.58
1.425
.0015
.0041

109
109
109
1225
1225

Note: ‘Intermediate input share’ refers to the sum of all intermediate inputs (materials) divided by gross(1)(2)
output. The correlation between zni and zni is 0.85.

B

A microfoundation for the contracting frictions

This section presents a contracting game between a buyer and supplier, where relationshipspecific investment leads to hold-up. Contracts are enforceable, but enforcement is costly:
the plaintiff has to pay a fraction δ of the value of the claim to the court. Courts award expectation damages, i.e. they order damage payments to compensate the innocent party for
any loss that has arisen due to the breach. As in Shavell (1980), this limits the contracting
space. In the presence of δ > 0, the optimal contract does not achieve the first-best. When
enforcement costs are sufficiently low, the outcome improves on the incomplete contract

46

Figure 6: Timeline of the contracting gamet1

t2

Buyer andsupplier sign
contract(q ∗ , M (q))

Supplier
produces q
units, delivers
min(q, q ∗ )t3
Buyer either
pays fee M (q)or holds up
the suppliert4
Nashbargaining tosettle contract

t5

t6

Nash
bargaining
over any
excessproduction

Buyer receives
R(q)outcome; if they are higher, parties will prefer the incomplete contract outcome, in whichcase the distortion depends only on the degree of relationship-specificity of the produced
goods. The resulting distortion is a special case of the assumed functional form for dni inthe main text.
The description of the contracting game proceeds as follows. I first describe the contracting space, and discuss the timing of events and the enforcement mechanism. I thensolve the contracting game. Going back in time, I describe the problem of finding an
optimal contract and characterize the equilibrium thereunder.

B.1

Setup of the contracting gameThe contract between buyer and supplier is a pair (q ∗ , M (·)), where q ∗ ≥ 0 is the quantityof the good to be delivered37 , and M : [0, q ∗ ] → R\R− is a nonnegative, increasing realvalued function that represents the stipulated payment to the supplier. M (q ∗ ) is the agreed
fee. If M (q) < M (q ∗ ) for q < q ∗ , this represents damage payments that are agreed upon at
the time of the formation of the contract, for enforcement in case of a breach of contract(“liquidated damages”).38 I will explain the exact enforcement procedure after stating thetiming of events.
Timing of events:
1. The buyer and the supplier sign a contract (q ∗ , M (q)) which maximizes the buyer’s
payoff, subject to the supplier’s payoff being nonnegative. At this point the buyer
cannot perfectly commit to paying M (q) once production has taken place, other than
through the enforcement mechanism explained below.
2. The supplier produces q units. He chooses q optimally to maximize his profits. I
assume that if q < q ∗ , he delivers all the produced units; if q ≥ q ∗ , he delivers q ∗and retains control of the remaining units.A unit that has been delivered is under
the control of the buyer.
37

The supplier’s chosen quantity q may likewise be interpreted as quality of the product, or effort. The
legal literature calls this relationship-specific investment reliance (Hermalin et al., 2007).
38
Most jurisdictions impose strong limits on punishment under these clauses. In English law, in terroremclauses in contracts are not enforced (Treitel, 1987, Chapter 20). German and French courts, following
the Roman tradition of literal enforcement of stipulationes poenae, generally recognize penal clauses incontracts, but will, upon application, reduce the penalty to a ’reasonable’ amount (BGB § 343, resp.
art. 1152 & 1231, code civil, and Zimmermann, 1996, Chapter 4). Given my assumptions on the courts
awarding expectation damages (see below), any restrictions on M are not going to matter.

47

3. The buyer decides whether or not to hold up the supplier by refusing to pay M (q).
4. If the contract has been breached (either because q < q ∗ or because the buyer did not
pay the fee M (q)), either party could enforce the contract in a court. The outcomeof enforcement is deterministic, and enforcement is costly. Hence, the two parties
avoid this ex-post efficiency loss by settling out of court. They split the surplus using
the symmetric Nash sharing rule, whereby each party receives the payoff under theoutside option (i.e. the payoff under enforcement), plus half of what would have been
lost to them in the case of enforcement (the enforcement costs). I explain the payoffs
under enforcement below.
5. In case the supplier has retained control over some of the produced units, q − q ∗ ,the two parties may bargain over them. Again I assume that they split the surplus
according to the symmetric Nash sharing rule. Since there is no contract to govern
the sale of these goods, the outside option is given by the supplier’s option to revert
the production process.
6. The buyer receives revenue/utility R(q).
Enforcement:
After the buyer’s decision whether or not to hold up the supplier, either party may feelthat they have been harmed by the other party’s actions: the supplier may have produced
less than what was specified (q < q ∗ ), and the buyer may have withheld the fee M (q). Either
party may enforce the contract in the court. The court perfectly observes all actions byboth parties, and awards expectation damages as a remedy. The basic principle to govern
the measurement of these damages is that an injured party is entitled to be put “in as
good a position as one would have been in had the contract been performed” (Farnsworth(2004), §12.8). The precise interpretation of this rule is as follows:• If the supplier has breached the contract, q < q ∗ , he has to pay the buyer thedifference between the buyer’s payoff under fulfillment, R(q ∗ ) − M (q ∗ ), and underbreach, R(q) − M (q). Hence, he has to pay
D(q, q ∗ ) = R(q ∗ ) − M (q ∗ ) − (R(q) − M (q)) .
• In addition, if the buyer has not paid the fee M (q), the court orders him to do so.
It is important to stress that the resulting net transfer may go in either direction, dependingon whether or not the parties are in breach, and on the relative magnitude of M (q) andD(q, q ∗ ).
I assume furthermore that the plaintiff has to pay enforcement costs, which amount toa fraction δ of the value of the claim to him. The value of the claim is the net transfer

48

to him that would arise under enforcement.39 These costs include court fees, fees for legal
representation and expert witnesses, and the time cost. The assumption that enforcement
costs are increasing in the value of the claim is in line with empirical evidence (Lee andWillging, 2010), and also strengthens the link between the model and the empirical analysis
in the main text: my data for enforcement costs are given as a fraction of the value of theclaim. In line with the situation in the United States, I assume that enforcement costs
cannot be recovered in court (Farnsworth, 2004, §12.8).40

B.2

Solving for the equilibrium of the contracting game:I solve for a subgame-perfect Nash equilibrium, which, for a given contract, consists ofthe supplier’s production choice qs and the buyer’s holdup decision, as a function of q.
The holdup decision function gives the buyer’s optimal response to a produced quantity q,
and the optimal production choice qs is then the supplier’s optimal quantity q, taking the
holdup decision function as given. The full solution of the game is in Appendix C.1. Here,I discuss the intuition for the optimal responses and the payoff functions.
Case 1: Seller breaches the contract. Consider first the case where the supplier decides
to breach, q < q ∗ . The buyer refuses to pay M (q), in order to shift the burden of enforcement (and thus the enforcement costs) on the supplier. Hence, in the case of enforcement,
the supplier would receive a net transfer of M (q) − D(q, q ∗ ). This transfer is positive: if
it was negative, the supplier’s overall payoff would be negative and he would not haveaccepted the contract in the first place. Thus, under enforcement, the supplier would be
the plaintiff and would have to pay the enforcement costs. To avoid the efficiency loss, thetwo parties bargain over the surplus and settle outside of court. Under the symmetric Nashsharing rule each party receives its outside option (the payoff under enforcement) plus one
half of the quasi-rents (the enforcement costs). Thus, the supplier’s overall payoff underbreach is(17)
πs (q, M, q ∗ ) = (1 − δ) (M (q) − D(q, q ∗ ))
{z
}
|

+

1
δ (M (q) − D(q, q ∗ )){z}2|
quasi-rents

payoff under enforcement−

qcni (j)| {z }

production cost

if q < q ∗ . Since D(q, q ∗ ) = R(q ∗ ) − M (q ∗ ) − (R(q) − M (q)), the above simplifies to
(18)



1
πs (q, M, q ) = 1 − δ (R(q) − R(q ∗ ) + M (q ∗ )) − qcni (j)2∗39

if q < q ∗ .

If the net transfer is negative, he would not have chosen to enforce in the first place. However, theother party would then have had an incentive to enforce, and would have been the plaintiff. I show laterthat in equilibrium the plaintiff is always the supplier.
40
Many countries have the enforcement costs paid by the losing party (’cost shifting’). See Jackson(2009a) for a comparative analysis. While cost shifting may mean that in some circumstances punishment
would be possible and therefore higher quantities could be implemented, the resulting model does not allow
for closed-form solutions.

49

Note that the buyer’s revenue function R appears in the supplier’s payoff function. Thisis due to the courts awarding expectation damages: the fact that damage payments areassessed to compensate the buyer for forgone revenue means that the supplier internalizes
the payoff to the buyer. The enforcement costs δ govern the supplier’s outside option,and hence the settlement: higher enforcement costs means that the supplier can recovera smaller fraction of his fee net of damages; therefore, the terms of the settlement are
worse for him. Note also that the contract (q ∗ , M ) enters (18) only through q ∗ and M (q ∗ ),and only in an additive manner. This is because the court awards damages such that thesum of liquidated damages and expectation damages exactly compensates the buyer. If
enforcement costs δ were zero, the expectations damages rule would ensure an outcomethat is efficient within the bilateral relationship.41
Case 2: Seller fulfills the contract. Consider next the case where the supplier fulfills hispart of the contract, q ≥ q ∗ . He delivers q ∗ units to the buyer, and keeps the remaining
units to himself. As in the case above, the buyer refuses to pay the fee M (q ∗ ): subsequent
enforcement of the contract would leave the seller with a payoff of only (1 − δ)M (q ∗ );hence, under the settlement with the symmetric Nash solution, the buyer only has to pay(1 − 12 δ)M (q ∗ ). After the settlement of the contract, the two parties may bargain over theremaining q − q ∗ units. The Nash sharing rule leaves the supplier with its outside option(what he would get by reversing the production process for the q − q ∗ units) plus one halfof the quasi-rents. Thus, the supplier’s overall profits are1
πs (q, M, q ) = 1 − δ M (q ∗ ) + ωni cni (j) (q − q ∗ )
|
{z
}
2
|
{z
} payoff under reverting
∗

(19)



contract payoff1+ (R(q) − R(q ∗ ) − ωni cni (j) (q − q ∗ )) −{z}
2|quasi-rents

qc (j)| ni{z }production cost

if q ≥ q ∗ . Hence, even in the case where the supplier fulfills his part of the contract, thecontract (q ∗ , M ) only enters additively in the supplier’s payoff function. The terms of thebargaining that governs the marginal return on production are now given by the degree ofrelationship-specificity. A higher degree of relationship-specificity, captured by a lower ωni ,worsens the supplier’s outside option and hence lowers his payoff under the settlement.
Going back in time, the supplier chooses q to maximize his profits, given piecewise by(18) and (19). The supplier’s profit function is continuous at q ∗ , and the shape of the exante specified payoff schedule M does not affect πs . This means that the buyer is unable
to punish the supplier for producing less than the stipulated quantity, and q < q ∗ may
happen in equilibrium.
The Optimal Contract:
41

This point was first made by Shavell (1980), who argued that when courts assign expectation damages,
the parties may achieve first-best even if the contractually specified payoff is not state-contingent. Similarly,
I argue here that under expectation damages the state-contingent payoffs do not matter, and that thepresence of proportional enforcement costs then leads to efficiency loss.

50

I now turn to the buyer’s problem of finding an optimal contract. He chooses a contract(q ∗ , M ) that maximizes his payoff πb subject to participation by the supplier,(q ∗ , M ) = arg max(qˆ∗ ,M̂ ) πb qs (qˆ∗ , M̂ ), qˆ∗ , M̂
s.t. πs qs (qˆ∗ , M̂ ), M̂ , qˆ∗ ≥ 0

(20)
(21)

where qs (qˆ∗ , M̂ ) is the supplier’s profit-maximizing quantity,qs (qˆ∗ , M̂ ) = arg maxq≥0 πs (q, M̂ , qˆ∗ ).
Since there is no ex-post efficiency loss, the buyer’s payoff πb is the total surplus minus the
supplier’s payoff,
πb q, M̂ , qˆ∗ = R(q) − qcni (j) − πs q, M̂ , qˆ∗ .
In the solution to the contracting game above, I have shown that a contract (q ∗ , M )enters the payoff functions in each case only in an additive manner. Therefore, by settingq ∗ and M , the buyer can only influence the supplier’s decision by shifting the threshold forbreach q ∗ . In choosing an optimal contract, the buyer thus decides whether he wants toimplement the interior maximum in the case of breach by the seller (case 1), or the interiormaximum in case of fulfillment by the supplier (case 2). He will choose the case that is
associated with the smaller amount of distortions. The following proposition formalizes
this intuition, and characterizes the equilibrium under an optimal contract. It describes(1) the produced quantity, (2) whether the equilibrium features a breach or a fulfillment
by the seller, and (3) the distribution of the rents between the two parties. Appendix C.1
contains the proof.
Proposition 2 (Equilibrium under an optimal contract) An optimal contract (q ∗ , M )satisfies the following properties:
1. The quantity implemented, qs (q ∗ , M ), satisfies
(22)



1
dR(q)
c
= min 2 − ωni ,dq q=qs (q∗ ,M )1 − 12 δ

2. qs (q ∗ , M ) < q ∗ if and only if (1 − 12 δ)−1 < 2 − ωni .
3. The whole surplus from the relationship goes to the buyer:
πs (qs (q ∗ , M ), M, q ∗ ) = 0
To interpret this result, it is helpful to compare the equilibrium quantity qs (q ∗ , M ) to
the first-best quantity q̃, which is defined as the quantity that maximizes the overall surplus
from the relationship,q̃ ≡ arg maxq≥0 R(q) − qcni (j).
51

The first statement of Proposition 2 says that the equilibrium quantity produced underan optimal contract, qs (q ∗ , M ), is lower than the first-best quantity q̃ (recall that R is
concave, and that 2 − ωni > 1). The intuition for the efficiency loss depends on whether
the equilibrium features a breach or a fulfillment by the supplier. If the supplier breaches
by producing q < q ∗ , the presence of proportional enforcement costs mean that the supplier
could only recover a smaller fraction of his fee net of damages by going to court. Under
the settlement he does not get the full return on his effort, which causes him to ex-ante
produce less than the efficient quantity. Note that in the absence of enforcement costs(δ = 0), the supplier completely internalizes the buyer’s payoff through the expectation
damages, and the resulting outcome would be first-best. The magnitude of the efficiency
loss in this case depends solely on the magnitude of enforcement costs. In the case where
the supplier fulfills his part of the contract, q ≥ q ∗ , the degree of relationship-specificity
governs the supplier’s outside option in the bargaining, and thus the marginal return on
production. A higher relationship-specificity (lower ωni ) means that the supplier’s outside
option becomes worse, which results in a lower payoff under the settlement. The supplier
anticipates the lower ex-post return on production, and produces less (Klein et al., 1979).
The second statement says that the optimal contract implements a breach by the seller if
and only if the cost of enforcement is low compared to the degree of relationship-specificity.
Given that it is impossible to implement the efficient quantity, the optimal contract implements the case with the lower associated distortions (hence also the minimum function in
expression (22)). If the cost of enforcement is relatively low, the optimal contract implements a breach by setting a high q ∗ : after the hold-up, the control over the produced units
is with the buyer, and the supplier’s only asset is the enforceable contract whose value
depends on the (relatively low) enforcement costs. On the other hand, when the degreeof relationship-specificity is low and enforcement costs are high, the optimal contract will
pick a low q ∗ to allocate the residual rights of control over the excess production q − q ∗with the supplier. In that case, his ex-post return on production depends on his ability toreverse the production (i.e. the parameter ωni ). Hence, the optimal contract maximizes
the surplus by maximizing the producer’s ex-post return on production.42
The third statement says that the above is implementable while still allocating thewhole surplus from the relationship to the buyer. This is not trivial, since the supplier’s
payoff schedule M is required to be nonnegative.
The reader may be concerned about the possibility of ’overproduction’ (q > q ∗ ) arising
as an equilibrium outcome in the model despite there being little evidence on this actually
happening in practice. The right way to interpret such an equilibrium is as an outcome to
an informal contract, where the option to enforce the claim in a court is either non-existentor irrelevant. Indeed, a contract where M = 0 and q ∗ = 0 would be equivalent to thesituation where enforceable contract are not available, as in the literature on incomplete
42This is similar to the optimal allocation of property rights (Grossman and Hart, 1986, Hart and Moore,1990).

52

contracts (Klein et al., 1979, and others). The only reason why the optimal contract inthis case features a small but positive q ∗ is because this allows the buyer to obtain the full
surplus from the relationship. If I allowed for an ex-ante transfer from the supplier to thebuyer, setting q ∗ and M to zero would be an optimal contract in the case where the degreeof relationship-specificity is relatively low compared to enforcement costs.43
To summarize, the main benefit of having enforceable contracts is that when the stipulated quantity q ∗ is sufficiently high, the degree of relationship-specificity does not matterfor the resulting allocation and the ex-ante investment. The drawback is that the presenceof enforcement costs distorts the supplier’s decision. Hence, choosing a high q ∗ will only be
optimal if the degree of relationship-specificity is sufficiently high, so that the efficiency loss
associated with a breach is lower than the efficiency loss associated with an unenforceable
contract.
The model also yields a qualitative prediction on the occurrence of breach.
Corollary 1 (Relationship-specificity and breach) Let δ < 1 and the parties sign an
optimal contract. Then, for sufficiently high degree of relationship-specificity (i.e. for a
sufficiently low ωni ) the seller breaches the contract in equilibrium.
If litigation can only happen in the case of breach, then this means that litigation should
be more frequent when goods are more relationship-specific.

C

Proofs and Further Results on the Model

C.1

ProofsC.1.1

Proof of Proposition 2

A contract is a pair (q ∗ , M (q)) where q ∗ ≥ 0 and M : [0, q ∗ ] → R\R− is a nonnegative increasing function. I call a contract C feasible if there is a quantity q ≥ 0 suchthat the ex-ante profit from the relationship to the seller if he produces q, πs (C, q), is
nonnegative. Feasible contracts will be accepted by a potential supplier. Moreover, I
call a quantity q̂ ≥ 0 implementable if there is a feasible contract C such that the seller
decides to produce q̂ once he has accepted the contract (i.e. q̂ = arg maxq πs (C, q)). Finally, a feasible contract C is optimal if the payoff to the buyer under the seller’s optimal production choice is maximal in the class of feasible contracts (i.e. Ĉ is optimal ifĈ = arg maxC, C feasible πb (C, arg maxq πs (C, q))).
Suppose the buyer and seller have signed a feasible contract C. The first step is to findthe payoff functions for the buyer and seller, πb and πs . Let q be the produced quantity.
Distinguish two cases:
43
The model thus makes a case for the possible desirability of informal contracts: if the degree ofrelationship-specificity is low and enforcement costs are high, it is preferable to choose an informal contract
rather than specifying a high q ∗ and have the supplier underperform due to the presence of high enforcement
costs.

53

1. The seller decides to breach the contract by producing less than the stipulated quantity: q < q ∗ . The buyer will then hold up the seller by refusing to pay M (q). I willshow later that this is indeed optimal. If one of the two parties decides to go tocourt, the court would (i) order the buyer to pay the agreed fee M (q) to the seller,(ii) order the seller to pay damages to compensate the buyer for the loss that hasarisen due to breach. Under fulfillment of the contract, the buyer should receive theproceeds from selling q ∗ to the downstream firm, R(q ∗ ), minus the fee paid to theseller, M (q ∗ ). Thus, the amount of damages areD(q, q ∗ ) ≡ R(q ∗ ) − M (q ∗ ) − (R(q) − M (q)) .

(23)

The plaintiff also has to pay enforcement costs. In order to determine who the plaintiff
would be, I need to distinguish between two subcases.
(a) M (q) − D(q, q ∗ ) > 0. In this case the fee that the seller would receive exceed thedamages that he would have to pay, thus the seller would have an incentive to go
to court. If he did that, he would receive the above amount minus enforcement
costs, which amount to a fraction δ of the value of the claim. Thus, underenforcement, the supplier would get(1 − δ) (M (q) − D(q, q ∗ )) ,(24)

whereas the buyer would get the revenue from selling to the downstream firm,
net of fees M (q) and plus damage payments
R(q) + D(q, q ∗ ) − M (q).

(25)

From the definition of the damages (23) it is easy to see that the latter equalsR(q ∗ ) − M (q ∗ ). Since enforcement entails a social loss of δ (M (q) − D(q, q ∗ )),the buyer and seller will bargain over the surplus and settle out of court. (24)and (25) are the seller’s and buyer’s outside options in the Nash bargaining. The
symmetric solution in the bargaining leaves each party with its outside option
and one-half of the quasi-rents (surplus minus the sum of outside options). Thus,
the total payoffs under breach are, respectively
1
if q < q ∗πs (q) =1 − δ (M (q) − D(q, q ∗ )) − cq21
πb (q) = R(q) − 1 − δ (M (q) − D(q, q ∗ ))if q < q ∗
2


(26)

Comparing πb here with the payoff in case the buyer did not hold up the seller,
R(q) − M (q), shows that it is preferable for the buyer to hold up. Note thatsince the buyer already has control over the produced goods, the seller cannot
54

revert the production process.
(b) M (q) − D(q, q ∗ ) < 0. In this case, the damages paid to the buyer exceed thefee that he would have to pay to the seller. The buyer thus has an incentive toenforce the contract in a court, and would have to pay the enforcement costs.
Thus, under enforcement, the seller’s payoff is
M (q) − D(q, q ∗ )and the buyer’s payoff isR(q) + D(q, q ∗ ) − M (q) − δ (D(q, q ∗ ) − M (q)) .
The two parties settle outside of court using the symmetric Nash sharing rule;each receives its outside option (i.e. payoff under enforcement) plus one half ofthe quasi-rents (enforcement costs). Thus, the seller’s ex-ante payoff is1
πs (q) = M (q) − D(q, q ∗ ) + δ (D(q, q ∗ ) − M (q)) − cq
2


1
=
1 − δ (M (q) − D(q, q ∗ )) − cq < 0
2
Since the ex-ante payoff of the seller is negative and I am only considering
feasible contracts (i.e. the seller’s payoff function is nonnegative for some q),
this case will never be chosen by the seller.
2. Fulfillment of the contract, q ≥ q ∗ . The supplier delivers q ∗ units and holds back therest. The buyer holds up the supplier by refusing to pay M (q ∗ ) (again, comparing
this to the non-hold-up payoff shows that this is optimal). If the supplier goes tocourt to claim his payment, he would receive M (q ∗ ) minus the enforcement costsδM (q ∗ ). The court awards no damages, since there has not been any loss in value.44
Since going to court entails a welfare loss, the parties are going to settle outsideof court using the symmetric Nash sharing rule. Under the settlement the supplier
receives M (q ∗ )−δM (q ∗ )+ 12 δM (q ∗ ) = 1 − 12 δ M (q ∗ ), and the buyer receives R(q ∗ )−M (q ∗ )+ 21 δM (q ∗ ). Once this is done, there may be excess production q−q ∗ left, whichis still more valuable to the buyer than to the seller. Again, the two parties bargain
over the surplus from these goods, which is the additional revenue from selling theexcess production to the downstream firm, R(q) − R(q ∗ ). Since there is no contract
governing the sale of these goods, the seller is left with the option to revert the
production process if the bargaining breaks down, in which case he gets ωc (q − q ∗ )(whereas the buyer gets nothing45 ). The quasi-rents are the difference between the
44

Cf. Farnsworth (2004), §12.10 in US law.
These payoffs are in addition to the payoffs from the first bargaining (R(q ∗ ) − 12 δM (q ∗ ) and (1 −1∗2 δ)M (q ) for the buyer and supplier, respectively).
45

55

surplus and the sum of the outside options, R(q) − R(q ∗ ) − ωc (q − q ∗ ). Under the
Nash sharing rule, the supplier receives in addition to his payoff from the settlementof the contract disputeωc (q − q ∗ ) +1
1(R(q) − R(q ∗ ) − ωc (q − q ∗ )) = (R(q) − R(q ∗ ) + ωc (q − q ∗ ))22which means that his overall ex-ante payoff is
(27)



1
1
πs (q) = 1 − δ M (q ∗ ) + (R(q) − R(q ∗ ) + ωc (q − q ∗ )) − cq
22

if q ≥ q ∗and the buyer receives in the second settlement
1(R(q) − R(q ∗ ) − ωc (q − q ∗ ))2
which means his total ex-ante payoff is1
1
πb (q) = R(q ) − 1 − δ M (q ∗ ) + (R(q) − R(q ∗ ) − ωc (q − q ∗ ))
2
2
∗



if q ≥ q ∗ .

I have now characterized the payoff functions for seller and buyer, for a given contract.
Going back in time, the supplier chooses q optimally to maximize his ex-ante payoff πs .
Establish first that the supplier’s payoff function is continuous at q ∗ , which means that it
is impossible to punish him for breaching the contract.
Lemma 1 Let (q ∗ , M (q)) be a feasible contract. The supplier’s payoff function πs is continuous at q ∗ .
Proof. The left-limit of πs at q ∗ only exists if q ∗ > 0, in which case it is1
lim πs (q) = 1 − δ M (q ∗ ) − cq ∗q%q ∗2
and the right-limit of πs (q) at q ∗ is1
lim πs (q) = 1 − δ M (q ∗ ) − cq ∗q&q ∗2
which is the same as the left-limit, thus πs is continuous at q ∗ .
Let us now look at the set of implementable quantities. The seller’s payoff maximization
problem is(28)

max πs (q) = maxqmax∗ πs (q), max∗ πs (q) .

q,q<q

q,q≥q

Denote the interior maxima of (26) and (27) by qδ and qω respectively. They satisfy the56

first-order conditions1c
1 − 12 δ
R0 (qω ) = (2 − ωi ) c.
R0 (qδ ) =From (28) and the fact that both expressions πs (q) for q < q ∗ and q ≥ q ∗ have uniquemaxima at qδ and qω respectively, it is clear that the arg maxq πs (q) can only be either qδ ,qω , or q ∗ . Because of the continuity of πs , q ∗ can only be implementable if either q ∗ ≤ qδor q ∗ ≤ qω .46 Also, note that both qδ and qω do not depend on the contract (q ∗ , M (q ∗ )) –though whether they will be chosen by the supplier depends of course on the contract.
I now turn to the optimal contracting problem. In a world where the Coase Theorem
holds, the buyer would implement the efficient quantity q̃ = arg maxq R(q) − cq and appropriate all the rents from the relationship. In the world of my model, since the implementable
quantities are all less or equal47 q̃, a contract that implements the largest implementable
quantity (either qδ or qω ) and leaves the full surplus from the relationship with the buyer
will be an optimal contract. In the following I will construct such a contract. Distinguish
two cases:
1. Case 1, 2 − ωi ≥ 1/(1 − 12 δ), or, equivalently, qω ≤ qδ . In this case, choosing q ∗ to begreater than qδ and setting
M (q) = M (q ∗ ) =1cqδ + R(q ∗ ) − R(qδ )1 − 21 δwill implement qδ . The seller’s payoff under q = qδ is then zero, and the buyer receives
R(qδ ) − cqδ .
2. Case 2, 2 − ωi < 1/(1 − 21 δ), or, equivalently, qω > qδ . The buyer wants to implementqω . Set M (q ∗ ) = 0 and q ∗ such that(29)

R(qω ) − (2 − ωi ) qω c = R(q ∗ ) + ωi q ∗ c.

Such a q ∗ exists because the RHS of this equation is zero for q ∗ = 0 and goes toinfinity for q ∗ → ∞, and is continuous in q ∗ , and the LHS is positive. Furthermore,
it satisfies q ∗ < qω . Distinguish two subcases.
(a) q ∗ ≥ qδ . Then the greatest profit that could be obtained by breaking the contract
Suppose q ∗ > qδ and q ∗ > qω . Because of continuity of πs and the fact that R is concave, either
πs (qδ ) > πs (q ∗ ) or πs (qω ) > πs (q ∗ ), thus q ∗ is not implementable.
47
Equal if and only if either ω = 1 or δ = 0.
46

57

is


1
1 − δ (R(qδ ) + M (q ∗ ) − R(q ∗ )) − cqδ
2


1
=
1 − δ (R(qδ ) − R(q ∗ )) − cqδ < 02thus q = qω is incentive-compatible.
(b) q ∗ < qδ . Since πs (q) is increasing for all q < q ∗ , an upper bound for the profitsthat could be obtained by breaking the contract is
1
1 − δ (R(q ∗ ) + M (q ∗ ) − R(q ∗ )) − cq ∗ = −cq ∗ < 02thus q = qω is incentive-compatible.
Thus, setting M (q ∗ ) = 0 and q ∗ as in (29) implements qω with πs (qω ) = 0.
C.1.2

Proof of Proposition 1

1. We havepni (j) = min plni (j), pxni (j)



and
w
sni (j)σn pi dni
pxni (j) =.
σn − 1 zni (j)plni (j) =From zni (j) following a Fréchet distribution,
P (zni (j) < z) = e−Ti z
we have thatP (plni (j) > c) = exp−θ w −θ −Sncand analogous for sni (j),P (pxni (j) > c) = exp −Ti

58

σn pi dni
σn − 1 c−θ !

P (pni (j) < c) = 1 − P (pni (j) > c) = 1 − exp −Sn= 1 − exp − Sn w−θ + Tiσnσn − 1 w −θ− Tic−θ ! !
pi dnicθ

σn pi dni
σn − 1 cθ= 1 − e−Φni c
where



(30)

Φni = Sn w−θ−θ

+ Ti (µn pi dni ).

and µn = σn / (σn − 1). Denote
Z 1
Qni =

qni (j)(σn −1)/σn dj

 σnσn−1

0

then
yn =

Y

Qγninii

Derive the demand function for sector n firms,
min
Qni

X

Pni Qnis.t. yn = 1

i

thus
(31)

Pni Qni = λγni

From plugging this into the formula for yn ,pn ≡ λ =γN YPni niγni

i=1

and similarly
Z
Pni =

pni (j)1−σn1/(1−σn ).

The latter becomes, using the distribution of pni (j) above,
Z 1
Pni =

1−σn

pni (j)1/(1−σn )
dj

Z ∞
=

0

θ
n +θ−1θp1−σ
Φni e−Φni c dc
ni

0
1
 
 1−σn1 − σn + θ
−1
= Γ
Φniθ
θ

59

1/(1−σn )−θ !

Thus the cost of one unit of yn is
pn =

N 
Y
αn

γni

i=1

where

−1
Φniθ

γni

1
 1−σ n1 − σn + θ
αn ≡ Γ
θand Φni as defined above.
2. The probability that activity (n, i, j) is outsourced is
πni (j) ≡P (pxni (j) ≤ plni (j)) =Z ∞exp −Sn

0

Z ∞
=


Ti

0


= Ti

σn
σn − 1−θ

σnσn − 1−θTi (µn pi dni )
=
Φni

=

−θ !
dFpx (p)(pi dni )−θ θpθ−1 exp −Φni pθ dp(pi dni )−θ

σn w
σn − 1 p

−θ

1
Φni

Z ∞


θpθ−1 Φni exp −Φni pθ dp

0

Ti (µn pi dni )−θ
Sn w−θ + Ti (µn pi dni )−θ

and because of a LLN, it is also the fraction of type-i varieties that sector n sourcesfrom sector i. The distribution of cost pni (j) conditional on activity (n, i, j) being
outsourced is

−θ !
Z p

σ
w
1
n
exp −SndFpx (z)pni|x (j) ≡ P pni (j) < p|pxni (j) ≤ plni (j) =πni (j) 0
σn − 1 z
−θ
Z p 

1
σn
=
Ti
(pi dni )−θ θz θ−1 exp −Φni z θ dz
πni (j) 0
σn − 1Z p−θTi (µn pi dni )1=
Φni θz θ−1 exp −Φni z θ dz
πni (j)Φni 0θ

= 1 − e−Φni p = P (pni (j) < p)
From this, it follows that the fraction of expenditure on outsourced type-i activities
in total expenditure on type-i activities is also πni (j),R10πni (j)pni|x (j)qni (j)dj= πni (j) = πni .
R1p (j)qni (j)0 ni

Let us calculate the expenditure on outsourced type-i activities in total expenditure.
From (31), the expenditure share on type-i activities is
Pni Qni= γni .
pn y n60

Thus, the expenditure share on outsourced type-i activities is
(32)

Xni
Ti (µn pi dni )−θ= γni
pn y nSn w−θ + Ti (µn pi dni )−θwhich is decreasing in dni .

C.2

Further Results on the Model

C.2.1

Relationship between the Reduced-form and Structural Regressions

Formally, the linear estimating equation in Section 1 is a linear approximation of equation (13) around an I-O structure where expenditure shares are proportional to technicalcoefficients γni :Proposition 3 (Relationship between estimating equations in Sections 1 and 3)c̄
Let c̄ be a country with parameters such that Xni/Xnc̄ ∝ γni for all n, i and εc̄ni = 0, and letc̄/Xnc̄ )/γni . Then, up to a first-order approximation in Tic , Snc , and dcni ,φ ≡ (Xni
c
c̄
Xni
Xni
≈
+(1−φ) ((ln Tic − ln Tic̄ ) − (ln Snc − ln Snc̄ ) − θ(ln pci − ln pc̄i ) − θ(ln dcni − ln dc̄ni )) .
Xnc
Xnc̄

The upstream sector × country fixed effect in equation (1) hence captures the deviationof the upstream sectors’ productivity Ti and cost index pi from the uniform benchmark;the downstream sector × country fixed effect captures the deviation of the downstream
sectors’ productivity from the benchmark. The interaction of δ c and zni corresponds to thecontracting frictions term ln dcni − ln dc̄ni .

D

Robustness checks: reduced-form regressions

D.1

Reduced-form regressions

D.1.1

Domestic Input-Output Shares

Table 14 shows the results of estimating equation (1) when replacing the dependent variableby the expenditure share on domestically sourced intermediate inputs.
D.1.2

Sensitivity: excluding top 3 sectors

Table 15 shows results estimating 1 but excluding the three most litigious sectors according
to z (1) , Insurance, Financial Services, and Business Services, from the sample (columns (1)and (2)); hence the results are not purely driven by those sectors. In columns (3) and (4),the regression explicitly controls for an interaction of enforcement costs with the US inputoutput shares, showing that the litigation ratio is not just proxying for unobserved buyer-

61

Table 14—: Results with expenditure on domestically sourced intermediate inputs
dom
Dependent variable: Xni
/Xn

(1)
(1)
δ c × zni

(2)-0.036∗∗∗(0.010)(2)-0.026∗∗(0.0084)

δ c × zni

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs

Yes
Yes
Yes

Yes
Yes
Yes

R2
0.465
0.465
Observations
133525133525
Note: Dependent variable is the fraction of expenditure of sector n on domestic inputs from sector i incountry c in total gross output of sector n in country c. Table shows standardized betas, with standard
errors clustered at the country level. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

seller relationships. In all specifications the coefficient of the interaction of enforcement
costs with enforcement-intensity remains negative and statistically significant.
Table 15—: Sensitivity: excluding top 3 sectors
Dependent variable: Xni /Xn(1)(1)

δ c × zni

(2)-0.021∗∗∗(0.012)(2)USδ c × Xni
/XnU S

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs(4)-0.028∗∗∗(0.0075)-0.023∗∗∗(0.0074)

δ c × zni

Sample(3)-0.024∗∗∗(0.0053)-0.041(0.024)-0.044(0.024)

Excl. I/F/B

Excl. I/F/B

Full

Full

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

R2
0.541
0.541
0.538
0.538
Observations
122080122080133525133525
Note: The first two columns exclude pairs where the upstream sector belongs to the three most litigious
sectors (Insurance, Financial Services, and Business Services). Table shows standardized betas, withstandard errors clustered at the country level. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

D.1.3

Heterogeneity by degree of differentiation of downstream sector

Table 16 further interacts δ c × zni with the fraction rn of the downstream sector’s productsthat are traded on organized exchanges or for which there is a reference price listed in a
trade publication, as indicated by Rauch’s (1999) classification. Products that are tradedon organized exchanges are more homogeneous. If the interaction δ c ×zni ×rn has a negative62

coefficient, it would suggest that contracting frictions lead firms to change the products
they produce (e.g. a car producer in India might produce low-tech cars instead of high-techcars if contracting frictions prevent the sourcing of tailored electronics components). Table
16 suggests that this is not the case: for both measures, the coefficient estimates of thetriple interactions are insignificant, and the signs of the point estimates are different.
Table 16—: Homogeneous vs Non-homogeneous Downstream Sectors
Dependent variable: Xni /Xn(1)(1)
δ c × zni

(2)-0.043∗∗∗(0.0095)(2)(3)-0.076∗∗∗(0.022)-0.037∗∗∗(0.0074)

δ c × zni(1)δ c × zni × rnlib-0.029∗∗(0.0085)0.035(0.018)(2)

δ c × zni × rnlib
Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs
R2
Observations(4)-0.011(0.0087)
Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

0.537
1335250.537
1335250.537
1335250.537
133525

Note: rnlib is the fraction of sector n’s products that are traded on organized exchanges, or reference-priced
in a trade publication, based on Rauch’s liberal classification. Results are very similar when using Rauch’s
conservative measure. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

D.1.4

Results with Rauch/Nunn measure

Table 17 shows the results from running specification (1) where the enforcement-intensity
variable is replaced by a measure of relationship-specificity that is constructed from the
Rauch (1999) classification of goods: ri measures the fraction of sector i’s products that aretraded on an organized exchange or where reference prices are listed in trade publications.
The resulting measure is hence similar to what Nunn (2007) uses to describe relationshipspecificity. The point estimates of the interaction term coefficient come out as statisticallysignificant at the 5% level when using Rauch’s conservative classification, and marginallyinsignificant when using the the liberal classification. This may be due to the presence ofunobserved heterogeneity across upstream sectors and countries, a problem that can be
avoided by using the bilateral enforcement-intensity measure.
D.1.5

Alternative construction of z-measure

Table 18 shows results when the enforcement-intensity variables is constructed in different
ways that avoid using the US IO table. Columns (1) and (2) refer to the z-measures when63

Table 17—: Results when using Rauch’s classification of goods
Dependent variable: Xni /Xn
(1)
δ

c

(2)
∗

× ricon-0.025(0.012)

δ c × rilib-0.020(0.011)

Upstream × Downstream FEs
Downstream × Country FEs

Yes
Yes

Yes
Yes

R2
0.454
0.454
Observations
133525133525
Note: Independent variable is an interaction of enforcement cost with the fraction of the upstream sector’s
goods that are traded on an organized exchange or reference-priced in trade publications (according toRauch’s (1999) liberal and conservative classifications). Table shows standardized betas, with standard
errors clustered at the country level. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

assuming that the plaintiff is the seller and the defendant is the buyer (as opposed to using
the relative sales volumnes in the I-O table). Column (3) constructs a litigation ratio justby dividing the number of cases in each sector-pair by the number of buyer-seller links
between the two sectors in the Japanese TSR data.
Table 18—: Alternative z-measures
Dependent variable: Xni /Xn(1)(1)
δ c × z̃ni

(2)

(3)

-0.043∗∗∗(0.010)(2)-0.029∗∗(0.0096)δ c × z̃ni

-0.0079∗(0.0038)δ c × (Cases / Links in Japan)ni
Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs
R2
Observations

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

0.537
1335250.537
1335250.542
118701

Note: z̃ (1) and z̃ (2) are the measures z (1) and z (2) but with plaintiffs/defendants assumed to belong to
the selling/buying industry. (Cases / Links in Japan) is the number of cases by sector pair divided by the
raw number of relationships between these sectors in Japan (using data from Bernard et al. (2015)). Table
shows standardized betas, with standard errors clustered at the country level. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗p < 0.001.

D.1.6

Controlling for interactions with the US input-output table

Table 19 addresses the concern that the bilateral measure of dependence on enforcement
could be proxying for the input output table. I repeat the regressions from 5 but also64control for interactions of variables u(1) and u(2) that are constructed analogously to z (1)and z (2) but use the US input output table in the numerator instead of the number of casesby sector-pair:US/XnU S
Xni(1)uni = p(33)

(# firms in sector i) (# firms in sector n)USXni/XnU S(2)uni =\ between i and n)(# buyer-seller relationships(34)

Including these controls does not affect the magnitude nor statistical significance of themain interactions of interest. The controls with u are all not statistically different fromzero.
Table 19—: Controlling for interactions with the US I-O table
Dependent variable: Xni /Xn(1)(1)
δ c × zni

(2)

(3)

(4)

(5)
-0.016∗-0.018∗(0.0078)(0.0080)(0.0076)(0.0083)(2)-0.029∗∗∗(0.0055)(1)-0.019∗∗(0.0058)-0.013∗(0.0063)0.045∗∗∗(0.0100)

F IN DEV c × zni(2)0.038∗∗(0.011)(1)

0.028∗∗(0.0090)0.19∗∗(0.063)log GDP C c × zni

(2)

(2)

δ c × uni

-0.030(0.024)-0.040(0.022)(1)

F IN DEV c × uni-0.021(0.027)-0.030(0.023)(2)-0.022(0.026)-0.023(0.027)0.024(0.020)0.030(0.017)(1)

log GDP C c × uni

0.022(0.019)0.18(0.13)(2)

log GDP C c × uni

R2
Observations

0.056(0.048)-0.022(0.028)0.033(0.018)F IN DEV c × uni

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs

0.077(0.069)0.14∗∗(0.046)log GDP C c × zni-0.041(0.023)(8)-0.015∗(0.0063)

0.033∗∗∗(0.0082)

F IN DEV c × zni

(1)

(7)

-0.024∗∗

δ c × zni

δ c × uni

(6)-0.037∗∗∗0.10(0.15)
0.16(0.12)

0.085(0.14)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

0.54
1335250.541335250.541323000.541323000.541335250.541335250.541323000.54132300Note: u(1) and u(2) are the z-measures with the number of cases replaced by the US input output table
expenditure shares. Table shows standardized betas, with standard errors clustered at the country level.
∗p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

65

D.1.7

Controlling for interactions of Nunn and Rauch measures

Table 20 shows the baseline results when adding interactions of the Nunn measure (bydownstream industry, constructed using the US IO table) with the upstream industry’s
Rauch measure and the country’s enforcement cost δ c . Our interactions of interest remain large and statistically significant; the controls are not statistically significant. The
enforcement-intensity measures hence add explanatory power beyond those used in theexisting literature.
Table 20—: Controlling for interactions of Nunn and Rauch measures
Dependent variable: Xni /Xn(1)(1)
δ c × zni

(2)

(3)

(4)

(5)

-0.043∗∗∗-0.043∗∗∗-0.043∗∗∗(0.0095)(0.0094)(0.0094)(2)-0.037∗∗∗(0.0074)

δ c × zni

δ c × ricon × Nunncon
n-0.037∗∗∗(0.0073)-0.032(0.039)R2
Observations-0.037∗∗∗(0.0073)-0.048(0.040)δ c × rilib × Nunnlib
nUpstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs(6)-0.018(0.031)-0.034(0.032)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

0.537
1335250.537
1335250.537
1335250.537
1335250.537
1335250.537
133525

Note: The table shows the baseline regressions but controlling for interactions of the Nunn (2007) measure(in the downstream industry) with the Rauch measure (in the upstream industry) and enforcement cost
δ c . Table shows standardized betas, with standard errors clustered at the country level. ∗ p < 0.05, ∗∗p < 0.01, ∗∗∗ p < 0.001.

D.1.8

PPML estimates of the reduced-form specifications

Table 21 shows the results from estimating the reduced-form specification (1) using a
Poisson Pseudo-ML estimator. This specification is somewhat closer to the structural
specification from Section 3.
D.1.9

Sensitivity to mismeasurement of court cases in sector pairs with weaklinks

How sensitive are the estimates to variation in the z measures for sector pairs with weakties? Figure 7 shows distribution of the interaction term coefficient in the baseline specification (columns 5 and 6 of Table 4) using a resampling estimator. I make 300 samplesof draws from the empirical distribution of court cases (across sector pairs), each having
the same size as the actual number of observed cases, and construct enforcement-intensity
measures analogously to z (1) and z (2) using these samples. The dispersion of estimates

66

Table 21—: PPML estimates of the reduced-form specifications
Dependent variable: Xni /Xn(1)(1)
δ c × zni

(2)-0.0536∗∗∗(0.0146)(2)-0.0487∗∗∗(0.0111)

δ c × zni

Estimator

PPML

PPML

Yes
Yes
Yes

Yes
Yes
Yes

0.733
1335250.733
133525

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs
R2
Observations

Note: The table shows coefficients estimated using a PPML estimator, with standard errors clustered at
the country level. Dependent and independent variables have been scaled to have a standard deviation ofone. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

is relatively low, which I interpret as saying that the estimates are not very sensitive togetting the number of cases in sector pairs with little economic activity wrong.
D.1.10Foreign ownership and I-O tables

It could be that foreign-owned firms operate a different production technology (that are
more or less intensive in certain inputs). While aggregate FDI data tend to be of relatively
poor quality, we can try to look at this question by seeing if countries tend to have particularly low or high cost shares in certain sectors (or sector-pairs) depending on the inward
FDI stock of the downstream sector. To do this, I use the FDIMap database on inward
FDI stocks from CEPII. More specifically, I run regressions where I control for quadratic
polynomials in the log stock of inward FDI in the downstream sector (in 2004), where thecoefficients are i or (n, i)-specific:
000
αni + αnilog(FDIcn ) + αnilog(FDIcn )2

Table 22 shows the results. Comparing columns (2) to (1) shows that FDI stocks do nothave much additional explanatory power for expenditures on particular input sectors (theR2 is virtually unchanged). When including the polynomials with (n, i)-specific coefficients,
the R2 goes up by three percentage points, showing that some of the variation in I-O table
entries may be coming from variation across countries in foreign ownership of firms inthe downstream sector. But even controlling for this variation, the contract enforcement
interactions come out very similar as in the benchmark specification.

67

50

50

40

40

30

30

20

20

10

10

0
-0.055-0.050-0.045-0.040-0.0350-0.06-0.030-0.05

Estimated coefficient of interaction term

-0.04

-0.03

-0.02

-0.01

0.00

Estimated coefficient of interaction term(a) When normalizing by geometric mean, as in z (1)(b) When normalizing by fitted number of links, as in z (2)Figure 7: Empirical distribution of interaction coefficient estimator, using resampled court casedata
Note: The graphs show the estimated distribution (N = 300) of the interaction term coefficient when the
sector-pairs of the court cases are re-drawn from its empirical distribution. In each simulation, the numberof drawn court cases equals the actual one in the data. In the left panel, the simulated number of court
cases is normalized by the geometric mean of the number of firms in each sector (as in z (1) ), and in theright panel it is normalized by the fitter number of links, as in z (2) .

Table 22—: FDI stocks and I-O tables
Dependent variable: Xni /Xn
(1)

(2)

(3)

(1)

(4)

(5)

-0.049∗∗∗(0.010)δ c × zni

(2)(6)-0.047∗∗∗(0.010)-0.047∗∗∗(0.011)

δ c × zni

i-specific polynomial in log FDI(n, i)-specific polynomial in log FDI

(7)

Yes

(8)
-0.029∗∗(0.0097)-0.046∗∗∗(0.011)
Yes

Yes

Yes

Yes

Upstream × Downstream FEs
Upstream × Country FEs
Downstream × Country FEs

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

R2
Observations
Note:

0.565
97335

0.567
97335

0.593
97335

0.566
97335

0.566
97335

0.567
97335

0.567
97335

0.588
97335

Table as in Table 4, but sample is the set of countries/sectors for which we have inward FDI stocks fromCEPII’s FDIMap database. Columns (2), (6), and (7) control for quadratic polynomials in log inward FDI
stocks in the downstream sector where the coefficients are i-specific ((n, i)-specific in columns (3), (8), (9)).
The table shows standardized betas, with standard errors clustered at the country level. ∗ p < 0.05, ∗∗p < 0.01, ∗∗∗ p < 0.001.

E

Robustness of the structural estimates: substitution of broad input baskets

This section shows results from the quantitative exercise when the sectoral production
functions exhibit more substitutability across the broad sets of inputs than what is implied68

by the Cobb-Douglas functional form used in section 2. Specifically, we assume that the
production function takes a CES form. Equation (4) is replaced by
ρ

(35)

yn =

N
X

1
ρ

Z 1

γni

qni (j)(σn −1)/σn dj! ρ−1
 σnσn−1 ρ−1ρ,n = 1, . . . , N.

0

i=1

P
where, again, i γni = 1 for all n = 1, . . . , N . The implied expression for the input-output
shares are then







Snc + Tic (µn pci dcni )−θ− θ1 1−ρ

 T c (µ pc dc )−θ γni αncXnin i nii=1−ρ  c
 
1

c
−
Xnc
 Sn + Ti (µn pci dcni )−θPθc + T c µ pc dc −θ
γ
α
S
nj
n
n
n
j
j nj
j
The expression in the bracket corresponds to the substitution across broad input baskets;a choice of ρ = 1 (Cobb-Douglas) reduces the expression to the one from the main text.
Estimating the parameters using a PPML with the conditional mean of the input shares
given by (35) is not straightforward; the parameters ρ and θ are quite collinear. To force
the CES structure on the model, I follow Caliendo et al. (2017) and calibrate the elasticity
across broad input baskets to ρ = 4. I also set the productivity draw dispersion to θ = 4, acommon parameter choice in quantitative calibrations of Eaton-Kortum-type models, andclose to the estimates from the main text. The remaining parameters I estimate using the
PPML.
Figure 8 shows the welfare counterfactuals under these estimates. The welfare gains
from moving enforcement costs to the levels of the United States are on average slightly
smaller than in the main text, but still in the range of zero to about five percent of income
per capita for most countries. Overall, the distortions are sufficiently small so that theadditional curvature (ρ > 1) in the production function does not have a strong impact on
the welfare effects of reducing frictions.

F

Results by country, and further details on structural estimates

F.1

Estimates of coefficients in distortion terms

Table 23 shows the estimates of the semiparameterically estimated functions dI = 1 +2
η1 zni + η2 zni
and dF = 1/(1 − β1 δ − β2 δ 2 ). The reported coefficients η1 and η2 in dI are thecoefficients after scaling z to have a unit variance.

69

Counterfactual welfare increase, in percentz^(2) used
15
KHM
10
IDN
BGD
5

HND
MYS
AZE

0

UKR

VEN

MWI
MOZ

PAN
COL

ALB UGA
QAT

NGA

LUX
-5
0.25

0.50

0.75

1.00

Enforcement cost

Figure 8: Counterfactual welfare gains from setting enforcement costs to US levels – CES specification
Note: Enforcement costs are top-coded at one to help exposition.

Table 23—: dI and dF estimates
Calibrated θ,
Estimated dF

Estimated θ,
Calibrated dF

(1)

(2)

0.34
(0.02)
0.66(0.07)
0.11(0.02)-0.0005(0.0000)

0.10(0.02)-0.0018(0.0004)

z (2)

z (2)

β1
β2
η1
η2
z measure used

F.2

Robustness to different θ

Figure 9 shows welfare counterfactuals for θ = 3, 4, 5, and 6, holding fixed the other estimated parameters. Among this range of values, the counterfactuals are not very sensitive
to the choice of θ. This is not a coincidence, but the result of the fact that for given changes
in the dni , the first-order impact on the households price level does not depend on θ (seeSection 2.4 in the paper.

F.3

Noise in z

10 compares the baseline counterfactual results (in blue) to estimates obtained when adding
multiplicative noise to the z measure before estimation (in green). Each zni is multiplied
by a scalar that is drawn from a uniform distribution between 0.8 and 1.2, i.i.d across (n, i).
Since the correlation between I-O shares and z is now weaker, the η estimates are lower,
which corresponds to lower distortions under informal contracting (dI ). The reduction in
enforcement costs δ only has bite for fewer sector pairs, namely where dF < dI , and at70

Estimates using variable theta, z^(2)
Counterfactual welfare increase, in percent

Counterfactual welfare increase, in percent

Estimates using fixed theta, z^(2)
0.15

0.10

Legendtheta = 3.0
theta = 4.0
theta = 5.0
theta = 6.0

0.05

0.00

-0.05
0.00

0.25

0.50

0.75

1.00

0.10

0.05

Legendtheta = 3.0
theta = 4.0
theta = 5.0
theta = 6.0

0.00

-0.05
0.00

0.25

0.50

0.75

1.00

Enforcement cost

Enforcement cost(a) Calibrated θ, estimated dF(b) Estimated θ, calibrated dF

Figure 9: Counterfactuals for varying θlower thresholds for dI . As a result, the welfare counterfactuals are biased downwards inthe presence of classical measurement error.
(b) Estimated θ, calibrated dF(a) Calibrated θ, estimated dF
Counterfactual welfare increase, in percent

Counterfactual welfare increase, in percent

15

10

Legend5baseline
noisy z

0

-5
0.00

0.25

0.50

0.75

1.00

10

5

Legendbaseline
noisy z0-5
0.00

Enforcement cost

0.25

0.50

0.75

1.00

Enforcement cost

Figure 10: Measurement error in z biases the counterfactual welfare increases downwards
The figure shows the counterfactual welfare increases from the baseline specifications(in blue) and from an estimate where the zni have been scaled by a factor that is
uniformly distributed between 0.8 and 1.2 and i.i.d. across (n, i).

F.4

Welfare counterfactuals, by country

Tables 24 shows the results of the welfare counterfactuals from Section 3 for each country.

G

A model with firm boundaries

The purpose of this section is to describe a variation of the model from the main text that
explicitly models the firm boundary. I show that the (macro) relationships used to estimate
the parameters emerge under a set of restrictions. These restrictions could be relaxed if
one had additional data on firm boundaries.
71

Assume that firms have the same production function (4) as in the main text, butinstead of two ways to satisfy activity (n, i, j), they have three options:
1. In-house production in the headquarter plant. The firm hires labor to performthe activity. One unit of labor generates sni (j) units of activity (n, i, j), thus the
production function is qni (j) = t0ni (j)l(n, i, j), where l(n, i, j) is labor used and t0ni (j)is a stochastic productivity realization that follows a Fréchet distribution,−θP (t0ni (j) < z) = e−Sn z .
The productivity draws sni (j) are independent across i, j, and n. There is a multiplicative distortion d0ni to the cost of in-house production.
2. In-house production in a separate plant, belonging to sector i. The sector
n firms can perform production of activity (n, i, j) in-house in a separate plant thatbelongs to sector i. The production function is qni (j) = t00ni (j)yi (n, i, j), with yi (n, i, j)being the amount of sector i’s composite good that is used for production. t00ni (j) is
distributed according to−θP (t00ni (j) < z) = e−Ti z
and independent across i, j, and n. There is a multiplicative distortion d00ni to theunit cost under this option.
3. Outsourcing production to a different firm, belonging to sector i. The sector
n firm can outsource production to a firm that belongs to sector i. The production
function is then qni (j) = t000
ni (j)yi (n, i, j), with yi (n, i, j) being the amount of sector
i’s composite good that is used for production. t000
ni (j) is distributed according to−Ti z
P (t000ni (j) < z) = e−θ

and independent across i, j, and n. We assume that the supplier prices at marginal
cost, but that there is a multiplicative distortion d000
ni to the unit cost under this option.
We assume that all three productivity draws are independent from each other. The standard discrete choice algebra yields the expressions for the expenditure shares observed in
input-output tables:
(36)
(37)

00 −θ
000 −θ
Xni
Ti p−θ
+ Ti p−θi (dni )i (dni )
= γni
00 −θ
000 −θXn
Sn w−θ (d0ni )−θ + Ti p−θ+ Ti p−θi (dni )i (dni )−θ
Ti p−θ
(d00ni )−θ + (d000
ni )
i
= γni
00 −θ
−θ
Sn wθ (d0ni )−θ + Ti p−θ+ (d000i ((dni )ni ) )

where Xni is the expenditures on activities from sector i (thus options 2 and 3 above), and72

Xn is sales of sector n. This expression is equivalent to equation (7) when−θ −1/θ
((d00ni )−θ + (d000ni ) )dni =d0ni

In other words, the identified distortions are an average of the intra- and inter-firm distortions when production is done by a sector i plant, relative to the distortion from in-houseproduction in the headquarter plant.48
The regressions therefore identify a wedge dni between production using primary factors
and production by a plant belonging to sector i, whether integrated or at arm’s length.
The reduced-form regressions parameterize this relative distortion by an interaction of δand z, and show that it is increasing in it. The structural regressions parameterize it as aminimum of a term that depends on δ and a term that depends on z. Viewed through thelens of this framework, the model from the main text imposes two additional constraints:
1. d00 = d000 . A richer dataset (where intermediate input transactions and firm borders
are observed) would be able to distinguish between the frictions associated with arm’s
length and in-house production. Atalay et al. (2019) uses such a dataset to study thedifferences between d00 and d000 .
2. d0 = 1. This is because distortions are only identified relative to one factor. Thisis a conservative assumption: if lowering enforcement costs not only decrease thewedge between (1) and ((2) or (3)), but also make (1) cheaper, then reductions in
enforcement cost would have an even bigger effect on the economy.

48

Strictly speaking, the model is not nested because the firm gets an additional productivity draw, butthat is not separately identified from Ti in the setup above. If we assume instead that the productivity
draw from options (2) and (3) is the same, then the model is exactly nested withd=min(d00 , d000 )
.
d0

73

Table 24—: Welfare counterfactuals, by country, in percent

Albania
Azerbaijan
Argentina
Australia
Austria
Bahrain
Bangladesh
Armenia
Belgium
Bolivia
Botswana
BrasilBulgaria
Belarus
Cambodia
Cameroon
CanadaSri Lanka
Chile
China PR
TaiwanColombia
Costa Rica
Croatia
CyprusCzech Republic
Denmark
EcuadorEl Salvador
Ethiopia
Estonia
FinlandFranceGeorgia
Germany
Ghana
GreeceGuatemalaHondurasHong Kong
Hungary
India
Indonesia
Iran
IrelandIsraelItaly
Cote dIvoire
Japan
Kazakhstan
Kenya
South Korea
KuwaitKyrgyzstan
Laos

Calibrated θ,
Estimated dF

Estimated θ,
Calibrated dF

δ

to US

to zeroto US

to zero

0.39
0.18
0.17
0.21
0.13
0.15
0.63
0.19
0.18
0.33
0.28
0.17
0.24
0.17
1.00
0.47
0.22
0.23
0.29
0.11
0.18
0.48
0.24
0.14
0.16
0.34
0.25
0.27
0.19
0.15
0.15
0.13
0.17
0.41
0.14
0.23
0.14
0.27
0.35
0.21
0.15
0.40
1.00
0.17
0.27
0.25
0.30
0.42
0.32
0.22
0.34
0.10
0.19
0.29
0.32

3.6
1.7
0.4
2.1
-0.5
0.0
7.6
2.0
1.4
3.8
1.8
0.5
2.7
0.7
7.9
3.5
2.3
1.3
4.4
-0.9
0.9
5.0
2.9
-0.2
0.5
5.7
3.0
2.4
0.9
0.1
0.2
-0.3
1.0
9.3
0.0
2.9
0.0
2.6
5.1
1.5
0.2
5.7
8.0
0.5
3.7
4.5
4.6
5.8
4.1
2.1
3.6
-1.3
0.6
4.5
7.2

8.6
8.3
4.5
8.5
4.6
2.5
14.2
8.9
8.6
10.1
5.4
4.8
8.7
4.3
15.3
8.1
8.4
5.0
11.7
3.8
6.0
10.4
9.8
5.2
5.2
13.8
9.1
6.8
4.6
2.6
5.7
4.6
6.9
17.4
4.6
10.4
3.8
8.3
12.1
6.4
6.0
12.0
15.0
3.9
10.5
13.5
12.3
12.5
10.5
7.3
8.4
4.6
3.2
10.2
13.8

2.4
1.3
0.3
1.5
-0.4
0.0
5.0
1.7
1.1
2.4
1.1
0.4
1.9
0.6
8.4
2.1
1.6
0.8
3.0
-0.8
0.7
3.0
1.9
-0.1
0.4
3.7
2.0
1.6
0.6
0.1
0.1
-0.3
0.8
6.6
0.0
1.9
0.0
1.7
3.3
0.9
0.2
3.8
5.7
0.4
2.5
3.1
3.0
3.8
2.6
1.5
2.4
-1.2
0.4
3.2
5.4

7.6
8.7
4.8
8.5
5.2
2.8
11.6
9.3
9.0
9.0
4.8
5.2
8.3
4.6
18.4
6.9
8.3
4.8
11.1
4.3
6.3
8.6
9.1
5.7
5.6
12.2
8.7
6.3
4.7
2.7
6.3
5.1
7.3
15.1
5.2
10.0
4.3
7.8
10.6
5.8
6.7
10.3
13.0
4.2
9.8
12.7
11.2
10.7
9.4
7.3
7.4
5.4
3.2
9.3
12.5

LatviaLithuania
Luxembourg
Madagascar
MalawiMalaysia
Malta
Mauritius
MexicoMongolia
MoroccoMozambique
Oman
Namibia
Nepal
Netherlands
New Zealand
Nicaragua
Nigeria
NorwayPakistan
PanamaParaguay
Peru
Philippines
PolandPortugal
Qatar
Romania
RussiaSaudi Arabia
SenegalSingapore
Slovakia
VietnamSlovenia
South Africa
Zimbabwe
Spain
SwedenSwitzerland
Thailand
United Arab Emirates
Tunisia
TurkeyUgandaUkraine
Egypt
United Kingdom
Tanzania
United States
Uruguay
Venezuela
ZambiaCalibrated θ,
Estimated dF

Estimated θ,
Calibrated dF

δ

to US

to zeroto US

to zero

0.17
0.24
0.09
0.42
1.00
0.28
0.36
0.17
0.32
0.31
0.25
1.00
0.14
0.36
0.27
0.24
0.22
0.27
0.32
0.10
0.24
0.50
0.30
0.36
0.25
0.12
0.14
0.22
0.20
0.13
0.28
0.27
0.18
0.26
0.31
0.20
0.33
0.32
0.17
0.31
0.21
0.14
0.26
0.22
0.27
0.45
0.41
0.26
0.22
0.14
0.14
0.19
0.44
0.39

0.5
1.7
-1.9
8.3
6.9
4.9
5.1
0.7
2.8
4.7
2.6
3.1
-0.1
5.1
2.6
2.9
2.4
2.5
1.8
-1.4
2.1
9.3
3.0
3.8
2.4
-0.8
-0.1
0.8
1.5
-0.3
1.8
2.2
1.3
3.6
4.4
1.7
4.7
5.3
0.8
3.8
2.0
-0.0
1.5
1.7
2.2
4.3
12.8
2.3
1.9
-0.0
0.0
1.1
6.3
3.9

4.7
5.8
3.5
16.3
12.6
13.8
10.8
4.2
6.7
10.2
8.7
6.6
2.2
12.6
6.6
8.8
9.1
7.9
4.0
4.1
6.4
17.2
8.3
9.1
7.5
5.3
5.8
3.0
6.7
5.1
4.6
6.3
9.3
10.6
10.2
8.2
11.7
11.1
6.1
8.9
7.5
4.4
4.4
6.9
6.3
9.2
26.3
6.7
6.7
3.8
4.6
6.1
13.9
10.0

0.4
1.1
-1.7
5.5
5.0
3.3
3.4
0.5
1.8
3.4
1.6
2.1
-0.1
3.2
1.9
2.0
1.7
1.7
1.2
-1.3
1.5
5.8
1.9
2.4
1.5
-0.7
-0.1
0.6
1.2
-0.2
1.2
1.5
0.9
2.4
3.0
1.2
3.0
3.8
0.6
2.6
1.4
-0.0
1.0
1.2
1.5
2.7
8.0
1.6
1.4
-0.0
0.0
0.8
3.8
2.4

5.0
5.5
4.1
14.0
10.9
12.9
9.4
4.5
6.0
9.1
8.1
5.8
2.5
11.0
6.2
8.5
8.9
7.5
3.6
4.8
6.3
13.9
7.5
8.0
7.1
6.1
6.4
3.0
6.9
5.8
4.3
5.9
9.0
10.0
9.0
8.2
10.4
9.9
6.4
8.0
7.5
4.9
4.1
6.8
5.9
7.6
21.9
6.4
6.7
4.2
5.1
6.3
11.7
8.7

Note: The table shows the the counterfactual increase in real income (in percent) when enforcement costs
are set to the level of the US, or to zero.

74