# R&D investment, patent life and patent value: An econometric analysis at the firm level

Emmanuel Duguet, Nicolas Iung

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Emmanuel Duguet, Nicolas Iung. R&D investment, patent life and patent value: An econometric analysis at the firm level. 1997. halshs-05101978

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CAHIERS ECO & MATHS

97.36

R & D INVESTMENT, PATENT LIFE AND PATENT VALUE
AN ECONOMETRIC ANALYSIS AT THE FIRM LEVEL

Emmanuel DUGUET

Nicolas IUNG

CEME
R&D investment, patent life
and patent value

An econometric analysis at the firm level

Emmanuel DUGUET*

Nicolas IUNG**

Avril 1997

We thank the participants at the Econometric Society European Meeting (Istambul, August 1996), at the 54th Association d'Econométrie Appliquée Workshop on «Innovation Econometrics» (Luxembourg, November 1996) and at the DMSE seminar for helpful suggestions and comments.

<footnote>* Université de Paris I-Panthéon-Sorbonne, Centre d'Économie Mathématique et d'Économétrie et CREST, Laboratoire d'Économie Industrielle.</footnote>

<footnote>** INSEE, Département des Études Économiques d'Ensemble.</footnote>
Résumé

De nombreuses études sur les performances à l'innovation sont basées sur la relation entre le nombre de brevets et les investissement en recherche et développement (Griliches, 1990). Cet article explore la question de la validité du nombre de brevet comme mesure de l'innovation. Les travaux antérieurs de Pakes et Schankerman (1986) suggèrent plutôt d'utiliser les données de renouvellement de brevet pour estimer la valeur des brevets. Nous étendons leur travail dans deux directions : d'une part, l'approche de Pakes et Schankerman est macroéconomique, aussi examinons nous la valeur et la durée de vie des brevets au niveaux sectoriel et de l'entreprise. D'autre part, nous étudions les relations entre la durée de vie des brevets, l'investissement en recherche et la structure de marché pour proposer une réponse à des questions plus traditionnelles : Quelle-est la valeur des brevets dans l'industrie manufacturière française? Croît-elle avec l'intensité de recherche? il y a t-il un effet de la taille? Un pouvoir de marché plus élevé incite-t-il les entreprises à maintenir leurs brevets plus longtemps? Quel-sont les effets de l'imitation des produits? Cette étude tient également compte du fait que les brevets peuvent avoir été déposés en commun et s'ils sont domestiques ou internationaux. Nous trouvons que les conditions sectorielles d'appropriabilité ont un effet important sur la valeur et la durée de vie des brevets.

**Mots-Clef** : appropriabilité, valeur des brevets, durée de vie des brevets, annuités, recherche et développement, structure de marché, modèles de durée, vraisemblance partielle de Cox.

**Classement J.E.L.** : L10, L60, 031, 034.

Abstract

Numerous papers on innovation output are based on the patent-R&D relationship (Griliches, 1990). This paper incidentally questions wether the number of patents is a good measure of innovation. Previous works by Pakes and Schankerman (1986) rather suggested to estimate the value of patents from the patent renewal data. We extend their work in two directions. First, the approach by Pakes and Schankerman is macroeconomic, thus we explore this field at the sectoral and firm levels. Second, we study the relationship between patent life, research and market structure variables in order to answer more traditional questions : What is the value of patents in French manufacturing? Does it increase with R&D intensity? Is there a size effect? Does market power entice firms to keep their patents in force longer? What are the effects of product imitation? This study also accounts for differences in the patent types, such as joint patenting and wether these patents are domestic or international. We find that appropriability conditions play a key role in explaining patent life and value.

**Keywords** : appropriability, patent value, patent life, renewal fees, research and development, market structure, duration models, Cox partial likelihood.

**JEL Classification** : L10, L60, 031, 034.
# 1. Introduction

Numerous papers on innovation output are based on the patent-R&D relationship (Griliches, 1990). This paper incidentally questions whether the number of patents is a good measure of innovation. Previous work by Pakes and Schankerman (1986) rather suggested to estimate the value of patents from the patent renewal data. We extend their work in two directions. First, the approach by Pakes and Schankerman is macroeconomic, thus we explore this field at the sectoral and firm levels. Second, we study the relationship between patent life, research and market structure variables in French manufacturing. We show that in fact firms rarely use the whole legal length of patent.

The origin of these decisions to shorten the patent life is studied at the patent level and at the firm level. The explanatory variables include measures of size, R&D, appropriability, diversification and market power. We also distinguish joint patents from the other patents in order to examine whether technical cooperation is associated to different patenting strategies or not. We first estimate structural models, then a semi parametric reduced form one which needs much less statistical assumptions.

The following section presents the estimation of Pakes and Shankerman model and its estimates at the macroeconomic and industry level. The data are presented in section 3. Then, we estimate the firm level models in the fourth section. The conclusions are given in the last section with some comments.

# 2. The patent renewal model

Following Pakes and Shankerman<fnref n="1" /> (1986), we assume that, before applying for patents, firms evaluate the benefits from patent protection. We denote $R_{j0}$ the initial return on a patented innovation with application date j. This initial return is supposed to decrease geometrically with time. Thus, the return on a patent aged t applied for on year j is given by :

<footnote n="1">¹ Pakes (1986) also developed another model in which holding a patent is considered as equivalent to holding an option on the revenues stemming from patenting.</footnote>
$$R_{jt} = R_{j0} \prod_{\tau=1}^{t} (1 - \delta_{j\tau})$$

where $R_{jt}$ is the revenue generated by a patent application from year j after t years of protection and $\delta_{j\tau}$ represents both the annual dissipation rate of the monopoly rent, that depends on the effectiveness of patent protection, and the obsolescence of knowledge embedded in the patent. A strong assumption of the model is that these returns are known at the date of the application.

The decreasing profile of these returns has several origins. On the one hand, it reflects the increasing obsolescence of inventions as new discoveries are made. On the other hand, competitors will try to imitate this innovation or to develop their own innovations from the knowledge provided by the patent disclosure, so that the monopoly power of the initial inventor decays as time passes by<fnref n="2" />.

In order to keep their patent rights, firms have to pay annuities denoted $C_{jt}$ that depends on both the application year j and the age of the patent t. Hence, the firms faces a trade-off between the cost and benefits from patenting. We assume that they maximize the present value of the benefit flow up to the date T at which the patent cancels. The program is :

$$\max_{T} V(T) \text{ with } V(T) = \sum_{t=1}^{T} (1+r)^{-t} (R_{jt} - C_{jt})$$

where r is the actualization rate of the firm and T is the patent length bounded by the law. For patents granted in France, T has to be lower or equal to 20 years. Since the returns $R_{jt}$ are decreasing and the annuities $C_{jt}$ are increasing, firms will pay the annuities until :

$$R_{jt} \geq C_{jt} \Leftrightarrow R_{j0} \geq C_{jt} \prod_{\tau=1}^{t} (1 - \delta_{j\tau})^{-1} \quad (1)$$

They stop paying the annuities on the first year for which this condition does not hold. If it always hold, the patent life will reach its statutory limit equal to 20 years. Modeling patent life this way reduces to model the initial returns and the rent dissipation rate since the annuities are given.

<footnote n="2">² It remains that other assumptions also make sense like a first increasing then decreasing return, recalling the product life cycle.</footnote>
Following the basic model, we account for heterogeneity in the patents initial returns. We assume that these returns are distributed according to a law with c.d.f. F(q) and p.d.f. f(q) where q is a parameter possibly depending on patent, firm or industry characteristics. In a first step, we will assume that the dissipation rates are identical across all patent. This assumption will be relaxed when we work at the industry and firm levels.

Due to data limitations, Pakes and Shankerman estimated aggregated models by patent cohorts. The parameter of their model depends on the year of application and GNP. As a matter of comparison we will first re-estimate their model with European patents data, which is the exact aggregation of the firm-level sample we use. Then, we will estimate the corresponding sectoral model.

For the firm-level study, the SIREN code<fnref n="3" /> allows us for matching our data sets, so that we are able to cross it with research and development and accounting firm-level data. We also include sectoral innovation indicators, representing the product imitation rate, demand pull and technology push, computed from the Innovation survey.

## 2.1 The aggregated structural model

In this approach, patents are grouped by cohort that is by year of application. It is also possible to separate each cohort by sector in order to compare the returns and depreciation rates. For a given cohort j, say, the proportion of patents still holding at age t according to equation (1) is given by $S_{jt}$:

$$S_{jt} = 1 - F[C_{jt} \prod_{\tau=1}^{t} (1 - \delta_{j\tau})^{-1}]$$

To estimate the model, we have to assume a specific form for F. In order to compare our results with previous studies we choose the log-normal distribution of initial returns. Thus:

$$r_{j0} = \ln R_{j0} \sim N(\mu_j, \sigma_j^2)$$

<footnote n="3">³ The SIREN code is a firm identification used by firms for all their relationships with administrations. Thus, nearly all the firm-level data sets in France can be matched easily. European patents were an exception but a data specific work was undertaken at INSEE by J.-C. Bussy, C. Carpentier and I. Kabla (1996) so that it is now “sirenised”.</footnote>
which gives us the theoretical proportion of surviving patents from cohort j at time t :

$$S_{jt} = 1 - \Phi \left[ \frac{c_{jt} - \mu_j - \sum_{\tau=1}^{t} \ln(1 - \delta_{\tau j})}{\sigma_j} \right]$$

where $c_{jt}=\ln C_{jt}$ and $F$ is the standard normal cdf. By a simple transformation we can write down the corresponding linear model :

$$y_{jt} = \Phi^{-1}(1 - S_{jt}) = \frac{1}{\sigma_j} [c_{jt} - \mu_j - t \times \ln(1 - \delta_{jt})] + \varepsilon_{jt} \quad (2)$$

where $\delta_{jt} = \delta \forall j, t$ in the basic model. The same model can be used at the industry level. The residual $\varepsilon_{jt}$ summarizes our ignorance about this relationship. We simply assume that $E(\varepsilon_{jt}|j,t) = 0$ and a finite conditional variance, possibly heteroskedastic.

## 2.2 The firm-level reduced form model

All the assumptions of the previous model could be thought of as problematic. First, the amount of the annuities is so low that one can doubt that they play such a role in the decision process under study. The structural model accounts for other variables through a modelisation of the average initial return and of the monopoly rent dissipation but it remains that the program underlying the patenting decision is based on the values taken by the annuities. Second, the normality assumption can also be too strong. We simply do not now what the true law is, so that semi parametric models would be preferred since they are less demanding. These are the reasons why we introduce another model.

We estimate a reduced form model for the hazard rate, which gives the instantaneous probability of canceling a patent at time t knowing that it was kept since t. Moreover, we do not assume a specific distribution. We use the semi parametric proportional hazard model of Cox (1972), which can be
estimated by the partial likelihood approach. The model for the firm-level hazard function is given by :

$$h(t|x_i; b) = h_0(t) \exp(x_i\beta)$$

The exponential form ensures the positivity of the hazard function and we let the baseline hazard $h_0(t)$ unspecified. This model allows a convenient interpretation of the parameter b. We have :

$$\ln h(t|x_i; b) = \ln h_0(t) + x_i\beta$$

thus b is a vector of elasticities for the variables that are taken in logarithm. In the following, we will look for a distribution that cope with the data and estimate a Weibull model. In all cases we account for right censoring. We now present the sample of the study.

## 3. The data

The first data base is the European patent (EPAT) one, which is different from Pakes and Schankerman (1986) who used national patent data from each country. It comes from the Institut National de la Propriété Industrielle and embeds information on all patent applications registered between June 1978 and December 1994 and applying for a protection in France<fnref n="4" />.

A European patent<fnref n="5" /> can be applied for in several countries at the same time, which grants the applicant with a protection in all the countries asked for. Patent applications are made directly to the European Patent Office (EPO), which then apply for the patent in all the countries. Basically, the patent remains a national right and applying for a European patent is just a way to avoid applications in all the countries. Annual lump sum taxes must be paid directly to EPO on the third year that follows the application, if the patent is granted. When the patent is granted, it generates as many national patents as the number of countries where the firm asked for patent protection. Then, the

<footnote n="4">⁴ Only a part of French patents are extended to European patenting.</footnote>

<footnote n="5">⁵ For a presentation of the patent systems in Europe, the United States and Japan, see the OECD patent manual (1994).</footnote>
applicant must pay the fee directly to the national patent offices where the patent is pending. Figure 1 shows the evolution of annuities for France as a function of the patent age. We took the deflated average<fnref n="6" /> over 1980-1994. The deflated annuities are clearly increasing with the patent age.

Depending on the success of its innovations, a patent applicant can select the countries in which he will maintain the protection. The patent falls if the taxes are not paid, separately in each country. Therefore we do not have a centralized data base that would allow us to know what the patent becomes in all the countries but in France. For this reason and the availability of firm-level data, we restrict our analysis to European patents applying for France that is 22670 patents. Inside these applications, we keep the granted patents only, that is 53% of European patent applications in France. Our analysis then reduces to evaluate the return on *granted* patents. There remains 7269 granted patents under analysis, protected in France and belonging to a manufacturing firm.

For each patent, we know the application date and its end if it is before 1994. We also know if it is a *joint* patent. Patent data are then matched with firm-level data, including accounting data coming from the BIC file<fnref n="7" />, a fiscal source, and from the Research survey<fnref n="8" />. The latter survey satisfies the Frascatti criteria, so that it includes firms employing at least one research employee or the equivalent in part-time jobs. We also drop the research laboratories from the sample, defined as firms with at least the half or their employees in research activities<fnref n="9" />. After this selection, we have 6673 patents left and it is the final set of patents we will work on.

We complete the explanatory variables set with firm-level measures of size, diversification, market power and sectoral measures of innovation. All this measures are presented in a companion paper on similar data (Crépon, Duguet

<footnote n="6">⁶ We used the value added deflator. The values presented are not indexes with basis 100 in 1980 but the annuities are merely 100 FRF in 1980 (for the first year).</footnote>

<footnote n="7">⁷ BIC: "Bénéfices Industriels et Commerciaux".</footnote>

<footnote n="8">⁸ "Enquête sur les moyens consacrés à la recherche et au développement".</footnote>

<footnote n="9">⁹ This convention is used in many studies on French manufacturing.</footnote>
and Kabla, 1996). To measure diversification we use another source : the
« fractions-EAE » annual survey which gives the industry line decomposition of
firms' sales. We simply compute the equivalent number to the Herfindahl index
for each firm, on its sale decomposition among the industry lines it participates
to. This gives us the equivalent number of activities which allows for detecting
diversification differences among firms having the same number of activities.
Using the share of each product in a firm's sales we compute a weighted
average market share for each firm and a weighted average Herfindahl index of
industry concentration. The industry is defined here at the finest level available,
that is level 600 in French classification, which breaks industry in about 250
industrial sectors. Both the market shares and industry concentration indexes
are computed from the whole industry surveys, not from the sample, so that
they give an accurate idea of market power and concentration<fnref n="10" />. Since we use
weighted averages for diversified firms, the weighted market share and
industrial concentration index are at the firm-level and account for the
diversification path of each firm.

Last but not least, we use three sectoral indicators from the Innovation
survey (Crépon, Duguet and Kabla, 1996). All the following indicators refer to
the overall<fnref n="11" /> period 1986-1990. The first one is the product imitation rate. It is
computed as the share of firms that answered to have launch a new product
that was both new to the firm and already existing on the market. The second
indicator, a technology push proxy, is the average of the 4 points scale<fnref n="12" />
answers to the item "From your firm's viewpoint, do you consider that
innovation is determined through technology's own dynamic ? ". It lies between
0 and 3 (at the firm-level). The third indicator, a demand pull proxy, is also an
average of the same 4 points scale answers but to the item "From your firm's
viewpoint, do you consider that innovation is determined through market
impetus (relationships with customers, competition) ? ". The scale is the same

<footnote n="10">¹⁰ The computations are made on domestic sales only, since export sales refer to foreign markets.</footnote>

<footnote n="11">¹¹ The "Enquête Innovation" (Innovation survey) does not provide yearly information but on this overall period only.</footnote>

<footnote n="12">¹² The 4 possible values for the answers are : "No", "Weakly", "Moderately" and "Strongly".</footnote>
as for the technology push proxy. We took the industries' averages at level 90 over the whole Innovation survey. This is a higher aggregation level than level 600, which breaks manufacturing in 38 sectors<fnref n="13" />. Globally, the sources used here make this study compatible with the previous studies of innovation in French manufacturing

## 4. Descriptive analysis

We observe the patent lives up to 15 years as shown in table 1. Right-censoring is frequent in our sample since 80% of the durations are in that case, thus we need to account for it. Figure 2 shows the non parametric Kaplan-Meier estimate of the survival function which accounts for right-censoring<fnref n="14" />. The salient fact is that although the patent fees are very low, the proportion of active patents declines sharply with time. The proportion of patents surviving steadily decreases after the fifth year from nearly 100% to about 30% on the 15th one. The decreasing part has a linear form. Hence, we have a steadily increasing hazard function, as shown in figure 3. Each year, about 7% of patents disappear although the fees are low.

Thus, there is an empirical rationale for a market structure interpretation of patent renewal, that is for the reduced form model of the hazard rate. Moreover the linearity of the hazard function from the fourth year will make us estimate a Weibull model for the variable t-4. The hazard function for this model is:

$$h(t|x_i; b) = \alpha \exp(x_i\beta)t^{\alpha-1}$$

where $\alpha$ is a parameter that can be estimated. We expect so to find for this parameter a value of nearly 2, which is consistent with a linear hazard function. This model is also a particular case of the models examined before (semi parametric proportional hazard model of Cox).

<footnote n="13">¹³ The reason for this grouping is to have enough observations to compute the product imitation rate proxy. Indeed, in this latter case, some firms were both imitators and innovators so that we counted a half imitator and a half innovator. To ensure that this measure is valid we needed enough observations that are pure imitators, this can only be the case if we use a higher level of aggregation. This is why we have to break manufacturing into 38 sectors instead of 250.</footnote>

<footnote n="14">¹⁴ Computed through SAS LIFETEST procedure.</footnote>
The density is another (equivalent) tool for the analysis of duration data.
the estimates presented in figure 4 indicate a mode about 13 years and that the
durations lower than 15 years seem to matter, confirming our results that most
firms do not renew their patent fees although they are not high.

It remains that this are aggregated figures and that we should account for
heterogeneity between firms. We will do it in two different ways. The first one is
a direct extension of Pakes and Shankerman model, the second one is the
estimation of a reduced form model for the hazard function that allows for
relaxing the distributional assumptions.

# 5. Results

## 5.1 The structural models

Two regression will be of interest here. The first one is the comparison with
previous works at the macroeconomic level. The second one is the extension of
this first regression to the sectoral level, with a structural model for both the
initial average return and the rent dissipation. We estimate the comparison
equation (2) by heteroskedasticity robust<sup>15</sup> OLS. We only keep the cohorts that
include a sufficient number of observations to estimate the survivors'
proportions. We took a minimum of 30 patents per cohort.

We find both a higher initial return and a higher depreciation rate than Pakes
and Schankerman (1986) found on French patents (table 2). The average
return turns out to be higher for European patents: the 95% asymptotic
confidence interval for our average patent return m is equal to [4.4,15.8] and
the one of the previous study is [6.2,7.0]. The standard deviations of the initial
return<sup>16</sup> are comparable for both types of patents, which give a variation
coefficient of the returns equal to 29% for French patents against 21% for
European patents. The average gross return can thus be consistently estimated
by $exp(10.191 + 2.141^2 / 2) \approx 263 798$ FRF against 1094 FRF for the previous

<footnote n="15"><sup>15</sup> The covariance matrix of the coefficients are given in White (1980).</footnote>

<footnote n="16"><sup>16</sup> It is different from the standard error of the *estimate* of the average innovation return.</footnote>
estimate on French patents. However, this estimate has a stronger variance than the previous one. This higher return is associated with a higher depreciation rate equal to 23% against 10% for French patents. Hence, European patents over 1978-1994 have both a higher initial return and depreciation than the French patents over 1951-1979. It remains that the high imprecision of the initial return estimate suggest to remain cautious since both estimates are not incompatible at the 5% level. From this distributional parameters (m, s and d) we can simulate the distribution of returns to patenting. The rent V(T*) is given by:

$$V(T^*) = \sum_{t=1}^{T^*} (1+r)^{-t} (R_{0j}(1-\delta)^t - C_{jt}) \text{ with } \ln R_{j0} \rightsquigarrow N(\mu_j, \sigma_j^2)$$

The results are presented in table 3. We find that the distribution of patent returns is highly skewed, with a median ten times smaller than the mean (64 057 FRF). The larger part of European patents gives only a small rent while the last percentiles make nearly all the profits.

We now turn to the richer sectoral model. In this approach we use the innovation sectoral indicators and look at the influence of demand pull, technology push and imitation on patenting return. We do not consider anymore that the average return and depreciation rate are constant but rather that they depend on industry characteristics. The model for the initial average return is :

$$\mu_j = \mu_0 + \alpha_1 \ln DP + \alpha_2 TP + \alpha_3 \ln IR$$

where :

* DP is the demand pull indicator from the innovation survey. It measures the importance of the relationship with customers and competitors as a determinant of firms innovations.

* TP is the technology push indicator from the innovation survey. It indicates the importance of the own dynamics of technology in generating innovations

* IR is the product ex post imitation rate from the innovation survey. It is an inverse appropriability measure of innovation benefits.
The imitation rate is taken in logarithm so that the corresponding coefficient is to be interpreted as an elasticity of the initial return. We also model the depreciation rate of patents :

$$δ = 1 - \exp(β_0 + β_1 DP + β_2 TP + β_3 \ln IR)$$

Here as well the coefficients of the variables in logarithm are the elasticities of the depreciation rate, but with the sign reversed. The estimates of the model are presented in table 4.

The first model maintains a constant depreciation rate and concentrates on the explanation of the average initial return. We find that all the variables are significant at the 5% level. Technology push and the imitation rate would have a positive effect on patenting return while demand pull would have a negative effect. Although this last result is counterintuitive for demand pull, we can provide a reasonable explanation. In this model a positive effect on the initial return is equivalent to a longer patent life, which is useful for interpretation. Thus demand pulled innovations would have a shorter patent life which leads to lower profit. But this is the return for *one* patent. It does not tell us that the overall return of demand pulled innovations is lower. Indeed, it is well known that firms do patent more often products than process, so that a compensation is likely to happen.

The technology pushed innovations have a longer life and thus enjoy higher returns. It could be interpreted as a consequence of patenting more innovative discoveries than for products. The ease to imitate a product would also increase the patent life and lead to a higher patent rent. This last result does not mean that spillovers increase innovation output, but that keeping a patent holding is a strategy to lower imitation and thus to secure more benefits. Moreover, anticipating that the patentee will keep its patent holding, the rivals are enticed to imitate the patented product. If they do not so, they must wait too much time to be authorized to use the technology. This effect in also tends to make the patentee more reluctant to give up its rigth properties. The same
effect is at stake in an article by N. Gallini (1992) on the socially optimal design of patents. According to it extending statutory patent life could reinforce imitation. If imitation is socially costly, the socially optimal patents are no more the infinitely-lived ones as it is usual in the literature but broad patents with no imitation allowed.

The constant depreciation rate is comparable to the aggregated model one, with $d=24.7$. The return at the average point also ($m=10.2$). But these results could be interpreted as reduced form one. It can be argued that the depreciation rate of patent rents depends also on industry characteristics. Therefore we estimate this model (table 4, second column). When one accounts for standard errors, we clearly see that the story does not change for demand pull and technology push.

But there is a change for the imitation rate. Its effect can be decomposed in two parts (at the 5% level): on the one hand, it is negative on the initial return and, on the other hand, it is negative on the depreciation rate. Thus, imitation both decrease the initial value of patents and make firms enforce it for a longer period of time. The net effect is positive on the patent rent however. Two economic interpretations can be made from it: first, firms would compensate a lower profit flow (i.e. a lower effective patent breadth) by a longer protection period, second, they would keep their patents pending in order to build imitation barriers, that is to increase the imitation cost by competitors. This result appears to be robust in the remaining of the paper.

One can also compare directly the initial returns and depreciation rates of our sectors. For the average return we find that chemical products would have a higher return than the average while motor vehicle have a lower one. Once we account for different dissipation rates, we find that the differences are no more significant for chemical products. For motor vehicles the whole effect passes in rent dissipation. Thus this sector would have a lower patent return because of its higher depreciation rate of innovation benefits. A last interesting result appears for computers and electronics. Although we find that its return is comparable to the average, this global effect can be decomposed in two parts:
this sector has both a strongly higher initial return and a higher depreciation
rate.

## 5.2 The reduced form model

The estimates of the firm level model are given in table 3. Here we explain patents hazard rates by patent level and mostly firm level data. The patent-level explanatory variables are the following: the number of countries covered by the patent and the fact that it is a joint patent. In the latter case, we distinguish domestic from international joint patents. A single patent is the common case analyzed in the literature, joint patents (more than one patent applicant) refer to the cooperative research and development issue and provide an interesting look in the innovation process<sup>17</sup>. The issue is whether joint patents exit less rapidly than other patents or not. Firm-level variables are the traditional one in studies of innovation and market structure : sales, research and development intensity, diversification, industry concentration and market share. We also keep the technology push and imitation rate at the sectoral level. In the following, we perform the regressions on two sets of firms: the whole sample and restricted sample of firms with a research and development activity. Several results emerge from our estimations (table 6). First, the results are similar for the two samples. Second, it will appear that the Cox semi parametric estimates are very close to the Weibull model ones.

In all the regressions, the patent level variables are not significant at the 5%
level, so that joint patenting and the number of countries covered by the patent
do not seem to influence its duration in France. The explanation of patent lives
lies in five variables: the R&D to sales ratio<sup>18</sup>, the diversification of firms'
productions, the industry sales concentration, the technology push sectoral
indicator and the sectoral product imitation rate. It is important to notice that we
find no significant effect of size once accounted for these variables.

<footnote n="17">17 Joint patents represent 15% of European patents in French manufacturing and joint patenting firms are involved in the half of research expenditures. For a more detailed presentation of joint patents in French manufacturing, see Duguet (1996).</footnote>

<footnote n="18">18 We also include a R&D dummy for the regressions on the large sample.</footnote>
The patent life is longer the bigger the R&D ratio, industry concentration, the technology push and the imitation rate. The effect of diversification is to reduce the patent length. The results on the sectoral indicators confirm what we have found in the structural model. The result on R&D suggest that the patents of R&D intensive would have a higher value and could be more easily protected than the other patents. Moreover, the R&D dummy has also a positive effect on patent duration, thus firms that do not do formal R&D have shorter patents than the others<fnref n="19" />. Finally, the effect of concentration, which is less robust than the other ones, would be positive on patent lengths. We have also performed another set of regressions with a sectoral fixed effect replacing the technology push and imitation indicators<fnref n="20" /> (table 7).

We then find that the effect of diversification vanishes. Then the main individual<fnref n="21" /> determinant of patent life is the effort in research and development, with a coefficient of 0.2. Industry concentration remain significant as well for the regression on the large sample, but does not among R&D firms.

Finally, the shape of the distribution of patent lives can be inferred from the data: the estimates of the Weibull model are nearly identical to the Cox ones for all the specification examined. We find that the patent lives would be distributed as a Weibull model with parameter a = 2.5.

## 6. Conclusion

This paper first extends the patent renewal model by Pakes and Shankerman to the sectoral and firm levels. The explanatory variables include patent, firm and sectoral levels variables. The extension of the analysis at the sectoral level shows that product imitation has a negative effect on both the initial patent return and the depreciation rate. This suggest that there are significant appropriability problems in manufacturing. The consequence of it are that, one the one hand, less innovations are likely to be patented since the

<footnote n="19">¹⁹ Firms in the French R&D survey must have at least one employee working full time on R&D.</footnote>

<footnote n="20">²⁰ The sectoral decomposition we use is slightly more aggregated in order to keep enough firms in each sector.</footnote>

<footnote n="21">²¹ The *sectoral* determinants remain implicitly present in the fixed effect.</footnote>
initial return is lower and, one the other hand, once innovations are patented
firms have interest in keeping it pending for a longer period of time.

The extension of the analysis at the firm level is motivated by both the
availability of new data and the strong theoretical and statistical assumptions of
the structural model. We relax these assumptions by estimating a reduced form
hazard model. The first result is that joint patenting and the number of countries
covered by the patent do not influence significantly the patent length. The
second result is that higher R&D intensities imply higher patent lives. The third
result is that the imitation rate has a strong negative effect on the patent exit
rate. This suggest a strategic use of patents as a mean to create barriers to
imitation.

References

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Cases C. and S. Lollivier, 1993, L'économétrie des modèles de durée avec SAS : présentation et mise en oeuvre, CREST working paper 9344 bis.

Crépon B. and E. Duguet, 1995, Research and development, competition and innovation: pseudo maximum likelihood and simulated maximum likelihood methods applied to count data models with heterogeneity. Eco&Maths WP9508, University of Paris I. *To appear in the Journal of Econometrics*.

Crépon B., E. Duguet and I. Kabla, 1996, Schumpeterian conjectures: a moderate support from various innovation measures. In Kleinknech ed. *Innovation: the message from new indicators*, Mc Millan, London.

Duguet E., 1996, Technical cooperation through European joint patents, *Insee Studies in Economics and Statistics*, N°1, pp. 96-111.

Gallini T., 1992, Patent policy and costly imitation, *Rand Journal of Economics*, Vol. 23, No. 1, Spring 1992.

Griliches Z., 1990, Patent statistics as economic indicators: a survey, Journal of Economic Literature, Vol. XXVIII, pp. 1661-1707.

Levin R., A. Klevorick, R. Nelson and S. Winter, 1987, Appropriating the returns from industrial research and development, *Brookings papers on Economic Activity*, 3, pp. 783-831.

Pakes A., 1986, Patents as options: some estimates of the value of holding European patent stocks, *Econometrica*, Vol. 54, 4, pp. 755-784.
Pakes A. and Shankerman, 1986, Estimates of the value of patent rights in European countries during the post 1950 period, *The Economic Journal*, December, pp. 1052-1076.

White H., 1980, Heteroskedasticity consistent covariance matrix estimator and a direct test for heteroskedasticity, *Econometrica*, vol. 48, pp. 817-838.
<figure><img src="image_3.png" /><figcaption>Figure 2 - Patent survival function</figcaption></figure>

<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4 - Patent life density</figcaption></figure>

<figure><img src="image_6.png" /></figure>
<table><caption>Table 1- Empirical distribution of patent lifes</caption><thead><tr><th>Observed patent life</th><th>Number of observations</th><th>Number failed</th><th>Number censored</th><th>Survival function (Kaplan-Meier)</th></tr></thead><tbody><tr><td>1</td><td>4</td><td>0</td><td>4</td><td>1</td></tr><tr><td>2</td><td>87</td><td>0</td><td>87</td><td>1</td></tr><tr><td>3</td><td>440</td><td>12</td><td>428</td><td>1</td></tr><tr><td>4</td><td>943</td><td>86</td><td>857</td><td>0.998</td></tr><tr><td>5</td><td>1064</td><td>181</td><td>883</td><td>0.983</td></tr><tr><td>6</td><td>912</td><td>179</td><td>733</td><td>0.946</td></tr><tr><td>7</td><td>734</td><td>194</td><td>540</td><td>0.901</td></tr><tr><td>8</td><td>591</td><td>158</td><td>433</td><td>0.842</td></tr><tr><td>9</td><td>468</td><td>152</td><td>316</td><td>0.783</td></tr><tr><td>10</td><td>407</td><td>132</td><td>275</td><td>0.715</td></tr><tr><td>11</td><td>325</td><td>110</td><td>215</td><td>0.642</td></tr><tr><td>12</td><td>300</td><td>91</td><td>209</td><td>0.565</td></tr><tr><td>13</td><td>216</td><td>54</td><td>162</td><td>0.478</td></tr><tr><td>14</td><td>111</td><td>27</td><td>84</td><td>0.397</td></tr><tr><td>15</td><td>63</td><td>5</td><td>58</td><td>0.320</td></tr><tr><td>Total</td><td>6665</td><td>1381</td><td>5284</td><td>-</td></tr><tr><td>Percentage</td><td>100</td><td>20.72</td><td>79.28</td><td>-</td></tr></tbody></table>

<table><caption>Table 2 - Aggregated patent renewal model</caption><thead><tr><th>Distribution of returns parameters</th><th>European patent*</th><th>French patent**</th></tr></thead><tbody><tr><td>μ<br>Average log return</td><td>10.191<br>(2.810)</td><td>6.58<br>(0.23)</td></tr><tr><td>σ<br>Standard error of log return</td><td>2.141<br>(0.454)</td><td>1.93<br>(0.24)</td></tr><tr><td>δ<br>Depreciation rate</td><td>0.234<br>(0.107)</td><td>0.10<br>(0.04)</td></tr><tr><td>R<sup>2</sup></td><td>0.977</td><td>0.98</td></tr><tr><td>df</td><td>65</td><td>128</td></tr></tbody></table>

<footnote>* The regression includes a full set of time dummies. Heteroskedasticity robust standard errors between parentheses.</footnote>

<footnote>** From Pakes and Schankerman. The figures have been converted in 1980 French Francs according to the formula : 1 US Dollar 1980 = 4.226 FRF 1980.</footnote>
<table><caption>Table 3 - Distribution of the total rent for the 1985 European patents</caption><thead><tr><td>Patent rent quantiles</td><td>French Francs</td></tr></thead><tbody><tr><td>25%</td><td>13 551</td></tr><tr><td>50%</td><td>64 057</td></tr><tr><td>75%</td><td>281 520</td></tr><tr><td>90%</td><td>1 049 620</td></tr><tr><td>95%</td><td>2 293 170</td></tr><tr><td>99%</td><td>9 667 000</td></tr><tr><td>Mean</td><td>653 460</td></tr></tbody></table>

<footnote>* Simulation with 50,000 random drawings from the estimates given in table 4. The actualisation rate is assumed constant, r=10%. The monetary unit is 1980 FRF.</footnote>
<caption>Table 4- Patent renewal model with sectoral explanatory variables</caption>

Log of average return : $\mu = \mu_0 + \alpha_1 DP + \alpha_2 TP + \alpha_3 \ln IR$
Depreciation rate : $\delta = 1 - \exp(\beta_0 + \beta_1 DP + \beta_2 TP + \beta_3 \ln IR)$

<table><thead><tr><th>Distribution of log return parameters*</th><th>With constant depreciation rate</th><th>With sectoral depreciation rate**</th></tr></thead><tbody><tr><td>Average log return : μ</td><td></td><td></td></tr><tr><td>- Constant term</td><td>11.426<br>(2.993)</td><td>8.271<br>(2.356)</td></tr><tr><td>- DP<br>(sectoral average)</td><td>-1.042<br>(0.232)</td><td>-2.540<br>(1.311)</td></tr><tr><td>- TP<br>(sectoral average)</td><td>2.176<br>(0.571)</td><td>2.925<br>(1.680)</td></tr><tr><td>- IR<br>(logarithm)</td><td>3.655<br>(1.174)</td><td>-4.157<br>(1.963)</td></tr><tr><td>1 minus depreciation rate : 1-δ</td><td></td><td></td></tr><tr><td>- Constant term</td><td>—</td><td>0.146<br>(0.181)</td></tr><tr><td>- DP<br>(sectoral average)</td><td>—</td><td>0.221<br>(0.150)</td></tr><tr><td>- TP<br>(sectoral average)</td><td>—</td><td>-0.128<br>(0.189)</td></tr><tr><td>- IR<br>(logarithm)</td><td>—</td><td>1.036<br>(0.323)</td></tr><tr><td>Standard error of log return (σ)</td><td>2.386<br>(0.586)</td><td>2.288<br>(0.523)</td></tr><tr><td>Depreciation rate (δ)</td><td>0.247<br>(0.075)</td><td>—</td></tr><tr><td>μ at the average point</td><td>10.197</td><td>9.840</td></tr><tr><td>δ at the average point</td><td>0.247</td><td>0.215</td></tr><tr><td>R<sup>2</sup></td><td>0.837</td><td>0.850</td></tr><tr><td>df</td><td>337</td><td>337</td></tr></tbody></table>

<footnote>* The regression includes a full set of time dummies. Heteroskedasticity robust standard errors between parentheses.</footnote>
Table 5- Sectoral comparison

Sector specific log of average return sector and depreciation rate : patent renewal model with sectoral dummies ($d_j=1$ if a firm belongs to sector j)

Log of average return: Depreciation rate:

$$ \mu = \mu_0 + \sum_j \alpha_j d_j \qquad \delta = 1 - \exp(\beta_0 + \sum_j \beta_j d_j) $$

<table><thead><tr><th>Distribution of log return parameters*</th><th>With constant depreciation rate</th><th>With sectoral depreciation rate**</th></tr></thead><tbody><tr><td><em>Average log return : μ</em></td><td></td><td></td></tr><tr><td>- Constant term</td><td>10.416 (2.469)</td><td>10.163 (2.411)</td></tr><tr><td>- Chemical products</td><td>0.644 (0.187)</td><td>0.114 (0.367)</td></tr><tr><td>- Drug</td><td>-0.243 (0.135)</td><td>0.389 (0.376)</td></tr><tr><td>- Fabricated metals</td><td>-0.297 (0.341)</td><td>1.515 (2.207)</td></tr><tr><td>- Non electrical machinery</td><td>0.081 (0.125)</td><td>0.260 (0.376)</td></tr><tr><td>- Computer and electronics</td><td>0.156 (0.123)</td><td>1.125 (0.429)</td></tr><tr><td>- Motor vehicle</td><td>-0.607 (0.182)</td><td>0.143 (0.375)</td></tr><tr><td><em>1 minus depreciation rate : 1-δ</em></td><td></td><td></td></tr><tr><td>- Constant term</td><td>-</td><td>-0.238 (0.093)</td></tr><tr><td>- Chemical products</td><td>-</td><td>0.062 (0.049)</td></tr><tr><td>- Drug</td><td>-</td><td>-0.086 (0.050)</td></tr><tr><td>- Fabricated metals</td><td>-</td><td>-0.344 (0.435)</td></tr><tr><td>- Non electrical machinery</td><td>-</td><td>-0.024 (0.049)</td></tr><tr><td>- Computer and electronics</td><td>-</td><td>-0.133 (0.053)</td></tr><tr><td>- Motor vehicle</td><td>-</td><td>-0.101 (0.050)</td></tr><tr><td><em>Standard error of log return (σ)</em></td><td>2.481<br>(0.572)</td><td>2.433<br>(0.532)</td></tr><tr><td><em>Depreciation rate (δ)</em></td><td>0.259<br>(0.069)</td><td>-</td></tr><tr><td><em>R<sup>2</sup></em></td><td>0.869</td><td>0.881</td></tr><tr><td><em>df</em></td><td>337</td><td>337</td></tr></tbody></table>

<footnote>* The regression includes a full set of time dummies. Heteroskedasticity robust standard errors between parentheses.</footnote>
<caption>Table 6 - Hazard function with sectoral indicators</caption>

Hazard specification: $h_i(t) = h_0(t) \exp(x_i b)$

<table><thead><tr><th rowspan="2">Estimation method</th><th colspan="2">Cox model<br>(partial likelihood)<br>semi parametric</th><th colspan="2">Weibul model<br>(maximum<br>likelihood)<br>parametric</th></tr><tr><th>All<br>Firms</th><th>Firms<br>with<br>R&D</th><th>All firms</th><th>Firms<br>with<br>R&D</th></tr></thead><tbody><tr><td>Sample</td><td></td><td></td><td></td><td></td></tr><tr><td>Sales<br>(logarithm)</td><td>-0.019<br>(0.031)</td><td>-0.001<br>(0.037)</td><td>-0.017<br>(0.030)</td><td>-0.002<br>(0.038)</td></tr><tr><td>R&D/Sales<br>(logarithm)</td><td>-0.164<br>(0.034)</td><td>-0.168<br>(0.035)</td><td>-0.169<br>(0.033)</td><td>-0.177<br>(0.035)</td></tr><tr><td>R&D dummy</td><td>-0.699<br>(0.156)</td><td>-</td><td>-0.724<br>(0.157)</td><td>-</td></tr><tr><td>Technology push<br>(sectoral indicator)</td><td>-0.150<br>(0.038)</td><td>-0.137<br>(0.054)</td><td>-0.156<br>(0.038)</td><td>-0.131<br>(0.053)</td></tr><tr><td>Sectoral product imitation<br>rate<br>(logarithm)</td><td>-1.830<br>(0.324)</td><td>-1.868<br>(0.361)</td><td>-1.949<br>(0.331)</td><td>-1.966<br>(0.370)</td></tr><tr><td>Number equivalent of<br>activities<br>(logarithm)</td><td>0.225<br>(0.091)</td><td>0.238<br>(0.100)</td><td>0.239<br>(0.091)</td><td>0.248<br>(0.099)</td></tr><tr><td>Diversification dummy</td><td>-0.139<br>(0.106)</td><td>-0.154<br>(0.124)</td><td>-0.151<br>(0.106)</td><td>-0.154<br>(0.124)</td></tr><tr><td>Herfindahl concentration<br>index<br>(logarithm)</td><td>-0.108<br>(0.049)</td><td>-0.105<br>(0.064)</td><td>-0.116<br>(0.048)</td><td>-0.104<br>(0.063)</td></tr><tr><td>Weighted market share<br>(logarithm)</td><td>0.073<br>(0.044)</td><td>0.046<br>(0.054)</td><td>0.073<br>(0.042)</td><td>0.043<br>(0.053)</td></tr><tr><td>Number of countries<br>covered by the patent<br>≥ 8 (dummy)</td><td>-0.024<br>(0.070)</td><td>0.034<br>(0.080)</td><td>-0.020<br>(0.070)</td><td>0.038<br>(0.081)</td></tr><tr><td>Domestic joint patent<br>(dummy)</td><td>-0.217<br>(0.144)</td><td>-0.149<br>(0.168)</td><td>-0.204<br>(0.143)</td><td>-0.137<br>(0.167)</td></tr><tr><td>International joint patent<br>(dummy)</td><td>0.154<br>(0.095)</td><td>0.184<br>(0.118)</td><td>0.166<br>(0.093)</td><td>0.182<br>(0.116)</td></tr><tr><td>Global significance test<br>(χ² with 12 degrees of<br>freedom)</td><td>207</td><td>139</td><td>336</td><td>278</td></tr><tr><td>α (Weibul)</td><td>-</td><td>-</td><td>2.525<br>(0.063)</td><td>2.538<br>(0.083)</td></tr><tr><td>log likelihood*</td><td>-9426</td><td>-6130</td><td>-2497</td><td>-1807</td></tr><tr><td>Observations (number of<br>patents)</td><td>4239</td><td>3168</td><td>4239</td><td>3168</td></tr><tr><td>Failed</td><td>1261</td><td>849</td><td>1231</td><td>849</td></tr><tr><td>Censored</td><td>2978</td><td>2319</td><td>2978</td><td>2319</td></tr></tbody></table>

<footnote>* Logarithm of the partial likelihood for the Cox model. All regressions include a full set of time dummies. Standard errors between parentheses.</footnote>
<caption>Table 7 - Hazard function with sectoral dummies</caption>

Hazard specification: $h_i(t) = h_0(t) \exp(x_i b)$

<table><thead><tr><th rowspan="2">Estimation method</th><th colspan="2">Cox model<br>(partial likelihood)<br>semi parametric</th><th colspan="2">Weibul model<br>(maximum<br>likelihood)<br>parametric</th></tr><tr><th>All<br>Firms</th><th>Firms<br>with<br>R&D</th><th>All firms</th><th>Firms<br>with<br>R&D</th></tr></thead><tbody><tr><td>Sample</td><td></td><td></td><td></td><td></td></tr><tr><td>Sales<br>(logarithm)</td><td>-0.045<br>(0.037)</td><td>-0.021<br>(0.042)</td><td>-0.040<br>(0.035)</td><td>-0.017<br>(0.040)</td></tr><tr><td>R&D/Sales<br>(logarithm)</td><td>-0.187<br>(0.036)</td><td>-0.220<br>(0.037)</td><td>-0.189<br>(0.035)</td><td>-0.227<br>(0.038)</td></tr><tr><td>R&D dummy</td><td>-0.732<br>(0.161)</td><td>-</td><td>-0.750<br>(0.162)</td><td>-</td></tr><tr><td>Number equivalent of<br>activities<br>(logarithm)</td><td>0.188<br>(0.103)</td><td>0.159<br>(0.115)</td><td>0.204<br>(0.103)</td><td>0.160<br>(0.113)</td></tr><tr><td>Diversification dummy</td><td>-0.096<br>(0.110)</td><td>-0.074<br>(0.131)</td><td>-0.106<br>(0.108)</td><td>-0.068<br>(0.128)</td></tr><tr><td>Herfindahl concentration<br>index<br>(logarithm)</td><td>-0.115<br>(0.051)</td><td>-0.043<br>(0.069)</td><td>-0.123<br>(0.050)</td><td>-0.040<br>(0.068)</td></tr><tr><td>Weighted market share<br>(logarithm)</td><td>0.083<br>(0.044)</td><td>0.025<br>(0.055)</td><td>0.080<br>(0.042)</td><td>0.015<br>(0.050)</td></tr><tr><td>Number of countries<br>covered by the patent<br>greater than 6 (dummy)</td><td>-0.081<br>(0.073)</td><td>-0.025<br>(0.084)</td><td>-0.078<br>(0.073)</td><td>-0.022<br>(0.083)</td></tr><tr><td>Domestic joint patent<br>(dummy)</td><td>-0.158<br>(0.144)</td><td>-0.078<br>(0.168)</td><td>-0.148<br>(0.143)</td><td>-0.051<br>(0.164)</td></tr><tr><td>International joint patent<br>(dummy)</td><td>0.051<br>(0.103)</td><td>0.014<br>(0.122)</td><td>0.060<br>(0.103)</td><td>0.010<br>(0.121)</td></tr><tr><td>Global significance (LRT,<br>12 degrees of freedom)</td><td>224</td><td>178</td><td>320</td><td>306</td></tr><tr><td>α (Weibul)</td><td>-</td><td>-</td><td>2.525<br>(0.063)</td><td>2.551<br>(0.078)</td></tr><tr><td>log likelihood*</td><td>-9478</td><td>-6142</td><td>-2505</td><td>-1793</td></tr><tr><td>Observations (number of<br>patents)</td><td>4239</td><td>3168</td><td>4239</td><td>3168</td></tr><tr><td>Failed</td><td>1261</td><td>849</td><td>1231</td><td>849</td></tr><tr><td>Censored</td><td>2978</td><td>2319</td><td>2978</td><td>2319</td></tr></tbody></table>

All regressions include a full set of time dummies and 14 industry dummies. Standard errors between parentheses.

* Logarithm of the *partial* likelihood for the Cox model.
<table><caption>Table 8 - Sample statistics</caption><thead><tr><th></th><th>Mean</th><th>Standard deviation</th></tr></thead><tbody><tr><td>Sales (logarithm)</td><td>14.067</td><td>2.029</td></tr><tr><td>R&D/Sales (logarithm)</td><td>-1.400</td><td>1.639</td></tr><tr><td>R&D dummy</td><td>0.478</td><td>0.499</td></tr><tr><td>Technology push (sectoral indicator)</td><td>1.748</td><td>1</td></tr><tr><td>Sectoral product imitation rate (logarithm)</td><td>-0.627</td><td>0.121</td></tr><tr><td>Number equivalent of activities (logarithm)</td><td>-0.614</td><td>0.476</td></tr><tr><td>Diversification dummy</td><td>0.861</td><td>0.345</td></tr><tr><td>Herfindahl concentration index (logarithm)</td><td>-2.653</td><td>0.962</td></tr><tr><td>Weighted market share (logarithm)</td><td>-2.754</td><td>1.498</td></tr><tr><td>Number of countries covered by the patent ≥ 8 (dummy)</td><td>0.574</td><td>0.494</td></tr><tr><td>Domestic joint patent (dummy)</td><td>0.053</td><td>0.224</td></tr><tr><td>International joint patent (dummy)</td><td>0.163</td><td>0.369</td></tr></tbody></table>