The duration of research joint ventures:

theory and evidence from the Eureka program

<this version: June 23, 2011>

Kaz Miyagiwa* and Aminata Sissoko**

Abstract: Research joint ventures (RJVs) provide governments with detailed information, including durations, to be exempted from antitrust investigation. Our theoretical analysis shows that such pre-commitment to durations can stabilize RJVs, and predicts that RJVs going after higher-valued innovation cooperate for longer durations. We test this hypothesis, using data from the European Eureka program. Applying proportional hazard models and using RJV costs as a proxy for unobservable innovation values, we find strong support for the hypothesis. We also find that RJVs with more partners tend to cooperate longer, while firm-initiated RJVs cooperate for shorter durations than non-firm initiated RJVs. JEL Classification Codes: L1, L2 Keywords: Research joint ventures, Duration, Monitoring, Cooperation, Innovation, Eureka projects

Corresponding author: Kaz Miyagiwa, Department of Economics, Emory University, Atlanta, GA 30322, U.S.A.; E-mail: kmiyagi@emory.edu; Telephone: 404-727-6363; Fax: 404-727-4639 We thank Muriel Dejemeppe, Laura Rovegno, Ilke Van Beveren, Hylke Vandenbussche, Linke Zhu, and seminar participants at Zhejian University for helpful comments. Errors are the authors’ responsibility.

* Emory University, U.S. A. and Kobe and Osaka Universities, Japan **Universite catholique de Louvain, Belgium

1. Introduction

A research joint venture (RJV) is an agreement whereby its members coordinate research

activities in order to share the innovation derived from the joint research efforts. The literature

has identified several incentives to form RJVs, including avoidance of costly duplications of

efforts (Katz 1986) and internalization of technical spillovers (d’Aspremont and Jacquemin

1988, Kamien, Muller and Zang 1992). It is also known that RJVs can solve the appropriability

problem. Since innovations eventually spill over to the rivals, an innovative firm fails to

appropriate the full value of innovation, making R&D privately unprofitable in extremely cases.

An RJV eliminates such problems by having the R&D costs shared by the eventual beneficiaries

of the innovation (Miyagiwa and Ohno 2002; Erkal and Piccinin 2010). However, innovation

sharing can make RJVs unstable if it intensifies product market competition ex post (Martin

1998, Lambertini, Podder and Sasaki 2002, and Miyagiwa 2009).

If the RJV partners cannot observe one another’s R&D efforts, however, innovation

sharing can give rise to the free-rider problem and may end up destabilizing the RJV. The first

part of this paper, drawing on the recent work of Miyagiwa (2011), shows that the RJV partners

can resolve this type of free-rider problem by pre-announcing when to dissolve the RJV. We

further show that there is an optimal dissolution date, i.e., the optimal duration for an RJV, and

that the latter is positively related to the value of the innovation.

The theoretical model, however, takes for granted the partners’ ability to commit to

dissolution of the RJV at a pre-announced date. However, such pre-commitment may lack

credibility since, if there is no innovation by that date, the partners have no incentive to dissolve

the RJV, given that cooperation is desirable in the first place. But without credible pre-

commitment, the RJV is plagued by the destabilizing free-rider problem.

In reality, however, this free-rider problem may inadvertently be resolved thanks to

antitrust laws and regulations designed to ensure that cooperation in R&D does not result in

collusion in market places. For example, the U.S. Department of Commerce requires an

applicant to supply on its application form detailed information about the RJV, including its

duration, so as to have its joint R&D activities exempted from antitrust investigations. Our

theory implies that such government requirements make dissolution of the RJV credible, thereby

helping firms launch joint R&D projects they would not otherwise be able to undertake.

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In the second half of this paper we empirically investigate the factors determining the ex

ante durations of RJVs using data from the European Eureka program. The Eureka program was

launched in 1985 as part of the EU innovation policy designed to promote joint research projects

for commercial innovation through private and public support.1 The Eureka program provides an

ideal environment for empirically testing our theory for two reasons. First, as part of

requirements for receiving financial support, each Eureka RJV must include partners from at

least two different European countries – a requirement that can give rise to the monitoring

problem since partners conduct research in labs in separate countries. Second, the Eureka

program requires an applicant to pre-announce the duration of the RJV.

Our main hypothesis from our theoretical part is that an RJV going after a higher-valued

innovation can cooperate for a longer duration, other things being equal.2 We test this hypothesis

by applying Weibull proportional hazard models to the Eureka data, and find strong support for

it. We also uncover a host of other factors affecting RJV durations; namely, the RJV duration

increases with the number of its partners, firm-initiated RJVs have shorter durations than those

initiated by research-centers and universities, and single-sector RJVs have shorter durations than

multi-sector RJVs. For robustness checks of these results we use the Cox and exponential

proportional hazard models as well as the stratified and the fraility Weibull model, obtaining

results similar to those from the basic Weibull models.

The remainder of the paper is organized as follows. Sections 2 – 4 present a theoretical

model in which partners of an RJV determine the ex ante duration to resolve the monitoring

problem. Section 5 discusses the Eureka data more in details. Section 6 explains the

methodology of our empirical study. Section 7, our main section, presents the estimation results

from the Weibull models, whereas their robustness is checked in section 8. The final section

concludes.

2. Research joint ventures

Suppose that m (≥ 2) symmetric firms engaged in R&D activities over an infinite number

of periods. All actions take place at the beginning of the periods, which are called dates and 1 R&D subsidies are provided not by the EU but by its member governments in the form of partial public support or interest-free loans. Partial support can reach 50% of the private expenditures of the RJVs. The loans need not be repaid if the RJVs fail (excepting those from France). 2 Henceforth, the term duration means ex ante or pre-announced duration, unless otherwise noted.

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enumerated by t = 1, 2, … At each date, each firm decides whether to invest in R&D. Investment

requires a fixed sum k per period and yields innovation with probability (1 – q) where q ∈(0, 1)

denotes probability of failure. If firms are in competitive R&D mode, each firm faces the

expected payoff v ≥ 0. Given the stationary environment of the model, v is time-invariant.

Suppose that at date 1 firms form an RJV whereby they agree to share innovation,

regardless of who actually discovers it. Assume, in line with the literature investigating similar

issues (e.g., Kamien, Muller and Zang 1992, Miyagiwa and Ohno 2002, Erkal and Piccinin

2010), that firms maintain independent research labs and conduct R&D independently – the

condition to be satisfied in our empirical analysis. Assume that each firm can dissolve the RJV at

any date t (or more precisely at t + ε, where ε is an arbitrarily small positive number). If they do

dissolve the RJV, firms go separate ways at t + 1 but must still share the innovation discovered

as a result of joint R&D conducted at date t.3

For the remainder of this section, assume that firms can observe one another’s R&D

activity and that they play the following grim trigger strategy: at date 1, invest in R&D and agree

to share the innovation; at any date t ≥ 2, do the same as long as all firms have invested in R&D

and agreed to share the innovation up to date t – 1; otherwise, switch to competitive R&D mode

forever.

If all firms adopt the above strategy, at each t there is innovation with (conditional)

probability (1 – qm) and no innovation with probability qm. With innovation each firm receives

the value Π and the game ends, whereas without innovation firms face exactly the same situation

at date t + 1 as they did at date t due to the stationary environment. Thus, if we let V denote the

expected equilibrium payoff, V satisfies this recursive structure:

V = – k + (1 – qm)δΠ + δqmV.

where δ ∈(0, 1) is the discount factor. Collect terms to obtain

V = [- k + (1 – qm)δΠ]/(1 - δqm).

Assume that formation of the RJV is worthwhile, i.e, .V > v.

Consider next a (one-period) deviation from the above strategy. A deviating firm saves

the R&D cost k but increases the joint probability of failure from qm to qm-1. Furthermore, if 3 This simply prevents an innovator from dissolving the RJV in order to monopolize the innovation.

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there is no innovation, all firms switch to competitive R&D mode, where the expected payoff is

v < V. Thus, a deviation yields the payoff

Vd = (1 – qm-1)δΠ + δqm-1v.

The RJV is stable if and only if

V – Vd = - k + δqm-1(1 – q)(Π - V) + δqm-1(V –v) ≥ 0.

3. RJVs with unobservable R&D efforts

Now assume that firms cannot observe each other’s R&D effort. If all firms exert efforts,

the expected profit per firm equals V as in the previous section. However, with unobservable

R&D efforts, the inherently uncertain nature of research makes it impossible to disentangle

failures due to the exogenous causes from those due to the lack of effort. If shirking goes

undetected and hence unpunished, then shirking reduces the probability of innovation without

causing a switch to competitive R&D mode. Thus, the payoff from shirking is given by

(1) Wd = (1 – qm-1)δΠ + δqm-1V.

Calculation shows that

V – Wd = – k + qm-1(1 – q)δ(Π – V).

The second term on the right is positive since V contains Π with positive probability. However, a

sufficiently large k can make V – Wd negative so the RJV cannot be maintained. We focus on

such cases. Thus,

Assumption 1: V < Wd.

4. Duration of the RJV

In this section we show that under assumption 1 firms may still be able to form an RJV

for a finite number of periods. To show it, begin with a one-period RJV; that is, firms agree to

share innovation if it is discovered only in date 1 and otherwise switch forever to competitive

mode. If all firms make efforts at t = 1, the payoff to each is

R(1) = - k + (1 – qm)δΠ + qmδv

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since firms switch to competitive model at t = 2. A firm that shirks saves k and lowers the

probability of innovation, yielding the expected payoff

Rd(1) = (1 – qm-1)δΠ + qm-1δv.

The one-period RJV is stable if

R(1) – Rd(1) = qm-1(1 - q)δ(Π – v) – k ≥ 0.

Since V > v, we can use (1) to rewrite Rd(1) as

Rd(1) = Wd + δq(v – V) < Wd,

implying that

R(1) – Rd(1) > V – Wd.

Thus, although V – Wd < 0 by assumption 1, it is possible that R(1) – Rd(1) ≥ 0.

Result 1: Since V > v, there is a k satisfying

qm-1(1 - q)δ(Π – v) ≥ k > qm-1(1 – q)δ(Π – V)

which implies that

R(1) – Rd(1) ≥ 0 > V – Wd.

Supposing that R(1) – Rd(1) > 0, proceed to consider whether a two-period RJV is stable.

If firms agree to such an arrangement, then the expected profit at date 1 is

R(2) = - k + (1 – qm)δΠ + qmδR(1).

In general, the expected profit from forming an n-period RJV can be written

R(n) = - k + (1 – qm)δΠ + qmδR(n – 1),

a first-order difference equation with the solution

R(n) = (v – V)(qmδ)n + V.

The fact that V > v and qmδ < 0 implies that R(n) is monotone increasing in n. As n goes to

infinity, R(n) approaches V, since the deadline set at an infinity is equivalent to no deadline at

all.

The payoff from deviating is

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Rd(n) = (1 – qm-1)δΠ + qm-1δR(n – 1)

which can be written, using the definition of Wd, as

(2) Rd(n) = Wd – δqm-1(V – R(n – 1)),

As n goes to infinity, the second term on the right of (2) goes to zero so Rd(n) approaches Wd.

Therefore, as n goes to infinity, R(n) – Rd(n) goes to V – Wd < 0. We have established the

following.

Result 2: If the conditions of result 1 holds, there exists a unique integer n* ≥ 1 such that

(3) R(n* + 1) – Rd(n* + 1) < 0 ≤ R(n*) – Rd(n*).

This result says that firms can form a stable RJV at most for the first n* periods. Further, since

R(n) is increasing, R(n*) is the maximal expected payoff; that is, n* is the optimal duration of

the RJV.

A calculation shows that

R(n) – Rd(n) = qm-1(1 - q)δ(Π – R(n – 1)) – k.

Suppose that Π increases. Then, the gap Π - R(n) widens since R(n) contains Π with positive

probability, increasing R(n) – Rd(n). Then, (3) implies that the optimal duration n* of the RJV

tends to increase with Π. This is formally stated in

Proposition. The higher the value of innovation per partner, the longer the optimal duration of

the RJV.

The optimal duration of an RJV also depends on the number of partners involved. Given

the total value of innovation, an increase in the number of partners reduces the value of

innovation per partner while increasing the joint probability of innovation for the RJV. These

conflicting effects make the net effect of the number of RJV partners on the duration ambiguous

in general. Therefore, we let the data determine the sign of this effect in our empirical analysis.

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5. Descriptions of data from the Eureka program

We now turn to an empirical investigation of the factors determining the duration of

RJVs using data from the European Eureka program. As already mentioned, the Eureka program

was created in 1985 to promote joint research projects in Europe. From 1985 through 2004,

8,520 organizations from 38 countries participated in the program, launching the total of 1,716

RJVs.4 Among participants, 4,698 were European firms, 1,937 were European universities,

research centers and national institutes, and the rest participated from outside the EU-15 member

countries. The majority of the RJVs were in manufacture, although some were in agribusiness

and services sectors.

More detailed information is available on the Eureka program’s website, including each

Eureka RJV’s initiation year, duration, costs, types of industries involved as well as the names,

addresses and nationalities of all its partners.5 Available also are the identities and nationalities

of RJV initiators. We thus know what type of organization – firm, research center or university –

initiated each RJV and from which sector or sectors (as defined by two-digit NACE categories)

each organization came.6

Table 1 shows the descriptive statistics of the 1,716 RJVs. Time is measured in months.

According to table 1, the average Eureka RJV comprises 5 partners, of which 3 are firms, and

costs 30,000 euros a month per partner.7 The average duration is 41.3 months.8 Note that the

durations in our data are taken from the applications submitted to the Eureka program so they are

not the actual durations but the pre-committed or ex ante durations. The significance of the RJV

initiator and the multi-sector RJV dummy will be discussed in section 7.

[Table 1 about here]

6. Methodology

4 A description of the RJV characteristics is reported in Table A1 in the appendix. 5 www.eurekanetwork.org. 6 NACE is the European economic activities classification system, similar to the American SIC system. The NACE classification is available from the EUROSTAT website: http://ec.europa.eu/eurostat/ramon. 7 Our data contains exceptional cases. The most costly Eureka RJV spent 4 billion € in R&D, involved 19 partners and had a duration of 96 months. The largest Eureka RJV had 196 partners, spent 796 000 € and had a duration also of 96 months. The results in section 7 are not affected by those extreme cases. 8 See Benfratello and Sembenelli (2001) and Alonso and Marin (2004).

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The durations in our data set show sufficient variations among the Eureka RJVs. If the

durations were optimally chosen as implied in our theory, their variations should reflect the

RJVs’ underlying characteristics. In the remainder of the paper we empirically investigate what

characteristics of the Eureka RJVs determine their durations.

A straightforward econometric analysis would involve OLS regressions. However, our

testing shows that the residuals of the OLS regressions are not distributed normally for the

Eureka data.9 For this reason, we conduct our econometric investigation through survival or

duration analysis, where ‘death’ of RJVs is considered an event.10 More specifically, in our

analysis we use proportional hazard models, the essential assumption of which is that the hazard

hj(t), or conditional probability of death, of individual RJVs j is split into two parts as in

hj(t)= h0(t) exp(xj βx).

The first part, h0(t), is the baseline hazard, i.e., the common hazard faced by all Eureka RJVs,

whereas the exponential part captures the idiosyncratic characteristics of individual RJVs j,

where xj represents the row vector of all explanatory variables for RJV j and βx is the column

vector of the coefficients of the explanatory variables. The proportional hazard function thus

assumes that at each t RJV j’s hazard function is a constant proportion of the baseline hazard;

that is, each individual RJV’s hazard is “parallel” to h0(t).

The Cox proportional hazard model is the most general proportional hazard model, as it

imposes no specific functional form (parameterization) on the baseline hazard h0(t). By contrast,

if a reason exists to assume that the baseline hazard follows a particular form, the Cox model can

be further specified. The belief that the baseline hazard follows a Weibull distribution gives the

Weibull model, which allows the baseline hazard to be increasing, decreasing or to remain

constant over time. More specifically, in the Weibull model the baseline hazard h0(t) takes the

form ptp-1exp (β0), where p is the ancillary parameter determining the shape of the hazard rate.

When p is above (below) one, the hazard rate is increasing (decreasing), whereas when p equals

9 The Jacque-Bera normality test performed on the error terms in OLS residuals is rejected for our Eureka data. It is found that the error terms of the regression on the log of RJV durations follows the type 1 extreme value (EV1) distribution, 10 Survival analysis is applied in biometrics to explain the survival of cancer patients, for example. It is also used in economics, where it is often called duration analysis, to study, for example, adoption of antidumping in international trade, firm exit behavior in industrial economics, and entry decisions of the unemployed in labor economics.

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one, the hazard rate remains constant so the Weibull model becomes an exponential proportional

hazard model.11 The Weibull model is more restrictive but more efficient than the Cox model.

In our case, there is evidence that the baseline hazard is increasing, i.e., the mortality rate

of the RJVs is increasing over time (Kogut, 1989). For this reason we use the Weibull model as

our main empirical model and utilize other models for robustness checks.

7. Results

Table 2 summarizes the regression results based on the Weibull model. Following the

standard procedure in duration analysis, we express the estimates in terms of the hazard ratios

instead of the coefficients. The hazard ratio captures the effect of a unit change in the

explanatory variable on the hazard of an event. As an illustration, suppose that the proportional

hazard takes the form hj(t) = h0(t) exp(β1 x1 + β2 x2), where x1 is a binary variable (dummy) and

x2 is a continuous variable. Then the hazard ratio of the dummy is defined as the hazard rate

when it takes the value one over the hazard rate when it takes the value zero, and hence equals

exp(β1). Similarly, the hazard ratio of the continuous variable represents the effect of a unit

change in value of the continuous variable and equals exp(β2).12

[Table 2 about here]

Each row in table 2 displays the hazard ratio of the corresponding explanatory variables.

The null hypothesis is that the hazard ratio of the explanatory variable equals one. This is

equivalent to the coefficient of the explanatory variable being equal to 0, implying that the

variable has no effect on death of RJVs. By contrast, if the hazard ratio is less than (greater than)

one, it is concluded that the explanatory variable delays (speeds up) death. For instance, if the

hazard ratio of a continuous explanatory variable is 0.9, a unit increase in value of this

explanatory variable decreases the mortality rate by 10%.

11 The exponential model is also known as the classic Poisson model. 12 Supposing that x2 is incremented by 1, the hazard ratio is given by the ratio h0(t) exp(β1 x1 + β2 (x2 +1)) over the ‘initial’ hazard rate h0(t) exp(β1 x1 + β2 x2 ), which equals exp(β2).

10

Turning to the selection of the explanatory variables, we know from the proposition in

section 4 that the value of innovation per partner is a key determinant of the duration of an RJV.

Unfortunately, however, the innovation values are not available on the Eureka website, so we use

proxies. Our main proxy is the RJV cost variable, which is defined as RJV cost per partner per

month. This is based on the notion that an RJV going for a high-valued innovation is willing to

spend more and hence should be associated with a high flow R&D cost. Thus, we expect higher-

cost RJVs to have longer durations or hazard ratios less than one.

We test this conjecture in five Weibull specifications and report the results in columns 1

through 5 in table 2. The conjecture is confirmed in all five cases, as the hazard ratio of the RJV

cost is clearly less than one. In particular, column 5, our preferred specification, suggests that a

unit increase in the flow RJV cost increases an RJV duration by 45.5%.13

Our theory also indicates that the number of partners can affect the duration of RJVs.

However, as mentioned earlier, an increase in the number of partners can increase the probability

of innovation but also reduces the value of innovation per partner, making the net effect

ambiguous a priori. Thus, we let it be determined by the data.

Table 2 shows that the number of RJV partners has hazard ratios less than one, implying

that RJVs with a greater number of partners have longer durations. This result is also significant

and robust across columns. More specifically, our results show that adding another partner to an

RJV delays its death by 4.2 percent.

The explanatory variables also include a number of dummy variables. The firm RJV

initiator dummy takes the value one if the RJV is initiated by a firm and the value zero if it is

initiated by a research center or a university. The RJV multi-sector dummy takes the value one

when the RJV draws partners from more than one sector and zero otherwise.14 The initiation-

year dummies are intended to reflect the general economic environments prevailing at the time

when RJVs were launched; that is, the ups and downs of the economy as well as diverse laws

and policies in effect when the RJVs are initiated. Lastly, the main industry dummies capture the

heterogeneity in characteristics of the main industry in which the RJV belongs.

Our results show the importance of the identity of RJV initiator dummy. Specifically, the

mortality rate is 15.3% higher when an RJV is initiated by a firm rather than by a research center 13 The RJV cost variable is in million euros. 14 The definitions of the multi-sector and multi-industry variables are taken from Bernard et al. (2010).

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or a university. This may have the following explanation. Since universities and research centers

are generally less concerned about the immediate payoffs of innovations, they are more likely to

pursue more fundamental innovations higher in scientific values rather than in commercial

values. In contrast, firm-initiated RJVs are more profit-driven and hence face severer free-rider

problems, the overcoming of which leads to a shorter duration as implied by our theory.

Table 2 also shows the importance of the initiation-year dummies in the significance of

the RJV initiator variable. This may reflect the effect of the general economic outlook prevailing

during the initiation years. When the future economic outlook is bad, lower expected innovation

values drive firm-initiated RJVs to agree to shorter durations according to the proposition,

making them more distinct from non-firm-initiated RJVs, which are less affected by the bad

economic outlook. In contrast, when the outlook is good, firm-initiated RJVs can agree to longer

durations, thereby blurring the distinction from non-firm-initiated RJVs. These interpretations

are consistent with our main hypothesis that higher innovation values result in longer durations.

The multi-sector dummy has hazard ratios less than one in columns 4 and 5, implying

that multi-sector RJVs have longer durations than single-sector RJVs. This may be explained as

follows. Since partners of a multi-sector RJV are less likely to compete with each other in the

same or similar products markets, they are likely to face higher innovation values per partner,

given the total innovation value. They may also enjoy the additional benefit through cross-

sectoral spillovers from innovations. If so, our results give indirect support for our main

hypothesis that higher-value innovations result in longer RJV durations, although this variable is

significant only in column 4.

8. Robustness

The results obtained in section 7 are based on the Weibull model, where it is assumed

that all Eureka RJVs have a common baseline hazard. In this section we check the robustness of

the Weibull model, in particular, the results of model 5, which we call our basic Weibull model,

with those obtained under alternative model specifications. The results are presented in columns

6 through 10 of table 3, where column 5 from table 2 is repeated to facilitate comparisons.

[Table 3 about here]

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Our first robustness check concerns the assumption of a Weibull distribution for the

baseline hazard. An alternative is to use the Cox model, which requires no specific functional

form for the baseline hazard. The estimation results are reported in column 6 of table 3.15 A

comparison shows a remarkable similarity of results between columns 5 and 6, confirming the

robustness of our basic Weibull model. Furthermore, this similarity demonstrates that the

Weibull model with an increasing baseline function is an appropriate choice.

We next turn to the assumption of a common baseline hazard faced by all the Eureka

RJVs in the basic Weibull model. To check the robustness of this assumption we appeal to the

stratified Weibull model. To apply the latter, we first classify all the Eureka RJVs in our data set

into three groups or strata. Stratum 1 comprises all the small RJVs, having 2 to 4 partners, which

make up 64.0 percent of all the Eureka RJVs in our data set. Stratum 2 includes all the medium-

sized RJVs, having 5 to 8 partners, and making up 27.3 percent of the Eureka RJVs, whereas

stratum 3 contains all the large RJVs, having 9 to 196 partners, which make up only 8.7 percent

of the total RJV in our data.

The results from the stratified Weibull model are reported in column 7. The ancillary

shape p parameter in column 7 corresponds to that of the small RJVs in stratum 1. This estimate

is significant and close to that of the basic (unstratified) Weibull model in column 5. Column 7

also displays the p parameter estimates for the medium-sized and the large RJVs, relative to that

of the small RJVs. The results shows that the ancillary shape p parameter of the large RJVs in

stratum 3 is significantly different from that of small RJVs in stratum 1 at a five percent level,

but indicate no significant difference between small and medium-sized RJVs. These findings

lead us to estimate a baseline hazard for each stratum as follows:

h0(t)= exp(-13.030) (2.974)t j1.974 (stratum 1: small RJVs) 16

h0(t)= exp(-14.029) (2.974)t j1.974 (stratum 2: medium-sized RJVs) 17

h0(t)= exp(-13.030) (2.542) tj 1.544 (stratum 3: large RJVs) 18

15 If the Cox model fits the data, the Cox-Snell residuals form a 45-degree line. The goodness of fit of our Cox model is demonstrated in figure A2 of the appendix, where it is seen that the empirical Nelson-Cumulative hazard function (a proxy for the Cox-Snell residuals) closely follows the 45-degree line. For more details, see Cleves et al. (2010). 16 The hazard ratio of the constant in column 7 of table 3 is exp(–13.030) ≈ 0.010. 17 exp(–13.030 – 0.999) = exp(–14.029) where – 0.999 is the coefficient of the medium-sized RJV dummy.

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These equations show that the baseline hazard functions of strata 1 and 3 are not proportional to

each other whereas the baseline hazard functions of strata 1 and 2 are proportional. In fact, the

hazard increases less for large RJVs than for small ones; see figure A1 in the appendix.19

Nonetheless, there is a striking similarity between the results in columns 5 and 7, confirming the

robustness of our basic (unstratified) Weibull model.

Next, since our data do not capture every characteristic of Eureka RJVs, it is possible that

any two RJVs appearing completely identical on the data have different durations due to some

unobserved heterogeneity. To check this possibility, we have computed the conditional

probabilities of RJV death from our sample population of 1,716 RJVs, and displayed the results

in figure 1, where each period corresponds to a two-year interval. They are essentially a non-

parametric approximation of the baseline hazard of the population. In contrast to a monotonic

baseline hazard associated with the basic Weibull model, the population hazard in figure 1

exhibits non-monotonicity, implying the possibility that RJVs with shorter and longer durations

may face different baseline hazards (Cleves et al., 2010).

[Figure 1 about here]

To address this issue we turn to a frailty Weibull model.20 A frailty Weibull model

modifies the basic Weibull model from column 5 by assuming that the baseline hazard takes the

form Zh0(t), where Z is the multiplicative random variable capturing unobserved individual

characteristics. The estimates from the frailty model are reported in column 8 in table 3. The

closeness of the results in columns 5 and 8 lends support to our basic Weibull specification.

As a final robustness check, we examine how well an alternative exponential proportional

hazard model can explain our results. In an exponential proportional model, a baseline hazard is

assumed constant over time, and hence time cannot affect the mortality rates of RJVs. The

results from this model are presented in column 9. Again, the results are qualitatively the same as

18 The ancillary shape parameter p is equal to exp(1.090 – 0.157) = 2.542, where – 0.157 is the coefficient of the p of the large RJVs (stratum 3). 19 The qualitative results of the stratified Weibull remain unaffected when we remove RJVs with more than 80 partners. 20 The frailty model in duration analysis can be compared to the panel data model with random effects

14

those yielded by the basic Weilbull model. The closeness of results between the exponential and

the Weibull model dispels the possibility that the results from the Weibull model are driven by

time.

9. Concluding remarks

In this paper we investigate the factors determining the durations of RJVs using data from

the European Eureka program. RJVs are inherently unstable when partners cannot monitor each

other’s R&D effort. The monitoring problem can be acute for Eureka RJVs because they are

made up of partners from different nationalities, who conduct research in labs in separate

countries. Our theoretical model shows that in such circumstances pre-commitment to durations

of cooperation, as required for Eureka projects, can have a stabilizing effect for RJVs, yielding

the testable hypothesis that RJVs going for high valued innovations tend to choose longer

durations, other things being equal. In our empirical analysis, we test that hypothesis and also

explore other determinants of durations, using proportional hazard models. In particular, we use

the Weibull model as the basic model specification, and check the robustness of its results under

alternative model specifications, including the Cox model and the stratified as well as the frailty

Weibull model.

Using the RJV cost per partner as the proxy for unobservable innovation values, we find

strong support for the hypothesis that higher innovations values per partner per time increase the

durations of Eureka RJVs. This result is significant and robust across different model

specifications. Another determinant of RJV durations that we find significant and robust across

model specifications is the number of RJV partners. Although our theoretical model yields

ambiguous predictions about this effect due to the two opposite sub-effects, our empirical

analysis shows that RJVs having a larger number of partners choose longer durations.

We also examine the effect of who initiates RJVs and what sector or sectors host RJVs. It

is found that RJVs initiated by firms tend to have shorter durations than those initiated by

universities and research centers. Since firm-initiated RJVs are more likely to be driven by

innovations values tha non-firm-initiated ones, our result is consistent with our theory’s

implication that profit-driven RJVs are more sensitive to monitoring issues and hence cannot

afford longer durations. Further, this result is significant especially when the initiation year

15

dummies are included as the explanatory variables. One possible explanation is that innovation

values may depend on prevailing economic conditions and future economic outlooks of the

initiation year.

The results concerning the multi-sector dummies reveal that multi-sector RJVs tend to

choose longer durations than single-sector RJVs. Since multi-sector RJVs are more likely to face

higher innovations values than single-sector RJVs due to softer competition among participants,

the result is consistent with our main prediction that higher innovation values result in longer

RJV durations.

16

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18

Tables and Figures

Table 1: Characteristics of all Eureka RJVs Obs Mean Std. Dev. Min Max RJV duration (months) 1716 41.32 20 6 168 RJV cost (Million €/month) 1716 0.03 0.1 0.0002 2.78 Number of partners 1716 5.14 8 2 196 Number of partner firms 1716 3.36 4 0 96 Firm-initiated RJV 1716 0.79 0.4 Multi-sector RJV 1716 0.69 0.5

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Table 2: The durations of Eureka RJVs

Weibull model 1 2 3 4 5 RJV cost 0.560*** 0.712** 0.640** 0.640** 0.545*** (0.099) (0.124) (0.130) (0.125) (0.114) Firm RJV initiator 1.072 1.178** 1.053 1.153** (0.086) (0.082) (0.081) (0.077) Multi-sector RJV 1.010 1.001 0.855** 0.915 (0.066) (0.058) (0.057) (0.055) Number of partners 0.946*** 0.960*** 0.946*** 0.958*** (0.012) (0.001) (0.012) (0.001)

Initiation year dummies NO NO YES NO YES Main industry dummies NO NO NO YES YES Shape parameter p 2.162*** 2.293*** 2.820*** 2.402*** 2.931*** (0.052) (0.054) (0.021) (0.054) (0.056) Observations 1716 1716 1716 1716 1716

Note. Table 2 summarizes the regressions results of the Weibull proportional hazard models. Robust standard errors are in brackets. *** denotes significance at the 1 percent level, ** at the 5 percent level and * at the 10 percent level. The ancillary parameter p of the Weibull model is reported with the robust standard errors.

20

Table 3: Robustness

5 6 7 8 9 RJV cost 0.545*** 0.570*** 0.584*** 0.442** 0.793*** (0.114) (0.103) (0.199) (0.147) (0.063) Firm RJV initiator 1.153** 1.130** 1.076 1.193** 1.064** (0.077) (0.065) (0.065) (0.100) (0.025) Multi-sector RJV 0.915 0.934 0.925 0.922 0.977 (0.055) (0.051) (0.060) (0.071) (0.021) Number of partners 0.958*** 0.967*** 0.954*** 0.989*** (0.001) (0.009) (0.013) (0.003) Large RJV dummy 0.368 (0.480)

Medium RJV dummy 2.416** (0.585) Constant 0.010*** (-0.001)

Initiation year dummies YES YES YES YES Main industry dummies YES YES YES YES Shape parameter p 2.931*** 2.974*** 3.652*** (0.056) (0.022) (0.130)

p of large RJV group 1.713** (0.040) p of medium RJV group 0.855 (0.054) Observations 1716 1716 1716 1716 1716

Note. Table 3 summarizes the regressions results from the Cox model (column 6), the stratified Weibull model (column 7), the frailty Weibull model (column 8), and the exponential model (column 9). Column 5 is reproduced from table 2. Robust standard errors are in brackets. *** denotes significance at the one percent level, ** at the five percent level and * at the ten percent level.

21

Figure 1: Conditional mortality rates of the Eureka RJVs population over time

Note: Each interval corresponds to two years.

0

20

40

60

1 2 3 4 5 6Prob

abilityofd

eath(%

) DeathoftheEurekaRJVsover;me

22

Appendix

Table A1: Description of RJV characteristics

Variables Description RJV Duration Pre-determined duration, in months

RJV cost Total cost of the Eureka RJV divided by the number of partners and months of duration.

The RJV total cost includes subsidies. Number of firms Number of firms in the Eureka RJV Number of RJV partners Number of firms, research centers, universities and national institutions forming Eureka RJV Firm RJV initiator Dummy variable equal to one if the first partner that starts to build the research is a firm Multi-sector RJV Dummy variable equals to 1 if the Eureka RJV involves more than one two-digit NACE category RJV initiation year Year in which the Eureka RJV starts RJV main sector Main two-digit NACE category of the Eureka RJV

Source: Eureka database built from the Eureka website (www.eurekanetwork.org).

Table A2: Correlation matrix for the all Eureka RJVs

RJV duration RJV cost Firm RJV

initiator Multi-sector

RJV Number of partners

RJV duration 1 RJV cost 0.087 1 Firm RJV initiator -0.087 0.061 1 Multi-sector RJV 0.012 0.019 -0.085 1 Number of

partners 0.302 0.083 -0.160 0.041 1

Note: The matrix displays correlations for the 1716 Eureka RJVs (1985-2004).

23

Figure A1: Baseline hazard rates for small and medium-sized RJVs and large RJVs

Note: Figure A1 shows the baseline hazard rates for the small RJVs (2 to 4 partners) and for the large RJVs (more than 8 partners). The baseline hazards are estimated from the results in column 7 of table 3.

Figure A2: Fit goodness of the Cox model

Note: Figure A2 displays the Cox-Snell residuals and the Nelson-Aalen cumulative hazard confirming the goodness of fit of the Cox proportional hazard model in column 6 of table 3.