VERTICAL INTEGRATION AND TECHNOLOGY: THEORY AND EVIDENCE

VERTICAL INTEGRATION AND

TECHNOLOGY: THEORY AND EVIDENCE

Daron Acemoglu

Massachusetts Institute of Technology

Rachel Grifﬁth

University College London

Philippe Aghion

Harvard University

Fabrizio Zilibotti

University of Zurich

Abstract

We study the determinants of vertical integration. We ﬁrst derive a number of predictions

regarding the relationship between technology intensity and vertical integration from a simple

incomplete contracts model. Then, we investigate these predictions using plant-level data for the

UK manufacturing sector. Most importantly, and consistent with the theoretical predictions, we

ﬁnd that the technology intensity of downstream (producer) industries is positively correlated

with the likelihood of integration whereas the intensity of upstream (supplier) industries is

negatively correlated with it. Also consistent with theory, both correlations are stronger when

the supplying industry accounts for a large fraction of the producer’s costs. These results are

generally robust and hold with alternative measures of technology intensity, with alternative

estimation strategies, and with or without controlling for a number of ﬁrm- and industry-level

characteristics. (JEL: L22, L23, L24, L60)

1. Introduction

Despite a large theoretical literature on the determinants of vertical integration,

the economics profession is far from a consensus on the empirical determinants of

vertical integration in general, and the relationship between technological change

The editor in charge of this paper was Xavier Vives.

Acknowledgments: We thank Richard Blundell, Robert Gertner, Oliver Hart, Bengt Holmstrom,

Ali Hortaçsu, Paul Joskow, Ariel Pakes, Helen Simpson, Helena Svaleryd, John Van Reenen, and sem-

inar participants at Canadian Institute of Advanced Research, Chicago, Harvard, IIES-Stockholm,

MIT and NBER, and the CEPR-IUI Waxholms Conference. This work contains statistical data from

ONS which is Crown Copyright and is reproduced with the permission of the controller of HMSO.

The use of the ONS statistical data in this work does not imply the endorsement of the ONS in rela-

tion to the interpretation or analysis of the statistical data. Grifﬁth acknowledges ﬁnancial support

from the Economic and Social Research Council (ESRC), and Zilibotti acknowledges the support

of the European Research Council (ERC Advanced Grant IPCDP-229883) and the Swiss National

Science Foundation (SNF Grant 100014-122636).

E-mail addresses: Acemoglu: [email protected]; Aghion: paghion@arrow.fas.harvard.edu; Grifﬁth:

rgrifﬁ[email protected]; Zilibotti: [email protected]

Journal of the European Economic Association September 2010 8(5):989–1033

990 Journal of the European Economic Association

and vertical integration in particular.

This paper provides a simple incomplete

contracts model of vertical integration and, in the light of the predictions of

this model, presents detailed empirical evidence on the determinants of vertical

integration using UK ﬁrm-level data over the period 1996–2001.

The two leading theories of vertical integration are the Transaction Cost

Economics (TCE) approach of Williamson (1975, 1985) and the Property Right

Theory (PRT) approach of Grossman and Hart (1986) and Hart and Moore

(1990).

Both approaches emphasize the importance of incomplete contracts and

ex post opportunistic behavior (hold up) on ex ante relationship-speciﬁc invest-

ments. The TCE approach views vertical integration as a way of circumventing

the potential holdup problems. In particular, it predicts that vertical integration

should be more common when there is greater speciﬁcity and holdup is more

costly, and that vertical integration should enhance investments by all contracting

parties. The PRT approach, on the other hand, focuses on the role of ownership

of assets as a way of allocating residual rights of control, and emphasizes both

the costs and the beneﬁts of vertical integration in terms of ex ante investment

incentives.

To illustrate the central insight of the PRT, consider a relationship between

a supplier (upstream ﬁrm) and a (downstream) producer. Moreover, suppose that

only two organizational forms are possible: (backward) vertical integration, where

the downstream producer buys up the upstream supplier and has residual rights of

control, and non-integration (outsourcing), where the producer and supplier are

separate ﬁrms. In this world, vertical integration does not automatically improve

efﬁciency. Instead, by allocating the residual rights of control to the producer, who

has ownership and thus control of the assets if there is a breakup of the relationship,

vertical integration increases the producer’s bargaining power and encourages its

investment. However, by the same mechanism, it also reduces the supplier’s ex

post bargaining power and hence her incentives to invest. Non-integration, on the

other hand, gives greater investment incentives to the supplier. Thus, in contrast to

the TCE approach, the PRT predicts that vertical integration should have opposite

effects on the supplier’s and the producer’s investments. Here, vertical integration

has both costs and beneﬁts in terms of ex ante investments, and its net beneﬁts

1. We discuss the empirical literature herein. On the theory side, see, among others, Williamson

(1975, 1985), Klein, Crawford, and Alchian (1978), Grossman and Hart (1986), Hart and Moore

(1990), Bolton and Whinston (1993), Aghion and Tirole (1994a, 1994b, and 1997), and Legros and

Newman (2008), together with the surveys in Holmstrom and Tirole (1989) and Hart (1995). Papers

on the potential impact of technology on vertical integration include, among others, Milgrom and

Roberts (1990), Helper (1991), Athey and Schmutzler (1995), Bresnahan, Brynjolfsson, and Hitt

(2002), Marin and Verdier (2003a, 2003b), Acemoglu, Aghion, and Zilibotti (2003), and Acemoglu

et al. (2007). See also the literature on international trade and vertical integration (or outsourcing),

for example, Feenstra and Hanson (1996, 1999), Feenstra (1998), McLaren (2000), Grossman and

Helpman (2002, 2005), and Antras (2003).

2. See Whinston (2001) and Joskow (2005) for recent discussions.

Acemoglu et al. Vertical Integration 991

depend on whether the investments of the producer or those of the supplier are

more important for the output and success of the joint venture.

Although the key predictions of the TCE approach could be tested by

investigating the relationship between measures of speciﬁcity and vertical inte-

gration, as Whinston (2001) also emphasizes, the PRT approach is more difﬁcult

to test directly because it makes no predictions about the overall relationship

between speciﬁcity and vertical integration or between vertical integration and

total investment. However, crucially for our paper, one can test some of its dis-

tinctive predictions, for example that vertical integration has opposite effects on

investments by the two contracting parties.

In this paper, we develop a simple methodology to study the forces empha-

sized by the PRT approach. First, we shift the focus from relationship-speciﬁc

investments to technology intensity. The presumption is that parties making tech-

nology investments, especially in R&D, are subject to holdup, and this will lead

to the type of problems highlighted by the TCE and PRT approaches.

Second, we

consider the relationship between pairs of supplying and producing industries and

focus on the prediction that the correlations between vertical integration and the

investment incentives of suppliers and producers should display opposite signs.

Our approach therefore exploits cross-industry (cross-product) implications of

the PRT.

We ﬁrst develop these points using a simple theoretical framework and derive

a number of predictions that are testable with the data we have available. The

framework highlights that backward vertical integration gives greater investment

incentives to the producer, while forward vertical integration encourages supplier

investment. Non-integration provides intermediate incentives to both parties. This

analysis leads to three key predictions:

1. The importance of the technology intensity of the producer and supplier

should have opposite effects on the likelihood of vertical integration. In par-

ticular, whereas a higher importance of the producer’s technology intensity

should increase the probability of backward integration, a higher importance

of the supplier’s technology intensity should reduce that probability.

2. Vertical integration should be more responsive to the technology intensities

of both the supplier and the producer when the supplier accounts for a larger

fraction of the input costs of the producer.

3. If the relevant margin of choice is between backward vertical integration and

non-integration, then technology intensity of the supplier should discourage

3. This could be for a variety of reasons. First, R&D investments are often made for technologies

speciﬁc to each ﬁrm (or their mix of products). Second, associated with any technological investment,

parties are also likely to make speciﬁc, non-tangible, and largely unveriﬁable innovative investments.

Finally, market imperfections, for example search frictions, typically turn “technologically general”

investments into speciﬁc investments (e.g., Acemoglu 1996; Acemoglu and Pischke 1999).

992 Journal of the European Economic Association

integration, the technology intensity of the producer should encourage inte-

gration, and the importance of the supplier to the producer (measured in terms

of share of costs) should encourage integration.

We investigate these predictions, and other determinants of vertical inte-

gration, using detailed data on all British manufacturing plants from the UK

Census of Production (ARD). To identify the effects of both supplier and pro-

ducer technology, we look across all manufacturing industries. To measure the

extent of vertical integration and to develop an empirical strategy to document the

determinants of integration, we need to take a stance as to whether backward or

forward vertical integration is the most important alternative to non-integration.

Motivated by the bulk of the prior empirical work (e.g., Joskow 1987, 2005;

Stuckey 1983), we focus on backward vertical integration.

Using this data set

and the UK Input–Output Table, we calculate two measures of (backward) ver-

tical integration, deﬁned at the level of ﬁrm–industry-pair (more precisely, for

ﬁrm i producing product j with input from industry k).

The ﬁrst measure is a

dummy variable indicating whether the ﬁrm owns a plant producing input k nec-

essary for product j . The second measure calculates how much of the inputs from

industry k, necessary for the production of j , the ﬁrm can produce in-house. It is

useful to emphasize that what we uncover are correlations, not necessarily causal

relations.

Using the ratio of R&D expenditures to value added (calculated from a sample

pre-dating our vertical integration measures), we ﬁnd the following correlations

in the data:

• Consistent with prediction 1, technology (R&D) intensities of the producing

(downstream) and supplying (upstream) industries have opposite effects on

the likelihood of vertical integration. In particular, backward vertical inte-

gration is more likely (relative to non-integration) the greater the technology

intensity of the producer and the lower the technology intensity of the supplier.

• Consistent with prediction 2, the correlations between vertical integration and

the technology intensities of both the producing and the supplying industry

are substantially larger and also more signiﬁcant when the share of costs of

the supplying industry in the total costs of the producing industry (for short,

“share of costs”) is high.

• Consistent with prediction 3 (provided that the relevant margin is between

backward vertical integration and non-integration), we also ﬁnd that

4. This is also the strategy implicitly adopted in other cross-industry studies of vertical integration;

see, for example, Antras (2003).

5. Note that these measures do not distinguish between backward or forward integration, because

we do not observe who has residual rights of control. Nevertheless, conceptually they are closer to

measures of backward integration, since the question is whether ﬁrm i is integrated with its upstream

suppliers (rather than ﬁrm j being integrated with downstream producers potentially using its inputs).

Acemoglu et al. Vertical Integration 993

technology intensity of the producing industry is associated with more vertical

integration, technology intensity in the supplying industry is associated with

less integration, and the share of costs is associated with more integration.

We subject these basic patterns in the data to a series of robustness checks.

The results are generally robust. First, including a range of ﬁrm-level covariates

does not change the relationship between R&D intensity and vertical integration.

Second, the results are broadly similar when we restrict attention to multiplant

ﬁrms and control for ﬁrm level ﬁxed effects.

Third, the results are similar when

we proxy for technology intensity by physical investments rather than R&D.

Fourth, the results are robust to excluding top or bottom quartiles of ﬁrms by size

and to using an alternative measure of vertical integration. Finally, the results

are also similar when we use a probit model rather than a linear probability

model.

We also investigate the relationship between competition (measured as the

number of ﬁrms in supplying and producing industries) and vertical integration.

Our results here are also consistent with theory and indicate that having more ﬁrms

in the supplying industry reduces the likelihood of vertical integration, while a

larger number of ﬁrms in the producing industry increases it.

In our regressions, a measure of vertical integration is on the left-hand side,

and industry and ﬁrm characteristics are on the right-hand side. However, in

theory, and most likely in practice, vertical integration also affects technology

choices. Moreover, other factors omitted in the regression could inﬂuence both

vertical integration and technology intensity, and in a cross-industry regression

there are many potential omitted variables. Although our ﬁxed effects regressions

control for many such omitted characteristics, there is still a concern regarding

causality. As an imperfect attempt at dealing with the endogeneity problem, we

report results where the technology intensity of each industry is instrumented

with the technology intensity of the same industry in the United States. This

instrumentation strategy generally yields results similar to, and in fact quanti-

tatively larger than, the ordinary least squares strategy.

Overall, we conclude

that there is an interesting pattern in the data, with technology intensity of pro-

ducing and supplying industries having opposite effects on the likelihood of

vertical integration. This pattern should be important in evaluating the predic-

tions of a range of different theories of vertical integration (even though we have

6. In particular, with ﬁrm ﬁxed effects, even though the main effect of producer R&D intensity

is no longer statistically signiﬁcant, both supplier R&D intensity and the interaction between both

supplier and producer R&D intensities and share of costs remain signiﬁcant. When we control for

endogenous selection, the effect of producer R&D intensity is again statistically signiﬁcant.

7. However, when we simultaneously instrument for the main effects and the interaction terms, the

results are imprecisely estimated.

994 Journal of the European Economic Association

motivated our empirical approach from a speciﬁc theory based on incomplete

contracts).

In addition to the theoretical studies mentioned earlier, this paper is related

to a large empirical literature on vertical integration. In contrast to our approach,

most empirical studies of vertical integration are motivated by the TCE approach

and focus on a single industry. These include Joskow’s (1987) seminal paper

on ownership arrangements in electricity generating plants, Stuckey’s (1983)

study of integration between aluminium reﬁneries and bauxite mines, Monteverde

and Teece’s (1982) investigation of integration in the automobile industry, Mas-

ten’s (1984) work on the aerospace industry, Ohanian’s (1994) work on the pulp

and paper industry, and Klein’s (1998) work on the Fisher Body and General

Motors relationship. More recently, important papers by Baker and Hubbard

(2003, 2004) study the trucking industry, Lerner and Merges (1998) consider

the biotech sector, Woodruff (2002) studies integration in the Mexican footwear

industry, Chipty (2001) investigates vertical integration and market foreclosure

in the cable television industry, and Hortaçsu and Syverson (2007) study vertical

integration in the U.S. cement industry. The only cross-industry evidence relevant

to our investigation of which we are aware is due to Caves and Bradburd (1988),

who document a positive cross-industry correlation between measures of speci-

ﬁcity and vertical integration, and from Antras (2003), who looks at the share of

intra-ﬁrm imports over total imports for 23 U.S. industries and relates this to cap-

ital intensity. We are not aware of any other papers investigating the prediction

that the technology intensity of suppliers and producers have opposite effects

on vertical integration decisions (see Lafontaine and Slade (2007) for a recent

survey).

The paper is organized as follows. Section 2 presents the theoretical

framework and derives the main testable implications. Section 3 details the con-

struction of our measure of vertical integration, and also discusses data sources

and the construction of the other key variables. Section 4 presents the main

results. Section 5 discusses robustness checks and additional tests. Section 6

brieﬂy investigates the effect of competition in producing and supplying indus-

tries on vertical integration. Finally, Section 7 discusses alternative theoretical

approaches that may account for the correlations presented in this paper and

then concludes.

8. Our proxies for technological intensity may be correlated with the relevant demand elasticities

and impact vertical integration decision through strategic considerations, though it is unclear why

this could generate the opposite-signed patterns that we ﬁnd robustly in the data.

More generally, although the speciﬁc regressions estimated in this paper are motivated by the

PRT approach, the results are informative about, and could be consistent with, other approaches to

vertical integration. In the concluding section, we discuss how these results could be reconciled with

other theories.

Acemoglu et al. Vertical Integration 995

2. Theory and Empirical Hypotheses

In this section, we construct a simple theory of the determinants of vertical inte-

gration in the spirit of Grossman and Hart (1986). The focus is on the relative

importance of technological investments in a bilateral relationship between a pro-

ducer and a supplier. In the model, the two parties can either remain as separate

entities (non-integration, NI), or the producer can employ the supplier and become

the residual claimant of the proﬁts generated by the joint venture (backward ver-

tical integration, VIB), or the supplier can employ the producer and become the

residual claimant (forward vertical integration, VIF). As already discussed in the

Introduction, when we turn to data we will focus on backward vertical integra-

tion. Nevertheless, it is useful to understand the implications of the theoretical

framework both for backward and forward integration.

2.1. Model Environment

We consider a one-period relationship between two risk-neutral parties who can

undertake technological investments to increase the productivity of the rela-

tionship. Throughout, we assume these investment decisions to have a speciﬁc

component in that greater technology intensity leads to a greater possibility of

holdup. Decision rights over these investments cannot be transferred between

the two parties, for example, because the investments require tacit knowledge

or human capital. This implies that the producer cannot make the supplier’s

investments, or vice versa. As is standard in this literature, we assume that the

investments and the output of the relationship are non-veriﬁable. Consequently,

neither contracts conditional on investments nor contracts specifying rules for

ex post revenue-sharing are possible. However, the allocation of property rights

(vertical integration or arms’ length) can be designed so as to provide the right

incentives for the non-contractible investments.

We adopt the usual timing assumptions: Before investments and production

take place, the parties can choose an organizational form and transfers. We denote

the amount of ex ante transfer to party i conditional on the organizational form z

by T

(z), where P and S denote the producer and the supplier, respectively. More

formally, the timing of events in this relationship is as follows:

1. The producer offers an organizational form (ownership structure) z ∈

{VIB, NI, VIF} and associated transfers, T

(z) and T

(z), such that T

(z) +

(z) = 0. There are no credit constraints, implying that T

(z) can be

negative.

2. The supplier decides whether to accept or reject the offer. If the offer is not

accepted, then the two parties remain independent, and the producer does

not receive any speciﬁc input from the supplier (in this case, the game ends

996 Journal of the European Economic Association

with payoffs {O

} deﬁned subsequently). Then, the producer and the

supplier simultaneously choose their investments, e

≥ 0 and e

≥ 0.

3. The supplier and the producer bargain over the division of the revenue, accord-

ing to the Nash bargaining solution given the organizational form z. Output

is realized and shared.

The production technology of the relationship is

F(x

) = ϕx

(pe

+ se

+ 1) + (1 − ϕ)(pe

+ 1). (1)

The ﬁrst term in equation (1) is the output generated by the producer and the sup-

plier conditional on the supplier providing a customized (relationship-speciﬁc)

input, denoted x

= 1. If x

= 0 and this input is not supplied, these activi-

ties generate no revenue. The value of the relationship can be further increased

by the producer’s and the supplier’s investments, e

and e

. The parameters p

and s designate the relative importance of investments by the producer and the

supplier, that is, the extent to which one type of investment brings more value

added than the other, and ϕ ∈ (0, 1) corresponds to the share of the producer’s

inputs accounted for by the supplier.

Note that ϕ also determines the importance

of the supplier’s investment, e

This production function has also normalized

the level of output in the absence of any investments to 1, which is without

any loss of generality. The feature that there are no complementarities between

the investments of the supplier and the producer is for simplicity, and high-

lights the fact that, for the results we emphasize, such complementarities are not

essential.

To simplify the expressions, we assume that the supplier can provide the

basic input x

at no cost, and also that the costs of investment for both parties are

quadratic:



) =

and 

) =

ϕe

. (2)

9. In this game form, the assumptions that the producer makes the organizational form offer and

that the parties receive their non-integration outside options are without loss of any generality.

Moreover, following other papers in this literature, we are using the Nash bargaining solution (see

Binmore, Rubinstein, and Wolinsky (1986) for a potential justiﬁcation for Nash bargaining and

a discussion of alternative bargaining rules), but our qualitative results do not depend on Nash

bargaining.

10. With competitive spot market transactions and without any speciﬁc investments, namely, e

= 0, ϕ would exactly correspond to the share of costs of the producer accounted for by the

supplier in question. Although with positive investments and ex post bargaining, there will be a

wedge between the two, we refer to ϕ as the “share of costs” to simplify the terminology.

11. Symmetrically, we could introduce another parameter, say η, to capture the importance of the

producer for the supplier. Comparative statics with respect to η are very similar to those with respect

to ϕ. We omit this generalization to reduce notation, and discuss empirical results regarding the

effect of a measure related to η in Section 5.

Acemoglu et al. Vertical Integration 997

Notice that the investment costs of the supplier are multiplied by ϕ. This ensures

that the costs are proportional to the scale of operation and that the socially optimal

levels of both e

and e

are independent of ϕ.

In the event of disagreement, the two parties receive their outside options,

which depend on the organizational form. We denote the outside option of party

i under organizational form z by O

With backward vertical integration (VIB), the producer owns all assets, and in

the event of ex post breakup the supplier simply walks away from the ﬁrm without

receiving anything.

The producer, who has residual control rights, keeps all the

assets and the customized input, but lack of cooperation from the supplier causes

the loss of a fraction λ of the supplier’s investment, so the “effective investment”

of the supplier is reduced to (1 −λ)e

where λ ∈[0, 1).

Therefore, the outside

options of the supplier and the producer in this case are

VIB

) = 0 and O

VIB

) = F(x

= 1,e

,(1 − λ)e

With non-integration (NI), the supplier and the producer own their separate

ﬁrms and assets. In case of disagreement, the producer does not receive the cus-

tomized input from the supplier (x

= 0), and consequently, generates no output

from the part of the operations relying on those inputs. The supplier can sell

her input in the market, but suffers in this case some revenue loss because of

the speciﬁcity of the input to this producer. Therefore, the outside options under

non-integration are

) = θϕ(se

+ 1),

) = F(x

= 0,e

) = (1 − ϕ)(pe

+ 1), (3)

where θ ∈[0, 1) is an inverse measure of how much the supplier loses if she

sells the input outside of the speciﬁc relationship.

The general equilibrium

12. The socially optimal levels of investment are e

= p and e

= s. Modifying the supplier’s

cost function to 

) = e

/2 would introduce an implicit “scale economies,” and an increase in ϕ

would make the supplier’s investment more proﬁtable (the socially optimal level of investment for

the supplier would become e

= sϕ). Consequently, the comparative static results with respect to ϕ

become ambiguous.

13. More generally, our analysis goes through if we assume that in case of ex post break-up the sup-

plier receives a positive fraction of what she would receive under non-integration, and symmetrically

for the producer under forward integration.

14. Alternatively, λ can be interpreted as the fraction of investment which is incurred at the end of

the period by the supplier to ﬁne-tune the quality of the input. The supplier would not undertake this

investment in the event of disagreement.

15. It is possible to also allow a secondary market in which the producer can purchase a less suitable

input, in which case his outside option would be:

) = (1 − ϕ)(pe

+ 1) + ρϕ(pe

+ 1),

where ρ + θ<1. This modiﬁcation has no effect on the results.

998 Journal of the European Economic Association

determination of θ is beyond the scope of our paper. Here it is treated as exogenous

and in the empirical section it is proxied by the relative number of producers to

suppliers (with more producers, it might be easier for the supplier to ﬁnd a suitable

buyer to her input in the secondary market).

The third organizational form is forward vertical integration (VIF), where the

supplier owns all the assets. In this case, with a similar reasoning as before, the

outside options are

VIF

) = F(x

= 1,(1 − λ



) and O

VIF

) = 0,

where λ



∈[0, 1) is the fraction of the producer’s investment the supplier loses

in case of disagreement.

Let y

denote the output accruing to party i under organizational form z.

Symmetric Nash bargaining implies that

) = O

) +



F(x

= 1,e

) − O

)



(4)

where the term in square brackets is the relationship-speciﬁc surplus over which

bargaining takes place, and is positive for all z ∈{VIB, NI, VIF}. The important

feature is that each party’s share of revenue will be increasing in her own outside

option, and decreasing in that of the other party. This feature creates a link between

outside options and investment incentives, and through this channel, between

organizational forms and investment incentives.

Finally, the utility of party i ∈{P,S} can be expressed as

), e

) = y

) − 

) + T

(z). (5)

2.2. Equilibrium

We next characterize the unique (subgame perfect) equilibrium of the game

speciﬁed in the previous section. Unless otherwise speciﬁed, we refer to

an equilibrium by the on-the-equilibrium-path actions and revenues, (z

∗

It is useful to deﬁne the “total surplus” of the relationship as

= U



∗

(z), e

∗

(z)



∗

(z)



+ U



∗

(z), e

∗

(z)



∗

(z)



where e

∗

(z) denotes party i’s optimal investment under ownership structure z,

using equations (4) and (5) and the fact that T

(z) +T

(z) = 0, we ﬁnd the total

surplus of the relationship is

= F



= 1,e

∗

(z), e

∗

(z)



− 



∗

(z)



− 



∗

(z)



. (6)

Acemoglu et al. Vertical Integration 999

Because both parties have access to perfect credit markets and ex ante trans-

fers, the subgame perfect equilibrium will always pick the organizational form that

maximizes the surplus, S.

In other words, S

∗

≥ S

for all z ∈{VIB, NI, VIF}.

We now characterize the equilibrium by calculating the levels of social surplus

under backward integration (S

VIB

), non-integration (S

), and forward integration

VIF

). The equilibrium organizational form is then given by

∗

= arg max

z∈{VIB,NI,VIF}

Equilibrium investments are determined as the Nash equilibrium of a game

where each party chooses its investment so as to maximize utility, given the other

party’s investment and the ownership structure. More formally, the equilibrium

conditional on the ownership structure z is given by the pair {e

∗

(z), e

∗

(z)} such

that

∗

(z) = max



∗

(z)



− 

)},

∗

(z) = max





∗

(z), e



− 

)



where the expressions for y

(.) are given in equation (4), and those for 

and



are given in equation (2). The Nash equilibrium investment levels under each

of the three ownership structures can be calculated as

∗

(VIB) = p, e

∗

(VIB) =

s, (7)

∗

(NI) =



1 −



p, e

∗

(NI) =

1 + θ

s, (8)

∗

(VIF) =



p, e

∗

(VIF) = s. (9)

These expressions highlight the effect of the different ownership structures

on investment incentives. The investment made by the producer is highest under

16. With credit constraints, the less constrained party may become the owner even when this

structure does not maximize the ex ante social surplus, because the other party does not have the

cash to compensate the ﬁrst party for giving up ownership (see, for example, Aghion and Tirole

(1994a), or Legros and Newman (2008)).

17. Suppose that the equilibrium involves z

∗

,butS

∗



. Then the producer, who has the

bargaining power in the ﬁrst stage of the game, can propose z



together with a compensating transfer

to the supplier, and increase its payoff. Namely, she can offer



) = T

∗

) + y

∗

− y



− 



∗

)



+ 



∗



)



+ ε

with ε>0, which would be at least as attractive for the supplier, and for ε<S



−S

∗

, also proﬁtable

for the producer, thus yielding a contradiction.

1000 Journal of the European Economic Association

backward vertical integration (i.e., e

∗

(VIB)>e

∗

(NI)>e

∗

(VIF)), whereas that

made by the supplier is highest under forward vertical integration (i.e., e

∗

(VIF)>

∗

(NI)>e

∗

(VIB)).

Most relevant for our empirical analysis are our results that backward vertical

integration increases the investment of the producer and reduces the investment

of the supplier relative to non-integration. This is a fundamental result in this

class of models: Backward vertical integration reduces the supplier’s outside

option and increases the share of the surplus accruing to the producer. It therefore

discourages supplier investment and encourages producer investment. Another

important feature is that with non-integration, the investment level of the pro-

ducer is decreasing in ϕ, because a greater share of costs increases the scope for

holdup by the supplier. Also with non-integration, the investment of the supplier

is increasing in θ because a greater θ provides her with a better outside market

(the outside market is irrelevant for the other organizational forms, since one of

the parties has residual rights of control over the input and the assets).

Finally, substituting for e

∗

(z) and e

∗

(z) in equation (6), we obtain the total

surplus under the three ownership structures, S

VIB

, S

, and S

VIF

, and the com-

parison of the surpluses gives the following proposition (the relevant expressions

and the proof are provided in Appendix A).

Proposition 1. There exist r

, ¯r, and ˆr such that the unique subgame perfect

equilibrium ownership structure, z

∗

, is given as follows.

• If r

< ¯r, then z

∗

= VIB for p/s > ¯r, z

∗

= NI for p/s ∈ (r, ¯r), and z

∗

= VIF

for p/s < r

. Moreover,

∂ ¯r

∂ϕ

< 0,

∂r

∂ϕ

> 0,

∂ ¯r

∂θ

> 0,

∂r

∂θ

< 0.

• If r

≥¯r, then z

∗

= VIB for p/s > ˆr, and z

∗

= VIF for p/s < ˆr. Moreover,

∂ ˆr

∂ϕ

> 0 and

∂ ˆr

∂θ

= 0.

Proposition 1 summarizes the most important comparative static results that

will be empirically investigated in the second part of the paper. Because the

empirical analysis will focus on the margin between backward integration and

non-integration, we assume henceforth that r<¯r and restrict the discussion of

the comparative statics to this margin.

First, the proposition implies that, given the other parameters, the choice of

organizational form depends on p and s. When p is high, or s is low, backward

integration is the equilibrium organizational form. Non-integration emerges when

p is low or s is high. Intuitively, backward integration becomes more likely when

p is large because, in this case, the tasks in which the producer specializes are

Acemoglu et al. Vertical Integration 1001

highly “technology intensive” (i.e., the producer’s activity brings more value

added), so increasing the producer’s investment is the ﬁrst priority. Backward

vertical integration achieves this by increasing the producer’s outside option and

reducing that of the supplier. In contrast, when s is large, backward integration

becomes less likely, because the investment of the supplier is now more important,

and by reducing the supplier’s outside option backward integration discourages

her investment.

Second, an increase in ϕ makes backward integration more likely relative

to non-integration. A greater share of costs (of the supplier’s inputs in the pro-

ducer’s total costs) increases the degree to which the producer will be held up by

the supplier. Backward vertical integration becomes more preferable because it

avoids this problem. In addition, this result also implies that there are important

interaction effects: The positive effect of p/s on backward vertical integration is

ampliﬁed by ϕ. To see this let us focus of the comparison between non-integration

and backward integration, and denote the surplus difference between these two

organizational forms by 

≡ S

VIB

− S

. Then we have that

∂



∂ϕ∂p

> 0 and

∂



∂ϕ∂s

< 0.

This prediction is also quite intuitive. It suggests that when the relation-

ship between the producer and the supplier is less important, their respective

technology intensities should have less effect on integration decisions.

Finally, a greater θ makes non-integration more likely relative to backward

vertical integration; with a greater θ, the supplier invests more under non-

integration because she has a better outside option, and this makes non-integration

a more desirable organizational form. If we interpret θ as the degree of competi-

tion in the market, this result would imply that, consistent with some of the claims

made in the popular press, greater competition encourages non-integration over

both backward and forward integration. However, a more appropriate interpre-

tation might be that θ is a function of the ratio of producers to suppliers in the

market because, with a larger number of producers, the supplier is more likely

to ﬁnd a suitable match in the secondary market after a breakup. In this case,

an increase in competition, associated with an increase in the numbers of both

suppliers and producers, need not increase non-integration.

2.3. Summary and Empirical Hypotheses

We can summarize the most important empirical hypotheses from our framework

as follows.

1. Technology intensities of the producer and the supplier should have opposite

effects on the likelihood of vertical integration.

1002 Journal of the European Economic Association

2. These effects should be ampliﬁed when the supplier accounts for a larger

fraction of the input costs of the producer.

3. Focusing on backward vertical integration, greater technology intensity of

the producer, lower technology intensity of the supplier, and greater share

of costs of the producer accounted by inputs from the supplier should make

vertical integration more likely.

4. Finally, again focusing on backward vertical integration, we may also expect

the number of producing ﬁrms relative to supplying ﬁrms to encourage non-

integration.

In light of these empirical hypotheses, we next investigate the potential

determinants of vertical integration.

3. Data and Measurement

3.1. Vertical Integration

Central to our empirical strategy is a measure of vertical integration. As discussed

in the Introduction, to compute such a measure we need to organize the data in

a speciﬁc way. Motivated by the previous literature, we look at the data from the

viewpoint of the producing ﬁrm and ask whether for each potential supplying

industry that producer is vertically integrated or not. This conceptual exercise

amounts to constructing a measure proxying for backward vertical integration

(even though because we do not observe which ﬁrm/manager has residual rights

of control, this is not identical to backward vertical integration in the theory).

More precisely, for each ﬁrm i = 1, 2,...,N, our ﬁrst measure is a dummy

ij k

for whether, for each product (industry) j = 1, 2,...,J it is producing, the

ﬁrm owns a plant in industry k = 1, 2,...,K supplying product j :

ijk



1 if ﬁrm i owns a plant in industry k supplying industry j ,

0 otherwise.

(10)

This measure provides a direct answer to the question of whether each producing

ﬁrm can supply some of its own input k necessary for the production of product

j. However, it does not use any information on how much the ﬁrm produces in

its own plants.

We also construct an alternative (continuous) measure using this information.

Let c

denote the total cost (including intermediate, capital, and labor costs) of

ﬁrm i in producing j, and w

denote the proportion of total costs of producing j

that are made up of input k, which is obtained from the UK Input–Output Table.

We can think of c

as the ﬁrm’s demand for input k for product j (to obtain

the ﬁrm’s total demand for k we sum over j). Let y

denote the amount of k that

Acemoglu et al. Vertical Integration 1003

ﬁrm i produces. The alternative measure of the degree of vertical integration of

ﬁrm i in the industry pair jk is calculated as

ijk

= min



, 1



. (11)

When a ﬁrm produces several different products that demand input k, and where

the total demand is greater than what can be supplied by the ﬁrm itself, we assume

that it allocates the input across plants proportionately to their demand, so that

the measure becomes

ijk

= min

⎧

⎪

⎨

⎪

⎩



, 1

⎫

⎪

⎬

⎪

⎭

. (12)

In practice, there is little difference between vi

ijk

and vi

ijk

, because when a ﬁrm

owns a plant in a supplying industry, it is typically sufﬁcient to cover all of its

input requirements from that industry. So for most of our analysis, we focus on

the vi

ijk

measure.

Our main source of data is the Annual Respondents Database (ARD).

This

is collected by the UK Ofﬁce of National Statistics (ONS) and ﬁrms have a legal

obligation to reply. These data provide us with information on input costs and

output for each production plant located in the UK at the four-digit industry level

and on the ownership structure of these plants.

These data do not, however, tell

us directly whether a plant purchases inputs from a related plant in the same ﬁrm.

Data on the demand for intermediate inputs are available at the two-/three-digit

industry level from the Input–Output Domestic Use Table. The Input–Output

Table contains information on domestic input ﬂows between 77 manufacturing

industries, giving 5,929 pairs of producing–supplying industries, 3,840 of which

have positive ﬂows. Appendix Table B.1 lists all 77 (supplying) industries together

with their largest purchaser and other information.

Because of the level of aggregation of the Input–Output Table, one difﬁculty

arises when we look at industry pairs where the input and output are in the same

18. Davies and Morris (1995) construct a related index with more aggregate data, whereas Fan and

Lang (2000) measure corporate relatedness using a similar measure.

19. This data set is constructed using the data from the Annual Business Inquiry from 1998 and

onward. Before that the name of the Inquiry was The Annual Census of Production (ACOP). See

Grifﬁth (1999) and Barnes and Martin (2002) for a description of these data.

20. Data on employment are available for all plants. Data on other inputs and output are available

at the establishment level. An establishment is often a single plant, but can also be a group of plants

owned by the same ﬁrm that operate in the same four-digit industry. We have input and output data

on all establishments with over 100 employees, data from smaller establishments are collected from

a random stratiﬁed sample and values for non-sampled plants are imputed. Throughout, we exclude

single plant ﬁrms with fewer than 20 employees.

1004 Journal of the European Economic Association

two-/three-digit industry. In this case, we consider a ﬁrm to be vertically integrated

only if it has plants in more than one of the four-digit industries within that

two-/three-digit industry. Further details on the construction of these measures

are provided in Appendix B.

We should emphasize again that all of the measures here are conceptually

similar to backward vertical integration. In particular, we are measuring the prob-

ability that a producer is vertically integrated with each potential supplier (rather

than the probability that a supplier is vertically integrated with each potential

producer).

3.2. Technology Intensity and the Share of Costs

Our main measure of technology intensity is R&D intensity, but we also report

robustness results using investment intensity. Both these measures are at the indus-

try level rather than at the ﬁrm level for two reasons: First, our methodology

focuses on the technology of an industry, not on whether a speciﬁc ﬁrm is more

R&D or investment intensive; second, we need measures that apply both to inte-

grated and non-integrated relationships, which naturally takes us to the industry

level.

R&D intensity is measured as R&D expenditure divided by total value

added.

We use R&D data pre-dating the vertical integration sample (1994–

1995). The total value added in the denominator includes all ﬁrms in the industry

(both those performing R&D and those that do not).

R&D intensity is our preferred measure because it is directly related to invest-

ment in new technologies. A possible concern is that the distribution of R&D

across industries is rather skewed. Another concern might be that R&D could be

spuriously correlated with vertical integration; for example, because it is better

reported in industries with many large ﬁrms and large ﬁrms are more likely to

be vertically integrated (though, in many speciﬁcations, we also control for ﬁrm

size).

For these reasons, we consider an alternative indicator of industry technology

by looking at physical investment intensity. This information is reported at the

level of the ﬁrm’s line of business and can be directly linked to the producing

or supplying part of vertically integrated ﬁrms. It is also more widely reported

and less skewed both within and between industries. As with R&D data, we use

data pre-dating the measure of vertical integration, 1992–1995, and aggregate the

data from the ﬁrm’s line of business to the industry level. The disadvantage of this

21. We have data on R&D and value-added at the ﬁrm–industry level. We use these data to construct

R&D and value-added by summing over all ﬁrm–industry observations in each industry. In the UK

these data on R&D are reported separated both by the industry of the ﬁrm conducting the R&D

and the product category for which the R&D is intended. This enables us to have a more accurate

measurement of R&D by producing and supplying industries.

Acemoglu et al. Vertical Integration 1005

Table 1. Descriptive statistics.

Producer R&D Supplier R&D

Variable Mean (s.d.) low high low high

Mean vi

ijk

0.008 0.007 0.010 0.008 0.009

(0.087)(0.078)(0.096)(0.084)(0.089)

Mean of vi

ijk

0.009 0.009 0.013 0.010 0.011

(0.091)(0.093)(0.114)(0.101)(0.104)

Firm age 10 10 10 10 10

(7) (7) (7) (7) (7)

Firm employment 111 99 125 109 112

(455) (346) (559) (444) (465)

Share of producer costs (j k) 0.010 0.010 0.010 0.012 0.009

(0.034)(0.038)(0.029)(0.040)(0.028)

Producing industry

R&D over value-added 0.027 0.004 0.055 0.026 0.028

(0.055)(0.002)(0.072)(0.055)(0.055

)

Investment over value-added 0.101 0.095 0.109 0.102 0.101

(0.041)(0.031)(0.049)(0.040)(0.041)

Mean number of ﬁrms in industry 5757 8267 2763 5755 5759

(6585) (7978) (1635) (6525) (6636)

Supplying industry

R&D over value-added 0.046 0.044 0.050 0.005 0.082

(0.107)(0.103)(0.113)(0.003)(0.137)

Investment over value added 0.122 0.123 0.122 0.106 0.136

(0.057)(0.057)(0.057)(0.038)(0.067)

Mean number of ﬁrms in industry 2316 2320 2309 3347 1433

(3730) (3727) (3733) (5065) (1471)

Source: Authors’ calculations using the UK ONS data. All statistical results remain Crown Copyright.

Notes:

ijk

is a continuous measure of the share of the producers demand that can be met by its own supply. vi

ijk

is a

dummy for whether a ﬁrm owns plants in both producing and supplying industries. Share of producer costs (j k) is the

share of producers in industry j total costs (including labour and capital) that is on input k (from the Input–Output Table).

The sample contains 2,973,008 observations on 46,392 ﬁrms. Numbers reported are means (standard deviations). The

ﬁrst column reports on the whole sample. Subsequent columns split the sample by median producer R&D and supplier

R&D intensities.

measure relative to R&D intensity is that physical investment intensity may be less

related to technology and may also have a more limited ﬁrm-speciﬁc component,

which is important for the model we have used to motivate our empirical analysis.

The share of costs between each industry pair jk, sc

, is calculated from

the Input–Output Table as the share of inputs from industry k in the total cost of

industry j (£ of input k necessary to produce £1 of product j ).

3.3. Descriptive Statistics

Table 1 gives descriptive statistics for the whole sample, and also for subsamples

separated according to whether the producer (supplier) has a high or low R&D

intensity. There are 3,840 industry pairs where the Input–Output table indicates

that transactions occur. There are 46,392 manufacturing ﬁrms with twenty or

more employees operating in the UK at some time over the period 1996–2001.

1006 Journal of the European Economic Association

Because individual ﬁrms seldom change their organization structure over this

short time period we collapse the data into a single cross-section. An observation

in our data represents a ﬁrm i producing product j which uses input k; this gives

us 2,973,008 observations at the ﬁrm–industry pair level.

The ﬁrst row of Table 1 gives the mean and standard deviation of the con-

tinuous measure of vertical integration,

ijk

. The mean is 0.008 with a standard

deviation of 0.087, which shows that there is substantial variation across ﬁrms

and at the sub-ﬁrm level. There is also substantial variation within industry pairs.

To illustrate this, we calculate the average within-industry-pair standard deviation

ijk

, which is 0.086 (not shown in the table). This indicates that, even within a

relatively narrow industry-pair, there is as much variation in the extent of vertical

integration as in the whole sample.

The low mean of this variable is driven by the large number of zeros. The

mean of

ijk

conditional on vi

ijk

> 0 (not shown) is 0.93. This indicates that

if a ﬁrm can produce some of its inputs k in-house, it can typically produce all

that input (k) necessary for production.

This motivates our focus on the simpler

dummy variable vi

ijk

, which indicates whether the ﬁrm owns a plant producing

input k which it needs in the production of the product j (see equation (10)). Not

surprisingly, the second row shows that the mean of this variable, 0.009, is very

similar to that of

ijk

The other columns illustrate the differences in the extent of vertical integration

when we separate ﬁrm–industry pairs by producer R&D intensity and supplier

R&D intensity. These differences, which will be investigated in greater detail

in the subsequent regression analysis, indicate that vertical integration is higher

when the R&D intensity of the producing industry is high. Interestingly, the

descriptive statistics do not show any difference between vertical integration when

we cut the sample by whether the R&D intensity of the supplying industry is high

or low.

The regression analysis will show a negative effect of supplier R&D

intensity as well as supplier investment intensity on vertical integration, but due

to nonlinearities in this relationship (see also Appendix Table B.3), the high–low

cut does not show this result.

R&D intensity is positively correlated with investment intensity, although the

correlation is quite low (0.251). The relatively weak correlation between these

measures means that each measure is an imperfect proxy for the overall technology

intensity of the sector, and consequently, there might be some attenuation bias

22. Naturally this does not imply that if a ﬁrm is vertically integrated for one of its inputs, it is also

vertically integrated for its other inputs. In fact, the mean of



ijk

conditional on vi

ij k



> 0

for some k



is 0.053, so on average, across ﬁrms that are vertically integrated in any one input, ﬁrms

are vertically integrated in around 5% of their total inputs demanded.

23. When we group ﬁrms on the basis of investment intensity, we see that greater supplier investment

intensity is associated with lower vertical integration. This cut of the data is not shown in Table 1 to

save space.

Acemoglu et al. Vertical Integration 1007

Table 2. Main results—R&D intensity.

(1) (2) (3) (4) (5) (6)

Dependent variable: vi

ijk

Share of costs (j k) 0.204 0.187 0.187 0.182

(0.029)(0.028)(0.028)(0.027)

R&D intensity, 0.038 0.040 0.044 0.037 0.030

producing (j ) (0.006)(0.005)(0.005)(0.005)(0.005)

× Share of costs 1.112 1.104 1.067

(0.402)(0.397)(0.374)

R&D intensity, −0.010 −0.007 −0.013 −0.013 −0

.007

supplying (k) (0.002)(0.001)(0.003)(0.003)(0.003)

× Share of costs −0.909 −0.914 −0.871

(0.353)(0.351)(0.324)

ln Firm size (ij) 0.0053 0.0052

(0.0002)(0.0002)

ln Firm age (ij) 0.0010 0.0009

(0.0001)(0.0001)

ln Average ﬁrm size, 0.0011

producing (j ) (0.0005)

ln Average ﬁrm size, −0.0036

supplying (k) (0.

0004)

ln Average ﬁrm age, 0.012

producing (j ) (0.003)

ln Average ﬁrm age, 0.004

supplying (k) (0.002)

Source: Authors’ calculations using the UK ONS data. All statistical results remain Crown Copyright.

Notes: The dependent variable is a dummy for whether a ﬁrm is vertically integrated in that industry pair at any time

over the years 1996–2001. There are 2,973,008 observations at the ﬁrm–industry pair level. Standard errors in parentheses

are clustered at the level of 3,840 industry pairs. The right-hand side variables ﬁrm size and ﬁrm age are measured at the

ﬁrm–industry pair level in 1996 (age is equal to 1 if the ﬁrm enters that industry pair after 1996). R&D intensity is R&D

carried out in the UK divided by value–added produced in the UK, taken from plant level R&D data, aggregated to the

two-/three-digit industry level and average over the years 1994–1995. Share of costs is from the 1995 Input–Output Table

and is at the industry pair level. Average ﬁrm size and age are calculated from the ﬁrm–industry pair data and average

over the years 1996–2001. In regression with interactions, all main effects are evaluated at sample means.

in our estimates of the relationship between technology intensity and vertical

integration. It also suggests that these measures capture different dimensions of

technology intensity, so that it is useful to study the relationship between each of

them and vertical integration separately.

Table 1 also shows the means and standard deviations of the other main

covariates, deﬁned in Appendix B.

4. Results

4.1. Benchmark Speciﬁcation

Table 2 reports the main results. It reports estimates from the following linear

probability model:

ijk

= αsc

+ β

+ X



ijk

η + ε

ijk

, (13)

1008 Journal of the European Economic Association

where sc

is the share of costs, RD

is R&D intensity in the producing industry

j, RD

is R&D intensity in the supplying industry k, X

ijk

is a vector including

the constant term and ﬁrm and industry characteristics (ﬁrm size and age, average

ﬁrm size and age in producing and supplying industries). The main coefﬁcients

of interest are α, β

, and β

. The regressions are at the ﬁrm–industry-pair level,

while some of the main regressors are at the (producing or supplying) industry

level. For this reason, throughout all standard errors are corrected for clustering

at the industry-pair level.

The ﬁrst two columns of Table 2 consider the bivariate relationship between

R&D intensity in the producing and supplying industries and vertical integra-

tion. Column (1) shows a positive and highly statistically signiﬁcant relationship

between R&D intensity in the producing industry and vertical integration. The

estimate of β

is 0.038 with a standard error of 0.006. Column (2) shows a nega-

tive and highly statistically signiﬁcant relationship between R&D intensity in the

supplying industry and vertical integration; the estimate of β

is −0.010 (standard

error of 0.002). These relationships are robust to the inclusion of other covariates

in the rest of the table.

The third column includes both R&D intensity variables and the share of

costs. The R&D intensity variables continue to be highly statistically signiﬁcant,

with coefﬁcients close to those in columns (1) and (2) (0.040 and −0.007), and the

share of costs is positive and also statistically signiﬁcant. The pattern of opposite

signs on R&D intensity of producing and supplying industries is consistent with

our ﬁrst empirical hypothesis discussed in Section 2.3.

Moreover, the directions of the effects of R&D intensities and the share of

costs are in line with our third empirical hypothesis, that is, they are consistent

with the theory provided that the relevant choice in the data is between backward

vertical integration and non-integration. This is reassuring, because we not only

believe that this is the case (based on the bulk of evidence in the prior literature)

but also because, as explained earlier, we organized the data to have a measure

conceptually corresponding to backward vertical integration.

Our second empirical hypothesis from Section 2.3 suggests the possibility of

interaction effects between the share of costs and R&D intensity. To investigate

this issue, we modify our estimating equation to

24. There is also a potential correlation between observations for the same ﬁrm in different industry

pairs. Unfortunately, we were unable to estimate a variance–covariance matrix with multiple random

effects or multiple levels of clustering, due the large size of the data set. Nevertheless, we believe that

the downward bias in the standard errors should be small in our case, because, as noted in footnote

22, the probability of a ﬁrm that is vertically integrated for one of her inputs also being integrated for

other inputs is relatively small. In any case, in Table 3, we estimate these models including a full set

of ﬁrm ﬁxed effects (for those ﬁrms that operate in more than one industry), which directly removes

any potential correlation across ﬁrm observations.

Acemoglu et al. Vertical Integration 1009

Table 3. Within-ﬁrm variation.

(1) (2) (3) (4) (5)

Dependent variable: vi

ijk

= 1 if multi product vi

ijk

Share of costs (j k) 0.434 0.434 0.414 0.025 0.475

(0.054)(0.053)(0.050)(0.094)(0.058)

R&D intensity, producing (j) 0.073 0.024 0.014 0.333 0.030

(0.012)(0.016)(0.017)(0.025)(0.012)

× Share of costs 2.725 2.786 2.607 −0.058 2.741

(0.917)(0.880)(0.816)(1.048)(0.

915)

R&D intensity, supplying (k) −0.041 −0.042 −0.021 0.019 −0.016

(0.009)(0.009)(0.008)(0.024)(0.005)

× Share of costs −2.434 −2.543 −2.303 0.914 −2.482

(0.897)(0.865)(0.786)(0.990)(0.891)

ln Firm size (ij) 0.0024 0.0044

(0.0004)(0.0008)

ln Firm age

(ij) 00004 0.0076

(0.0005)(0.0007)

ln Average ﬁrm size, 0.003 0.014

producing (j ) (0.002)(0.005)

ln Average ﬁrm size, −0.012 −0.0005

supplying (k) (0.001)(0.0042)

ln Average ﬁrm age, −0.006 0.352

producing (j ) (0.010)(0.021)

ln Average ﬁrm age, 0.017 −0.0019

supplying (k) (0.005)(0.0224)

Observations 891,942 891,942 891,942 2,973,008 891,942

Fixed effects no 6,713 ﬁrms 6,713 ﬁrms no no

Source: Authors’ calculations using the United Kingdom Ofﬁce of National Statistics data. All statistical results remain

Crown Copyright.

Notes: In columns (1)–(3) and (5) the dependent variable is a dummy for whether a ﬁrm is vertically integrated in that

industry pair at any time over the years 1996–2001. In column (4) the dependent variable is whether or not the observations

are for a multiplant ﬁrm. Standard errors in parentheses are clustered at the level of 3,840 industry pairs. R&D intensity

is R&D carried out in the UK divided by value added produced in the UK, taken from plant level data, aggregated to the

two-/three-digit industry level and average over the years 1994–1995. Share of costs is from the 1995 Input–Output Table

and is at the industry pair level. In regression with interactions, all main effects are evaluated at sample means.

ijk

= αsc

+ (β

+ γ

)RD

+ (β

+ γ

)RD

+ X



ijk

η + ε

ijk

, (14)

with γ

and γ

as the additional coefﬁcients of interest. Theory suggests that γ

should have the same sign as β

, and that γ

should have the same sign as β

,so

that the effects of R&D intensity in producing and supplying industries should

be ampliﬁed when there is a greater share of costs. Throughout, when including

interaction terms, we report the main effects evaluated at the sample mean, so that

these estimates are comparable to those in the models without interaction effects.

The estimates in column (4) are consistent with the theoretical predictions.

The main effects are close to those in the previous columns, and the interaction

effects are large and statistically signiﬁcant: γ

is positive (1.112 with a standard

error of 0.402), while γ

is negative (−0.909 with a standard error of 0.353).

1010 Journal of the European Economic Association

Columns (5) and (6) add a number of characteristics at the ﬁrm-line of busi-

ness and industry level, namely ﬁrm size and age (in that line of business), and

average ﬁrm size and average ﬁrm age in producing and supplying industries. All

ﬁve coefﬁcients of interest are robust, and remain close to their baseline values

(the only minor exception is β

, which declines from 0.040 in column (3) to

0.030 in column (6)). The coefﬁcients on the controls are also interesting. They

indicate, for example, that larger and older ﬁrms are more likely to be vertically

integrated, which is plausible. Furthermore, greater average ﬁrm size in the pro-

ducing industry makes vertical integration more likely, while average ﬁrm size

in the supplying industry appears to reduce the probability of integration. This

opposite pattern of coefﬁcients, with ﬁrm size in the producing industry having a

positive effect, is also consistent with our conjecture that the relevant margin in

the data is backward integration.

Overall, the results in Table 2 show an interesting pattern of opposite-signed

effects from technology intensity in producing and supplying industries (which is

consistent with our ﬁrst empirical hypothesis in Section 2.3). They also show that

these effects are magniﬁed when the share of costs accounted for by the supplying

industry in the total costs of the producing industry is large (which is consistent

with our second empirical hypothesis). In addition, the direction of the effects is

also consistent with our measurement strategy and the theory provided that the

relevant margin in the data is backward vertical integration (our third empirical

hypothesis).

Before further investigating the robustness of our ﬁndings, it is useful to

discuss the economic magnitudes of the estimates in Table 2. The implied mag-

nitude of the main effects is very small. For example, the coefﬁcient of −0.013

in column (4) of Table 2 suggests that a one standard deviation (0.107) increase

in the R&D intensity of supplying industry reduces the probability of vertical

integration by slightly more than 0.1% (−0.013 × 0.107 ≈−0.001). However,

this small effect applies at the mean of the distribution of share of costs, which

is 0.010. If, instead, we evaluate the effect at the 90th percentile of the share of

cost distribution, which is about 0.20, then the overall effect is much larger; again

using the numbers from column (4), a one standard deviation increase in sup-

plier R&D intensity leads to almost a 2% decrease in the probability of vertical

integration (−0.001 +[−0.909 × 0.19 × 0.107]≈0.02). Similarly, the impact

of producer R&D intensity is small when evaluated at the mean, about 0.2%,

(0.037 × 0.055 ≈ 0.002), but sizable, 1.4%, when evaluated at higher levels of

share of costs (0.002 +[1.104 × 0.19 × 0.055]≈0.014).

This pattern is in fact quite sensible. For the vast majority of industry pairs,

the scale of the relationship between the producer and the supplier is so small

that it would be surprising if technology intensity were of any great importance

for integration decisions. Our theory should instead be relevant for industry pairs

where the scale of the relationship (as measured by the share of costs) is large,

Acemoglu et al. Vertical Integration 1011

and this is exactly where we see a signiﬁcant positive effect of the R&D intensity

of producing industries and a signiﬁcant negative effect of the R&D intensity of

supplying industries. This discussion also implies that the interaction effects are

as important as the main effects for the relevance of the pattern documented here.

4.2. Within-Firm Variation

A more demanding test of the relationship between technology intensity and

vertical integration is to investigate whether a particular ﬁrm is more likely to

be vertically integrated in producing industries that are more technologically

intensive and with supplying industries that are less technology intensive. This is

done by estimating a model including ﬁrm ﬁxed effects.

Naturally, this can only be investigated using multiplant ﬁrms, namely, those

that produce in more than one industry, which introduces a potential selection

bias. At some level, this is mechanical; vertically integrated ﬁrms have to be

multiplant ﬁrms. More generally, producer and supplier technology intensity may

affect the likelihood of being a multiplant ﬁrm differentially, and if so, regressions

on the subsample of multiplant ﬁrms may lead to biased estimates of the effect

of technology (R&D) intensity on vertical integration.

In Table 3, we investigate both the robustness of our results to the inclusion

of ﬁrm ﬁxed effects and potential selection issues.

Column (1) reports our basic speciﬁcation (without ﬁxed effects) on multi-

plant ﬁrms only. Comparing this to column (4) of Table 2, a number of features

are noteworthy. First, the number of observations is now 891,942 rather than

2,973,008 as in Table 2. Second, despite changes in coefﬁcient estimates, the

overall pattern is quite similar. In particular, there is a positive effect of producer

R&D intensity and a negative effect of supplier R&D intensity on vertical inte-

gration. Both these effects are larger than those in Table 2. The interaction effects

also have the expected signs. This pattern of results is reassuring, because it shows

that our main results in Table 2 were not driven by the contrast of single to multi-

plant ﬁrms. Within multiplant ﬁrms, those with greater producer R&D intensity

are also more likely to be vertically integrated, while those with greater supplier

R&D intensity are less likely to be vertically integrated.

Column (2) adds a full set of ﬁrm ﬁxed effects to the speciﬁcation in column

(1). This has surprisingly little effect on the results. The coefﬁcients on the share of

cost, the interaction between producer R&D intensity and share of cost, supplier

R&D intensity and the interaction between share of costs and supplier R&D

intensity, are essentially identical to those in column (1). The only change is in

the main effect of producer R&D intensity, which falls from 0.073 to 0.024 and

is no longer statistically signiﬁcant.

However, it is important to emphasize that even though producer R&D inten-

sity is insigniﬁcant when evaluated at the mean, the overall pattern is not very

1012 Journal of the European Economic Association

different; due to the signiﬁcant interaction effect, producing industries with sub-

stantial R&D intensity are much more likely to vertically integrate activities

that are important for their products. In fact, because the interaction effect is

larger than in Table 2, the effect of a one standard deviation increase in pro-

ducer R&D intensity on the probability of vertical integration for a pair at the

90th percentile of the share of costs distribution is now greater than in Table

2at3%(0.03 × 0.055 +[2.741 × 0.19 × 0.055]≈0.030), rather than 1.4%

when using the estimates from column (5) of Table 2. Similarly, now a one-

standard deviation increase in supplier R&D intensity has a larger effect, 5%

(−0.016 × 0.107 +[−2.482 × 0.19 × 0.107]≈0.052), rather than 2% when

using the estimate from column (5) of Table 2.

Column (3) repeats the model of column (2) including the full set of covari-

ates. The results are similar to those in column (2), except that the coefﬁcients on

the level of producer and supplier R&D decline.

These speciﬁcations do not deal with the potential selection problem. In

columns (4) and (5) we estimate a standard Heckman selection model. Column

(4) shows estimates from the probit model of the probability of a ﬁrm being a

multiproduct ﬁrm as a function of the full set of variables used to explain vertical

integration. Among the main variables of interest, only the R&D intensity of the

producing industry turns out to have an effect on the probability of a ﬁrm of

being multiproduct, whereas the share of costs, R&D intensity of the supplying

industry, and the interaction of producer and supplier R&D intensities with the

share of costs appear to have no inﬂuence on multiplant status. This implies that

the R&D intensity of the producing industry is most likely to suffer from a bias

due to endogenous selection (interestingly, this is the only coefﬁcient for which

the estimate changed substantially after the introduction of ﬁrm ﬁxed effects).

Column (5) shows the second stage of whether a ﬁrm is vertically integrated,

conditional on being a multiplant ﬁrm. The second-stage equation excludes the

ﬁrm and industry characteristics.

Given the pattern in column (4), it is not sur-

prising that the most remarkable change occurs in the main effect of the producer

R&D intensity which is now larger (0.030) and statistically signiﬁcant (standard

error 0.012). The main effect of the supplier R&D becomes smaller (in absolute

value), but remains highly signiﬁcant.

In summary, Table 3 subjects our basic speciﬁcation to a more demanding

test by including a full set of ﬁrm ﬁxed effects. These ﬁxed effects control for

various unobserved ﬁrm characteristics which may be potentially correlated with

the propensity to become integrated. These speciﬁcations still show a negative

effect of supplier R&D, and a positive (sometimes signiﬁcant, and sometimes

25. This implies that the selection results have to be interpreted with caution, because there are

various natural reasons for why ﬁrm and industry characteristics may need to be in the second

stage. Unfortunately, we do not have any natural exclusion restrictions that can be exploited in this

regression.

Acemoglu et al. Vertical Integration 1013

insigniﬁcant) effect of producer R&D. Most importantly, all of these speciﬁca-

tions show large, statistically signiﬁcant, and opposite-signed interaction effects

between producer and supplier R&D intensities and the share of costs.

4.3. An Instrumental Variables Strategy

So far, the results point to statistically signiﬁcant associations between vertical

integration and the technology intensity in the producing and supplying industries.

However, these associations do not necessarily correspond to the causal effects of

the technology intensity variables on vertical integration decisions. First, as high-

lighted by the theory, vertical integration also affects investment in technology, so

that there is scope for reverse causality. Second, there may be other variables that

are omitted from the regressions, which have a causal effect on both technology

intensity and vertical integration. This will mean that the error term is correlated

with the regressors and will lead to biased estimates of the coefﬁcients of interest.

To the extent that the omitted variables are at the ﬁrm level, this is controlled for

by the within-ﬁrm estimates shown herein, but there may still be omitted variables

at the ﬁrm–industry level affecting the estimates.

A more satisfactory approach would be to use an instrumental variable strat-

egy, with instruments that affect technology intensity, without inﬂuencing vertical

integration through other channels (i.e., they should be orthogonal to the error

term, ε

ijk

, in equations (13) and (14)). Although we do not have such perfect

instruments, measures of technology intensity in the same industry in the U.S. are

potential candidates. These instruments are useful in avoiding the potential reverse

causality problems and in removing the effect of UK-speciﬁc omitted variables,

although this procedure would not help with omitted industry-speciﬁc variables

that are common across the U.S. and the UK. Therefore, these results should not

necessarily be interpreted as causal estimates, but as estimates investigating a

different source of variation in the data.

Because we do not have U.S. data on R&D intensity at the same level of

disaggregation, we use the investment intensity of the corresponding supplying

and producing sector in the United States (at the same two-/three-digit industry)

as the instrument for R&D intensity. The ﬁrst-stage equations for the model in

equation (13) are

= π

+ Z



+ X



ijk

+ u

ijk

= π

+ Z



+ X



ijk

+ u

ijk

, (15)

where the Z

s is the vector of instruments for technology intensity in the supply-

ing and producing industries (in other words, investment intensity in the supplying

and producing industries in the U.S.), and π

and π

are vectors of parameters.

1014 Journal of the European Economic Association

Table 4. Instrumental variables.

Dependent variable: vi

ijk

(1) (2) (3) (4)

Share of costs (j k) 0.183 0.054 −0.085 0.210

(0.028)(0.069)(0.081)(0.134)

R&D intensity, 0.492 0.627 −1.025 0.418

producing (j ) (0.061)(0.077)(0.239)(0.246)

× Share of costs 9.832 29.763 22.288

(4.207)(6.773)(7.977)

R&D intensity, −0.158 −0.202 −0.497 −1.158

supplying (k) (0.

014)(0.031)(0.089)(0.198)

× Share of costs −7.519 −16.872 −8.561

(3.733)(4.884)(6.042)

First stage producing industry R&D intensity

U.S. producing industry 0.172 0.177 −0.059 −0.158

investment intensity (0.029)(0.029)(0.027)(0.017)

× Share of costs 0.786 0.506 0.333

(0.814)(0.580)(0.429)

U.S. supplying industry 0.011 0.009 −0.

007 −0.007

investment intensity (0.022)(0.022)(0.021)(0.013)

× Share of costs −1.121 −0.576 −0.363

(0.515)(0.365)(0.261)

F -stat p-value 0.000 0.000 0.091 0.000

0.007 0.007 0.175 0.487

First stage supplying industry R&D intensity

U.S. producing industry −0.028 −0.010 −0.033 −0.040

investment intensity (0.082)(0.081)(0.084)(0.083)

× Share of costs 4.272 3.812 4.207

(1.436)(1.034)(1.521)

U.S. supplying industry 0.366 0.356 0.093 0.063

investment intensity (0.060)(0.60)(0.056)(0.056)

× Share of costs −3.635 −3.

268 −3.254

(1.136)(1.046)(1.188)

F -stat (p-value) 0.000 0.000 0.015 0.029

0.024 0.024 0.069 0.065

Observations 2,973,008 2,973,008 2,973,008 891,942

Fixed effects no no no yes

covariates no no yes yes

Source: Authors’ calculations using the United Kingdom Ofﬁce of National Statistics data. All statistical results remain

Crown Copyright.

Notes: The dependent variable is a dummy for whether a ﬁrm is vertically integrated in that industry pair at any time

over the years 1996–2001. Standard errors in parentheses are clustered at the level of 3,840 industry pairs. Covariates

included in columns (3) and (4) are: producing ﬁrm size, age, mean ﬁrm size, and mean ﬁrm age in producing and

supplying industries. R&D intensity is R&D and investment carried out in the UK divided by value-added produced in the

UK, taken from plant level data, aggregated to the two-/three-digit industry level and average over the years 1994–1995.

Share of costs is from the 1995 Input–Output Table and is at the industry pair level. In regression with interactions, all

main effects evaluated at sample means. Instruments are investment intensity in the same industry in the U.S.

In column (1) of Table 4, we start with instrumental variables (IV) estimates

of equation (13). The top panel shows the second-stage results, and the lower

panels report the ﬁrst-stage coefﬁcients from equation (15) as well as the R

and the p-value of the F -statistics for the signiﬁcance of the instruments in the

ﬁrst stage. The ﬁrst-stage relationships are highly signiﬁcant, and show a very

Acemoglu et al. Vertical Integration 1015

appealing pattern: Producer investment technology intensity in the U.S. is corre-

lated with producer R&D intensity in the UK, but not with the supplier technology

intensity in the UK. The pattern is similar (i.e., the coefﬁcients are reversed) for

supplier technology intensity in the U.S. This gives us conﬁdence that the IV

estimates are capturing a useful source of variation.

The second stage estimates in column (1) are interesting: The producer R&D

intensity is positive and supplier R&D intensity is negative. Both estimates are

highly signiﬁcant and much larger than the OLS estimates. The larger IV esti-

mates for the main effects of the technology intensity variables likely reﬂects the

fact that the IV procedure is reducing the attenuation bias in the OLS estimates

resulting from classical measurement error. This type of attenuation bias might

be quite important here, because our measures of technology (R&D) intensity are

highly imperfect proxies for the importance of relationship-speciﬁc technology

investments. Another possible interpretation is that, consistent with the signiﬁ-

cant interactions between technology intensity and the share of costs, which show

heterogeneous effects conditional on observables, there are also heterogeneous

effects conditional on unobservables. In that case, because OLS and IV have

different weighting functions, it is natural that they will lead to different esti-

mates (see Angrist and Imbens 1995). In any case, we interpret these results as

supportive of the main prediction of our theory.

For the model in equation (14), we have four ﬁrst-stage equations, which are

= π

+ Z



+ (sc

· Z

)



+ X



ijk

+ u

ijk

· sc

= π

+ Z



+ (sc

· Z

)



+ X



ijk

+ u

ijk

= π

+ Z



+ (sc

· Z

)



+ X



ijk

+ u

ijk

· sc

= π

+ Z



+ (sc

· Z

)



+ X



ijk

+ u

ijk

where, for example, RD

·sc

is the interaction between producer R&D intensity

and share of cost, and (sc

· Z

)



denotes the interaction between the vector of

instruments and the share of cost.

In columns (2)–(4) of Table 4 we report IV estimates based on these (to save

space, in the bottom panel we report only the two ﬁrst-stage equations for the main

effects).

Whereas the instrumental variable strategy works reasonably well for

the main effects, instrumenting for the interaction effects is more challenging,

because instruments constructed by interacting the original instruments with the

share of costs are highly correlated with the instruments for the main effects. In

column (2), we report estimates where both main effects and interaction terms are

26. Given the size of the data set, all IV estimates are implemented using the “control function”

approach, which involves including the residuals from the ﬁrst stages as additional regressors in the

second stage (see, for example, Wooldridge 2002, chapter 18).

1016 Journal of the European Economic Association

instrumented. The main effect estimates are similar to those in column (1), but

the interaction estimates are quite large and imprecisely estimated (though still

statistically signiﬁcant). This reﬂects the difﬁculty of simultaneously instrument-

ing for main effects and interaction effects that are mechanically correlated.

column (3), we add our usual set of covariates to this speciﬁcation. Now the mul-

ticolinearity issue becomes worse and the main effect of producer R&D intensity

turns negative, and the interaction terms are even larger and more imprecisely

estimated. Finally, in column (4), we add ﬁxed effects. Interestingly, in this case,

the estimates are more similar to those in column (2).

Overall, the IV estimates using the U.S. values as instruments for UK producer

and supplier R&D intensity are mixed. When we only instrument the main effects,

the results conﬁrm the overall picture emerging from the OLS regressions. When

we also instrument the interaction terms, there is too much multicolinearity to

learn much from the estimates.

5. Robustness

In this section we consider a number of robustness checks. First, we investigate

whether the use of a linear probability model versus a probit model matters for

the results. Second, we report results using our alternative measure of technology

intensity, which uses information on physical investment. Finally, we consider a

number of other robustness checks. In Appendix B, we also check the robustness of

our main results in various subsamples and investigate the role of nonlinearities.

5.1. Probit Estimates versus Linear Probability Models

Tables 2–4 use linear probability models. These have a number of attractive fea-

tures, including being easier to interpret and estimate (for example, with large

samples and individual ﬁxed effects). Nevertheless, it is important to investi-

gate whether alternative estimation strategies lead to similar results. This issue is

addressed in Table 5.

27. As an additional experiment, we used only the control functions from the two levels equations,

which essentially amounts to only instrumenting for the main effects. This yields results that are

much more favorable to our hypothesis and similar to the OLS. For example, the coefﬁcient estimates

for the main effects and interactions of producer and supplier R&D in the equivalent speciﬁcation to

column (2) are, respectively, 0.509 (s.e = 0.061), 1.126 (s.e = 0.401), −0.164 (s.e = 0.015), and

−0.958 (s.e = 0.352).

28. We also investigated the stability of the basic relationship between technology intensity and

vertical integration over years, and the results are stable across years (details available upon request).

In addition, we estimated speciﬁcations controlling for the share of the output of the supplying

industry going to the producing industry in question. When entered by itself, this variable is signiﬁcant

with the expected sign, but when entered together with the share of cost, it is no longer signiﬁcant

and typically has the opposite of the sign predicted by our model (the results are available upon

request, and see also footnote 11).

Table 5. LPM and probit.

(1) (2) (3) (4) (5) (6) (7) (8) (9)

LPM PROBIT PROBIT LPM PROBIT PROBIT LPM PROBIT PROBIT

mean of mean of mean of

marginal marginal marginal marginal marginal marginal

Dependent variable: vi

ijk

effects

Share of costs (j k) 0.204 0.090 0.094 0.187 0.088 0.092 0.182 0.072 0.087

(0.029)(0.007) min 0.044 (0.028)(0.007) min 0.014 (0.027)(0.006) min 0.002

max 1.087 max 1.059 max 1.306

R&D intensity, 0.040 0.027 0.029 0.044 0.024 0.026 0.030 0.010 0.013

producing (j ) (0.005)(0.002) min 0.014 (0.005)(0.003) min 0.004 (0.005)(0.002) min 0.0003

max 0.331 max 0.293 max 0.188

× Share of costs 1.112 0.293 0.572 1.067 0.171 0.337

(0.402)(0.126) min 0.146 (0.374)(0.080) min 0.007

max 14.104 max 8.230

R&D intensity, −0.007 −0.009 −0.010 −0.013 −0.008 −0.009 −0.007 −0.001 −0.001

supplying (k) (0.001)(0.002) min −0.114 (0.003)(0.002) min −0 .101 (0.003)(0.002) min −0.011

max −0.005 max −0.001 max −0.00001

× Share of costs −0.909 −0.271 −0.384 −0.871 −0.140 −0.199

(0.353)(0.149) min −7.189 (0.324)(0.099) min −4.298

max 0.027 max −0.004

Covariates no no no no no no yes yes yes

Source: Authors’ calculations using the United Kingdom Ofﬁce of National Statistics data. All statistical results remain Crown Copyright. Notes: The dependent variable is a dummy for

whether a ﬁrm is vertically integrated in that industry pair at any time over the years 1996–2001. Standard errors in parentheses are clustered at the level of 3,840 industry pairs. Covariates

included in columns (7)–(9) are: producing ﬁrm size, age, mean ﬁrm size and mean ﬁrm age in producing and supplying industries. R&D intensity is R&D carried out in the UK divided

by value added produced in the UK, taken from plant level data, aggregated to the two-/three-digit industry level and average over the years 1994–1995. Share of costs is from the 1995

Input–Output Table and is at the industry pair level.

Evaluated at mean value of explanatory variables.

Calculated for each individual observation using Ai and Norton (2004) formula.

1017

1018 Journal of the European Economic Association

Speciﬁcally, Table 5 compares estimates from the linear probability model

and the probit model. Column (1) repeats column (3) from Table 2. Column (2)

reports marginal effects from a probit model evaluated at the mean value of all

right-hand side variables. Column (3) reports the mean, minimum, and maximum

values of the marginal effects (from the same probit model as in column (2)).

Columns (4)–(6) repeat this for the speciﬁcation shown in column (4) of Table

2 and columns (7)–(9) for the speciﬁcation shown in column (6) of Table 2. The

marginal effects of the interaction terms are calculated using the formula given

by Ai and Norton (2003).

These results show that, on the whole, our main results are not sensitive to

the choice of functional form. With probit, the main effect for producer R&D

intensity is somewhat smaller, but similar and statistically signiﬁcant (e.g., com-

pare column (2) to column (1)). For the interaction effects, the probit results are

substantially smaller when the marginal effects are evaluated at the mean. How-

ever, more interesting is the mean of the marginal effects, reported in columns

(6) and (9); here, the interaction effects are larger, though still smaller than the

linear probability models. These columns also show that the range of estimates

includes much larger interaction effects. Therefore, our interpretation of the some-

what smaller interaction effects in the probit estimation is that the nonlinearity

in the probit speciﬁcation is giving us information about a different part of the

distribution of heterogeneous effects.

Overall, despite some differences in magnitudes, these results are generally

supportive of the patterns shown in Tables 2–4.

5.2. Results with Investment Intensity

Our alternative measure of technology intensity uses information on physical

investments instead of R&D. Even though greater physical investment need not

be associated with more speciﬁc investments, we expect ﬁrms making more

investments overall to also undertake greater investments in technology and

relationship-speciﬁc assets. In this light, it would be reassuring if the results

were similar when using the investment intensity measure of technology.

Table 6 repeats the benchmark regressions of Table 2 using our alternative

measure of technology intensity. Overall, the results point to a similar pattern:

investment intensity in the producing industry is positively associated with ver-

tical integration, and investment intensity in the supplying industry is negatively

associated with integration. For example, column (3) shows a coefﬁcient of 0.030

(standard error = 0.006) on producer technology intensity, and the coefﬁcient

on supplier technology intensity is −0 .046 (standard error = 0.004).

The exception to this pattern is for producer investment intensity when the

full set of additional covariates are included. In this case producer technology

Acemoglu et al. Vertical Integration 1019

Table 6. Alternative technology measure—investment intensity.

(1) (2) (3) (4) (5) (6)

Dependent variable: vi

ijk

Share of costs (j k) 0.203 0.191 0.191 0.187

(0.028)(0.023)(0.023)(0.024)

Investment intensity, 0.027 0.030 0.038 0.021 −0.002

producing (j ) (0.007)(0.006)(0.006)(0.006)(0.008)

× Share of costs 1.488 1.471 1.402

(0.456)(0.460)(0.453)

Investment intensity, −0.050 −0.046 −0.055 −0.055

−0.041

supplying (k) (0.004)(0.004)(0.005)(0.005)(0.005)

× Share of costs −1.681 −1.666 −1.562

(0.490)(0.487)(0.489)

ln Firm size (ij) 0.0054 0.0052

(0.0002)(0.0002)

ln Firm age (ij) 0.0009 0.0008

(0.0001)(0.0001)

ln Average ﬁrm size, 0.0023

producing (j ) (0.0006)

ln Average ﬁrm size, −0.0024

supplying (k) (

0.0004)

ln Average ﬁrm age, 0.011

producing (j ) (0.003)

ln Average ﬁrm age, 0.004

supplying (k) (0.002)

Source: Authors’ calculations using the United Kingdom Ofﬁce of National Statistics data. All statistical results remain

Crown Copyright.

Notes: The dependent variable is a dummy for whether a ﬁrm is vertically integrated in that industry pair at any time

over the years 1996–2001. There are 2,973,008 observations at the ﬁrm–industry pair level. Standard errors in parentheses

are clustered at the level of 3,840 industry pairs. Investment intensity is investment carried out in the UK divided by value

added produced in the UK, taken from plant level investment data, aggregated to the two-/three-digit industry level and

average over the years 1994–1995. Share of costs is from the 1995 Input–Output Table and is at the industry pair level.

Firm size and ﬁrm age are measured at the ﬁrm–industry pair level in 1996 (age is equal to 1 if the ﬁrm enters that industry

pair after 1996). Average ﬁrm size and age are calculated from the ﬁrm–industry pair data and average over the years

1996–2001. In regression with interactions, all main effects are evaluated at sample means.

intensity is no longer statistically signiﬁcant. Nevertheless, there continues to

be a positive, signiﬁcant, and large effect of the interaction between producer

investment intensity and the share of costs. Consequently, producer technology

intensity has no effect on vertical integration when evaluated at the mean share of

cost, but has a substantial effect when the share of cost is large (e.g., at the 90th

percentile). Supplier technology intensity continues to be highly signiﬁcant, both

at the mean and for large shares of costs.

29. We also repeated our other robustness checks using investment intensity. The results are gener-

ally similar to those with R&D intensity. For example, with ﬁrm ﬁxed effects, producer investment

intensity loses signiﬁcance when we include ﬁxed effects, but once we control for selection as in

column (5) of Table 3, we recover an estimate very similar to that in Table 6. Similarly, instrumental

variable estimates show a similar pattern to those with R&D intensity. These results are available

upon request.

1020 Journal of the European Economic Association

5.3. Other Robustness Checks

The rest of the robustness checks are presented in the Appendix.

Appendix Table B.2 reports estimates from the speciﬁcation including all the

covariates as in column (6) of Table 2 for two subsamples (we do not report the

coefﬁcients on the covariates to save space). In the ﬁrst column, we show the

results excluding the bottom quartile of ﬁrms by size, in the second column we

exclude the top quartile by size. These models are useful to check whether our

results are driven by the comparison of large to small ﬁrms. The results hold up

in these subsamples.

In column (3), we use our alternative measure of vertical integration,

ijk

The results are very similar to those using the vertical integration dummy,

ijk

. In particular, producer R&D intensity has a positive and signiﬁcant effect

on vertical integration and supplier R&D intensity has a negative effect. The

interaction effects are signiﬁcant and have opposite signs as in our baseline

estimates.

Finally, Appendix Table B.3 considers potential nonlinearities. It reports

results with dummies for share of cost, and a producing (or supplying) industry

being at the second, third, or fourth quartile of the corresponding distribution (with

the ﬁrst quartile as the omitted group). The results show that there is generally

a monotonic pattern, consistent with the linear regressions reported in previous

tables, with the exception of the effect of R&D intensity in the supplying industry.

Here the second quartile has the largest negative effect, and the third quartile has

a small, and sometimes insigniﬁcant, sometimes positive effect. This nonlinear

pattern, for which we do not have a good explanation, is the reason why the differ-

ence in vertical integration by the R&D intensity of the suppliers was not visible

in the descriptive statistics in Table 1.

6. Outside Options and Competition

Finally, we now brieﬂy look at the fourth empirical hypothesis suggested by our

model, which concerns potential links between competition and vertical integra-

tion (recall Section 2.3). In Table 7, we brieﬂy investigate this relationship using

the number of ﬁrms in producing and supplying industries as our main indicator

of competition. The table shows that a greater number of ﬁrms in the producing

industry is associated with lower vertical integration, whereas a greater number

of ﬁrms in the supplying industry leads to more vertical integration. When we

include ﬁxed effects (columns (2) and (4)), the effect of the number of ﬁrms in

the producing industry is no longer signiﬁcant, but the effect of the number of

ﬁrms in the supplying industry remains signiﬁcant and of a similar magnitude to

the estimate without ﬁxed effects.

Acemoglu et al. Vertical Integration 1021

Table 7. Outside option.

(1) (2) (3) (4)

Technology measure = Technology measure =

Dependent variable: vi

ijk

R&D intensity Investment intensity

Share of costs (j k) 0.154 0.328 0.161 0.359

(0.027)(0.042)(0.024)(0.039)

technology, 0.029 0.010 −0 .002 −028

producing (j ) (0.005)(0.016)(0.007)(0.027)

× Share of costs 0.863 1.571 1.352 0.358

(0.338)(0.628)(0.440)(1.330)

technology, −0.004 −0.005 −0.031 −0.073

supplying (k) (0.003)(0.007)(0.005)(0.014)

× Share of costs −0.762 −1.313 −1.282 0.400

(0.287)(0.595)(0.475)(1.129)

ln Firm size (ij) 0.0052 0.0024 0.0052 0.0023

(0.0002)(0.0004)(0.0002)(0.0004)

ln Firm age (ij) 0.0009 0.0004 0.0009 0.0003

(0.0001)(0.0005)(0.

0001)(0.0005)

ln Average ﬁrm size, −0.0012 0.016 −0.0001 0.003

producing (j ) (0.0006)(0.002)(0.0006)(0.002)

ln Average ﬁrm size, −0.0022 −0.0018 0.0029 0.0008

supplying (k) (0.0004)(0.0010)(0.0005)(0.0011)

ln Average ﬁrm age, 0.010 −0.004 0.009 −0.004

producing (j ) (0.002)(0.009)(0.002)(0.009)

ln Average ﬁrm age, 0.

017 0.021 0.017 0.023

supplying (k) (0.002)(0.005)(0.002)(0.005)

ln number of ﬁrms, −0.0018 −0.0004 −0.0019 −0.0004

producing (j ) (0.0003)(0.0009)(0.0003)(−0.0009)

ln number of ﬁrms, 0.0055 0.019 0.0053 0.019

supplying (k) (0.0003)(0.002)(0.0003)(0.002)

Observations 2,973,008 891,942 2,973,008 891,942

Fixed effects no yes no yes

Source: Authors’ calculations using the United Kingdom Ofﬁce of National Statistics data. All statistical results remain

Crown Copyright.

Notes: The dependent variable is a dummy for whether a ﬁrm is vertically integrated in that industry pair at any

time over the years 1996–2001. Standard errors in parentheses are clustered at the level of 3,840 industry pairs. R&D

and investment intensity are R&D and investment in the UK divided by value added produced in the UK, taken from

plant level data, aggregated to the two-/three-digit industry level and average over the years 1994–1995. Share of

costs is from the 1995 Input–Output Table and is at the industry pair level. Firm size and ﬁrm age are measured at

the ﬁrm–industry pair level in 1996 (age is equal to 1 if the ﬁrm enters that industry pair after 1996). Average ﬁrm

size and age are averages over the years 1996–2001. In regression with interactions, all main effects are evaluated at

sample mean.

It is also noteworthy that the coefﬁcient on the number of ﬁrms in the supply-

ing industry is about four times the magnitude of the coefﬁcient for the number

of ﬁrms in the producing industry. Ignoring this difference in magnitude, for

which we do not have any good explanation, these results are consistent with the

theory, where we showed that as long as the relevant margin is backward inte-

gration, a greater θ , which increases the outside option of the supplier, should

make vertical integration less likely. A greater number of ﬁrms in the produc-

ing industry is likely to increase the supplier’s outside option, whereas more

1022 Journal of the European Economic Association

ﬁrms in the supplying industry should reduce it. This is the pattern we ﬁnd in

the data.

Interestingly, if we think of an increase in overall competition as correspond-

ing to a proportional increase in the number of producing and supplying ﬁrms,

since the coefﬁcient on the number of supplying ﬁrms is larger, our estimates sug-

gest that there should be an increase in vertical integration. Although this result is

not our main focus, it sheds some doubt on the popular claims that greater (global

or national) competition necessarily leads to less integrated ﬁrms.

7. Summary and Conclusions

Despite a number of well-established theories and a prominent public debate on

the effect of technology and technical change on the internal organization of the

ﬁrm, there is little evidence on the determinants of vertical integration. This paper

proposes a new approach to investigate the predictions of the PRT approach of

Grossman and Hart (1986) and Hart and Moore (1990). This approach relies on

comparing vertical integration patterns across pairs of industries (products). We

use data from the entire population of UK manufacturing plants, and document a

number of empirical regularities in the relationship between technology intensity

and vertical integration.

Our results show that vertical integration in a pair of industries is less likely

when the supplying industry is more technology intensive and the producing

industry is less technology intensive. Moreover, both these effects are larger when

inputs from the supplying industry constitute a large fraction of the total costs of

the producing industry. This pattern of opposite effects of technology intensity

of producing and supplying industries is consistent with the PRT approach. In

addition, the direction of these effects, for example, that vertical integration is

more likely when the producing industry is more technology intensive, and the

other patterns we document, are consistent with the theory, provided that the

relevant margin in the data is the choice between backward vertical integration

and non-integration.

We report similar results controlling for ﬁrm ﬁxed effects and instrument-

ing UK technology intensity measures with U.S. measures. We also show the

robustness of our results to a variety of other speciﬁcations.

Finally, we ﬁnd that vertical integration is more likely when the average

number of producing ﬁrms is greater relative to the average number of supplying

ﬁrms, which is also consistent with the theoretical predictions we derived from

30. We also experimented with Hirﬁndahl indices for producing and supplying industries. Although

the Hirﬁndahl indices were sometimes signiﬁcant, the results were not robust. The addition of the

Hirﬁndahl indices did not change the effects of the number of ﬁrms in the producing and supplying

industries on vertical integration, however. Also, these results are robust to using physical investments

instead of R&D as a measure of technology intensity.

Acemoglu et al. Vertical Integration 1023

a simple incomplete contracts model (and not entirely consistent with the claims

made in the popular press about the effect of competition on the structure of

ﬁrms).

The results in this paper provide a number of empirical patterns that may

be useful for theories of vertical integration to confront. Although our empirical

investigation is motivated by a speciﬁc theoretical approach (the PRT), the empiri-

cal patterns we document should be of more general interest and may be consistent

with various alternative theories. Nevertheless, the current versions of the most

popular alternative approaches are not easily reconciled with the ﬁndings. For

example, the emphasis of Williamson’s TCE approach that vertical integration

circumvents holdup problems would be consistent with the positive association

between vertical integration and producer technology intensity, but not with the

negative effect of supplier technology intensity. Theories based on supply assur-

ance (e.g., Green 1986; Bolton and Whinston 1993) could also account for part of

the results if more technology-intensive ﬁrms require more assurance. But these

theories do not provide an explanation for why greater technology intensity of

suppliers is associated with less vertical integration. Theories based on securing

intellectual property rights (e.g., Aghion and Tirole 1994b) could account for

both main effects of producer and supplier technology intensity, for example,

because creating a vertically integrated structure may provide better protection of

intellectual property rights. These theories would not explain why these effects

become stronger when the share of costs is high. A theoretical investigation of

various alternative explanations for these patterns, as well as further empirical

analysis of the robustness of these results with data from other countries, appear

to be interesting areas for future research.

Finally, as noted previously, we organized the data in this paper so as to mea-

sure the likelihood of a ﬁrm being integrated with one or multiple input suppliers.

This makes our measure of vertical integration conceptually similar to backward

vertical integration. In this light, the fact that our results are consistent with the

theory when the relevant choice is between backward vertical integration and

non-integration is reassuring. It would be interesting to construct empirical mea-

sures that are closer to forward vertical integration and investigate the empirical

determinants of backward and forward vertical integration simultaneously. We

believe that a more systematic investigation (and measurement) of joint determi-

nation of backward and forward integration, and how they interact with industry

structure, are promising areas for future research.

Appendix A: Proof of Proposition 1

Substituting the optimal investments given by equations (7), (8), and (9) into

equation (6), social surplus under the three organizational forms is obtained as

1024 Journal of the European Economic Association

VIB

= 1 +



1 −



= 1 +



1 −

2 − ϕ





1 −



(1 + θ)



1 −

1 + θ



, (A.1)

VIF

= 1 +





1 −





Let



≡ S

VIB

− S

= ϕ

/8 − (3 − θ − λ)(1 + θ − λ)ϕs

/8.

It is straightforward to verify that 

is increasing in p, decreasing in s, and



= 0 if and only if



(3 − θ − λ)(1 + θ − λ)/ϕ ≡¯r>0.

When p/s > ¯r, backward integration is preferred to non-integration. When p/s <

¯r, it is dominated by non-integration. Differentiation establishes that ∂ ¯r/∂ϕ < 0

and ∂ ¯r/∂θ > 0.

Similarly, let



≡ S

VIF

− S

=−((2 − λ



)

− ϕ

/8 + ϕ(1 − θ)

/8.



is decreasing in p and increasing in s. 

= 0 if and only if



ϕ(1 − θ)

(2 − λ



)

− ϕ

≡ r > 0.

When p/s < r

, forward integration is preferred to non-integration. In contrast,

when p/s > r

, non-integration is preferred. Again, differentiation establishes

that ∂r

/∂ϕ > 0 and ∂r/∂θ < 0.

First, suppose that r

< ¯r. Then, the analysis so far establishes that the

equilibrium organizational form is given by

∗

⎧

⎪

⎨

⎪

⎩

VIB if

≥¯r,

NI if

∈ (r, ¯r),

VIF if

≤ r.

The set of parameters such that r

< ¯r is non-empty. For instance, as θ → 1

we have that r

→ 0, whereas ¯r → (2 − λ)/

√

ϕ>0.

Next, suppose that r

≥¯r. Then NI is always dominated by either VIF and

VIB. Let



≡ S

VIB

− S

VIF

= (2 − λ



)

/8 − ϕ(2 − λ)

/8.

Acemoglu et al. Vertical Integration 1025



is increasing in p and decreasing in s, and also 

= 0 if and only if

2 − λ



√

ϕ ≡ˆr.

When p/s > ˆr, backward integration is preferred to forward integration, and

when p/s < ˆr, forward integration is preferred. Differentiation establishes that

∂ ˆr/∂ϕ > 0 and ∂ ˆr/∂θ = 0. This completes the proof of the proposition.

Appendix B: Data Sources and Construction

Our main source of data is the plant level production data underlying the UK

Census of Production (ARD). This is collected by the UK Ofﬁce of National

Statistics (ONS) and ﬁrms have a legal obligation to reply. We use the data on all

manufacturing plants from 1996–2001, along with information from the Input–

Output Domestic Use Table for 1995, to measure vertical integration and other

ﬁrm characteristics. We use data from the ARD from 1992–1995 to measure a

number of other industry characteristics and data from the annual Business Enter-

prise Researcher and Development (BERD) survey from 1994–1995 to measure

R&D expenditure at the industry level. U.S. variables are measured using the U.S.

Census data at the four-digit level (available on the NBER Web site). The UK

and U.S. data are matched based on a mapping of UK SIC92 to US SIC87 and

then aggregated up to input–output industry level. See Acemoglu et al. (2004) for

further discussion of the data.

B.1. The Plant-Level Production Data

The ARD contains information on all production activity located in the UK. The

basic unit for which information on inputs and output is reported is a reporting

unit. A reporting unit can be a single plant or a group of plants owned by the same

ﬁrm operating in the same four-digit industry. Information on the location and

number of employees is available on all plants (called local units) within each

reporting unit. There are over 150,000 reporting units in manufacturing industries

with non-zero employment in the ARD each year, 1996–2000. Detailed data are

collected from a random stratiﬁed sample.

Data on value added and costs for

non-sampled reporting units are imputed.

Single plant ﬁrms are identiﬁed as those reporting units which represent only

one plant and which have no sibling, parent, or child plants. Single plants with

31. The sampling probabilities vary over time, with industry and with reporting unit size. Reporting

units with 100 or more employees are always sampled. Below that, the sampling probabilities range

from1in5to1in2.

1026 Journal of the European Economic Association

fewer than 20 employees are dropped from the analysis, resulting in between

100,000 and 130,000 reporting units being dropped per year. In addition 1,000–

2,000 reporting units per year that are owned by foreign ﬁrms, are dropped, as

we do not observe their foreign activities.

Plants in the ARD in these years are classiﬁed by their major product accord-

ing to the 1992 revision of the four-digit standard industrial classiﬁcation (SIC

code). Input–Output (IO) tables are reported at the two-/three-digit level. Where

more than one reporting unit exists within an IO industry these are aggregated so

that there is only one observation per ﬁrm in each IO industry. The total number

of ﬁrms used (after dropping the small and single and foreign owned ﬁrms and

averaging over years) is 46,392. We measure ﬁrm age in each producing industry

as the number of years since the ﬁrst plant in that industry was established. We

measure ﬁrm size in each industry by the number of employees it has in that

industry. The average number of ﬁrms in an industry is measured from the ARD.

Table 1 (in the main text) shows means for these variables.

B.2. The Input–Output Table

We use the Input–Output Table for 1995.

The Input–Output Table contains

information on 77 manufacturing industries (supplying and producing). There

are 5,929 pairs of producing–supplying industries, for which 3,840 the Input–

Output Table indicates positive trade ﬂows. For each industry pair we calculate

the proportion of total costs (including intermediate, labor, and capital) of pro-

ducing j that are made up of input k, denoted w

. In 2,766, or just under half

of industry pairs, at least one ﬁrm is vertically integrated to some extent. Table

B.1 contains descriptive statistics on the share of output from each supplying

industry that is sold for intermediate consumption, to all industries and to man-

ufacturing industries, and shows the largest purchasing industry along with the

share of sales this purchaser represents (which ranges from 0.5% to over 50% and

averages 3.7%) and the share of the purchaser’s total costs this input represents

(which ranges from zero to 37% and averages 2.7%).

B.3. Technology Indicators

Our measures of technology intensity are all at the industry level. R&D intensity

is measured using the micro data underlying the annual BERD matched to the

ARD. The micro data is aggregated to the industry level using the product code

for which the R&D was targeted. This is scaled by total value-added in ﬁrms

producing in the industry (including both R&D and non-R&D ﬁrms).

32. This is available at www.statistics.gov.uk.

Table B.1. Summary of Input–Output Table statistics.

% of total

supplying % of total

% sales for intermediate industry sales purchasing industry

consumption going to this purchases coming

Supplying industry all industries manufacturing Largest purchasing industry purchaser from this supplier

8 Meat processing 0.441 0.250 29 Leather goods 0.019 0.502

9 Fish and fruit processing 0.461 0.195 9 Fish and fruit processing 0.085 0.141

10 Oils and fats 0.694 0.534 10 Oils and fats processing 0.161 0.208

11 Dairy products 0.403 0.183 11 Dairy products 0.109 0.143

12 Grain milling and starch 0.666 0.580 14 Bread, biscuits, etc. 0.192 0.191

13 Animal feed 0.751 0.020 8 Meat processing 0.017 0.009

14 Bread, biscuits, etc. 0.433 0.009 14 Bread, biscuits, etc. 0.001 0.002

15 Sugar 0.817 0.639 16 Confectionery 0.217 0.153

16 Confectionery 0.380 0.160 16 Confectionery 0.097 0.176

17 Other food products 0.332 0.137 17 Other food products 0.043 0.075

18 Alcoholic beverages 0.100 0.070 18 Alcoholic beverages 0.065 0.127

19 Soft drinks and mineral waters 0.192 0.003 19 Soft drinks & mineral waters 0.003 0.005

20 Tobacco products 0.001 0.001 20 Tobacco products 0.001 0.001

21 Textile ﬁbres 0.681 0.646 27 Knitted goods 0.189 0.269

22 Textile weaving 0.274 0.261 28 Wearing apparel & fur products 0.158 0.092

23 Textile ﬁnishing 0.976 0.415 23 Textile ﬁnishing 0.053 0.129

24 Made-up textiles 0.193 0.052 24 Made-up textiles 0.010 0.026

25 Carpets and rugs 0.356 0.115 25 Carpets and rugs 0.004 0.009

26 Other textiles 0.513 0.427 28 Wearing apparel & fur products 0.203 0.109

27 Knitted goods 0.030 0.019 28 Wearing apparel & fur products 0.013 0.013

28 Wearing apparel and fur products 0.099 0.018 28 Wearing apparel & fur products 0.017 0.048

29 Leather goods 0.312 0.078 30 Footwear 0.042 0.076

30 Footwear 0.219 0.065 30 Footwear 0.064 0.177

31 Wood and wood products 0.894 0.519 31 Wood and wood products 0.203 0.395

32 Pulp paper and paperboard 0.672 0.559 33 Paper and paperboard products 0.243 0.285

33 Paper and paperboard products 0.885 0.520 33 Paper and paperboard products 0.055 0.133

34 Printing and publishing 0.613 0.211 34 Printing and publishing 0.132 0.334

(continued)

1027

Table B.1. (Continued).

% of total

supplying % of total

% sales for intermediate industry sales purchasing industry

consumption going to this purchases coming

Supplying industry all industries manufacturing Largest purchasing industry purchaser from this supplier

35 Coke ovens, reﬁned petroleum, & nuclear 0.450 0.108 38 Organic chemicals 0.013 0.093

36 Industrial gases and dyes 0.535 0.459 19 Soft drinks & mineral waters 0.089 0.120

37 Inorganic chemicals 0.676 0.603 37 Inorganic chemicals 0.043 0.111

38 Organic chemicals 0.056 0.052 41 Pesticides 0.005 0.051

39 Fertilisers 0.839 0.154 39 Fertilisers 0.146 0.273

40 Plastics & synthetic resins, etc. 0.599 0.557 48 Plastic products 0.249 0.209

41 Pesticides 0.508 0.006 41 Pesticides 0.001 0.005

42 Paints, varnishes, printing, ink, etc. 0.692 0.477 42 Paints, varnishes, printing, ink, etc. 0.054 0.107

43 Pharmaceuticals 0.380 0.125 43 Pharmaceuticals 0.094 0.206

44 Soap and toilet preparations 0.229 0.105 44 Soap and toilet preparations 0.085 0.146

45 Other chemical products 0.185 0.116 45 Other chemical products 0.033 0.085

46 Man-made ﬁbres 0.273 0.259 21 Textile ﬁbres 0.058 0.100

47 Rubber products 0.552 0.243 47 Rubber products 0.041 0.102

48 Plastic products 0.759 0.405 48 Plastic products 0.081 0.179

49 Glass and glass products 0.775 0.549 49 Glass and glass products 0.133 0.276

50 Ceramic goods 0.402 0.125 50 Ceramic goods 0.046 0.113

51 Structural clay products 0.723 0.003 51 Structural clay products 0.001 0.004

52 Cement lime and plaster 0.882 0.336 53 Articles of concrete stone, etc. 0.286 0.136

53 Articles of concrete stone, etc. 0.851 0.024 53 Articles of concrete stone, etc. 0.022 0.044

54 Iron and steel 0.596 0.561 54 Iron and steel 0.138 0.253

55 Non-ferrous metals 0.658 0.611 55 Non-ferrous metals 0.218 0.450

56 Metal castings 0.973 0.790 62 Mechanical power equipment 0.175 0.107

57 Structural metal products 0.472 0.115 57 Structural metal products 0.025 0.050

58 Metal boilers and radiators 0.348 0.158 58 Metal boilers & radiators 0.084 0.174

59 Metal, forging, pressing, etc. 0.964 0.864 80 Aircraft and spacecraft 0.077 0.212

(continued)

1028

Table B.1. (Continued).

% of total

supplying % of total

% sales for intermediate industry sales purchasing industry

consumption going to this purchases coming

Supplying industry all industries manufacturing Largest purchasing industry purchaser from this supplier

60 Cutlery, tools, etc. 0.545 0.453 60 Cutlery, tools, etc. 0.024 0.063

61 Other metal products 0.690 0.563 71 Insulated wire and cable 0.014 0.114

62 Mechanical power equipment 0.285 0.210 62 Mechanical power equipment 0.055 0.125

63 General purpose machinery 0.202 0.110 63 General purpose machinery 0.020 0.042

64 Agricultural machinery 0.132 0.009 64 Agricultural machinery 0.006 0.015

65 Machine tools 0.181 0.133 65 Machine tools 0.011 0.023

66 Special purpose machinery 0.293 0.246 66 Special purpose machinery 0.046 0.102

67 Weapons and ammunition 0.554 0.170 67 Weapons and ammunition 0.154 0.336

68 Domestic appliances nec 0.187 0.019 68 Domestic appliances nec 0.007 0.014

69 Ofﬁce machinery & computers 0.060 0.049 69 Ofﬁce machinery & computers 0.035 0.094

70 Electric motors and generators, etc. 0.390 0.301 70 Electric motors and generators, etc. 0.072 0.165

71 Insulated wire and cable 0.550 0.304 71 Insulated wire and cable 0.031 0.073

72 Electrical equipment nec 0.491 0.388 74 Transmitters for TV, radio, and phone 0.112 0.274

73 Electronic components 0.126 0.115 69 Ofﬁce machinery & computers 0.048 0.052

74 Transmitters for TV, radio, and phone 0.204 0.020 74 Transmitters for TV, radio, and phone 0.014 0.032

75 Receivers for TV and radio 0.134 0.091 75 Receivers for TV and radio 0.055 0.126

76 Medical and precision instruments 0.360 0.129 76 Medical and precision instruments 0.036 0.090

77 Motor vehicles 0.200 0.112 64 Agricultural machinery 0.005 0.200

78 Shipbuilding and repair 0.536 0.061 78 Shipbuilding and repair 0.061 0.142

79 Other transport equipment 0.275 0.154 79 Other transport equipment 0.152 0.305

80 Aircraft and spacecraft 0.107 0.011 80 Aircraft and spacecraft 0.011 0.029

81 Furniture 0.233 0.077 81 Furniture 0.053 0.114

82 Jewelry and related products 0.020 0.017 82 Jewelry & related products 0.016 0.044

83 Sports goods and toys 0.014 0.001 12 Grain milling and starch 0.001 0.001

84 Miscellaneous manufacturing nec & recycl 0.543 0.406 56 Metal castings 0.034 0.117

Source: UK ONS, 1995 Input–Output Tables.

1029

1030 Journal of the European Economic Association

Table B.2. Robustness checks.

(1) (2) (3)

Dependent variable: exclude bottom quartiles exclude top quartiles of dependent variable:

ijk

of ﬁrms by size ﬁrms by size vi

ijk

Share of costs (j k) 0.201 0.103 0.114

(0.030)(0.021)(0.016)

R&D intensity, 0.030 0.014 0.022

producing (j ) (0.006)(0.003)(0.004)

× Share of costs 1.146 0.477 0.554

(0.389)(0.254)(0.224)

R&D intensity, −0.0074 −0.005 −0.004

supplying (k) (0.0038)(0.002)(0.002)

× Share of costs −0.953 −0.474

−0.413

(0.352)(0.211)(0.199)

Observations 2,249,095 2,234,459 2,973,008

Covariates yes yes yes

Source: Authors’ calculations using the UK ONS data. All statistical results remain Crown Copyright.

Notes: The dependent variable is a dummy for whether a ﬁrm is vertically integrated in that industry pair at any time

over the years 1996–2001. Standard errors in parentheses are clustered at the industry pair level. R&D intensity is R&D

carried out in the UK divided by value added produced in the UK, taken from plant level data, aggregated to the two-

/three-digit industry level and average over the years 1994–1995. Share of costs is from the 1995 Input–Output Table and

is at the industry pair level. In regression with interactions, all main effects evaluated at sample means. Covariates in all

speciﬁcations include: ﬁrm size and age, producing and supplying industry, average size, and average age.

Table B.3. Nonlinearities.

Dependent variable: vi

ijk

(1) (2) (3) (4)

Share of cost:

2nd quartile 0.0027 0.0024

(0.0004)(0.0004)

3rd quartile 0.0092 0.0081

(0.0007)(0.0006)

4th quartile 0.0186 0.0176

(0.0011)(0.0011)

Producing industry R&D intensity:

quartile 0.0036 0.0034 0.0015

(0.0010)(0.0009)(0.0008)

quartile 0.0050 0.0040 0.0028

(0.0010)(0.0009)(0.0008)

quartile 0.0057 0.0049 0.0029

(0.0010)(0.0008)(0.0009)

Supplying industry R&D intensity:

quartile −0.0080 −0.0062 −0.0049

(0.0014)(0.0011)(0.0010)

quartile −0.0039 −0.0019 0.0002

(0.0014)(0.0012)(0.0011)

quartile −0.0043 −0.0040 −0.0008

(0.0014)(0.0012)(0.0012)

Covariates no no no yes

Source: Authors’ calculations using the United Kingdom Ofﬁce of National Statistics data. All statistical results remain

Crown Copyright.

Notes: The dependent variable is a dummy for whether a ﬁrm is vertically integrated in that industry pair at any time

over the years 1996–2001. There are 2,973,008 observations at the ﬁrm–industry pair level. Standard errors in parentheses

are clustered at the level indicated. R&D intensity is R&D carried out in the UK divided by value added produced in the

UK, taken from plant level data, aggregated to the two-/three-digit industry level and average over the years 1994–1995.

Share of costs is from the 1995 Input–Output Table and is at the industry pair level. Covariates included where indicated

are: producing ﬁrm size, age, mean ﬁrm size, and mean ﬁrm age in producing and supplying industries. The reference

group is zero share of costs and bottom quartiles of R&D intensity in producing and supplying industries.

Acemoglu et al. Vertical Integration 1031

The ratio of physical investment (capital expenditure on machinery, buildings,

land and vehicles) to value added is constructed in a similar manner from the ARD

data at the industry level and averaged over the years 1992–1995.

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