patent, r & d and technological spillovers

PATENTS, R&D, AND TECHNOLOGICAL SPILLOVERSAT THE FIRM LEVEL: SOME EVIDENCE FROM

ECONOMETRIC COUNT MODELSFOR PANEL DATA

MICHELE CINCERA�

UniversiteÂ Libre de Bruxelles CP 140, Ave F.D. Roosevelt, 50, 1050 Bruxelles, Belgium

SUMMARY

This paper analyses the relationship between the main determinants of technological activity and patentapplications. To this end, an original panel of 181 international manufacturing ®rms investing substantialamounts in R&D during the late 1980s has been constructed. The number of patent applications by ®rms isexplained by current and lagged levels of R&D expenditures and technological spillovers. Technological andgeographical opportunities are also taken into account as additional determinants. In order to examine thisrelationship, several econometric models for count panel data are estimated. These models deal with thediscrete nature of patents and ®rm speci®c unobservables arising from the panel data context. The main®ndings of the paper are ®rst, a high sensitivity of results to the speci®cation of patent distribution. Second,the estimates of the preferred GMM panel data method suggest decreasing returns to scale in technologicalactivity and ®nally a positive impact of technological spillovers on ®rm's own innovation. # 1997 by JohnWiley & Sons, Ltd.

J. Appl. Econ., 12, 265±280 (1997)

No. of Figures: 0. No. of Tables: 7. No. of References: 27.

1. INTRODUCTION

Recent economic studies on Research and Development (R&D) activities indicate an increasinginterest in the relationship between ®rms' R&D investment and patent applications. Thoughpatents are not a perfect measure of R&D output (Griliches, 1990), they constitute a relevantmeasure of the technological e�ectiveness of R&D activities. Over the past years, several authorshave examined the dynamic structure of the patent±R&D relationship1 by considering thenumber of patent applications as a function of present and lagged levels of R&D expenditures.The purpose of this paper is to further explore the link between patent applications and ®rms'R&D activities by applying recently developed econometric techniques on a new internationaldata set of R&D ®rms over the period 1983±91. Besides the international feature of the dataset,the paper extends the framework of previous studies on the patent±R&D relationship by takinginto account additional determinants of patenting. These determinants are a measure of

CCC 0883±7252/97/030265±16$17.50 Received 15 June 1995# 1997 by John Wiley & Sons, Ltd. Revised 3 February 1997

JOURNAL OF APPLIED ECONOMETRICS, VOL. 12, 265±280 (1997)

� Correspondence to: Michele Cincera, DULBEA, CP 140, 40, Ave F.D. Roosevelt, B-1050 Bruxelles, Belgium.

Contract grant sponsor: UniversiteÂ Libre de Bruxelles.

1 For example, see Hausman, Hall and Griliches, henceforth HHG, (1984, 1986), Montalvo (1993), Blundell, Gri�thand Windmeijer, henceforth BGW, (1995), and CreÂ pon and Duguet (1993, 1997) for studies measuring the e�ects ofR&D on patents with ®rms' panel data. In Blundell, Gri�th and Van Reenen, henceforth BGVR, (1995), the dependentvariable is the count of the number of innovations.

technological spillovers, i.e. technological knowledge borrowed by one ®rm from other ®rms, aswell as technological and geographical opportunities. Despite all di�culties encountered whenmeasuring technological spillovers, evidence of their importance has been found in manyempirical studies.2 Moreover, such e�ects take time to be expressed in new patents and it is worthgiving attention to their precise timing.

In order to treat appropriately speci®c issues arising from the discreteness of patent counts inthe context of panel data, ad hoc econometric models for count panel data have to beimplemented.3 For instance, the discrete non-negative nature of the dependent patent variablegenerates non-linearities that make the usual linear regression models inappropriate. Moreover,in panel data, the presence of ®rm-speci®c unobservables or unobserved `heterogeneity' such asthe aptitude of engineers to invent new products are not uncommon and these unobservablesin¯uence the way by which ®rms decide to apply for patents. It is well known from the analysis ofpanel data that the treatment of these ®rm unobserved speci®c e�ects leads to the so-called `®xed'and `random' e�ects models. Although the question of whether to treat the e�ects as ®xed orrandom is not an obvious one,4 when ®rm-speci®c e�ects are correlated with some right-hand-side explanatory variables, the random e�ects model is no longer consistent. In the context ofthe patent±R&D relationship, there are reasons to believe that the unobservables are notindependent of the regressors. For instance, if the aptitude to invent is high, then R&Dinvestments will be higher. This (positive) correlation shows itself in upward-biased estimates andthe random speci®cation is no longer valid. In order to get around this problem, one possibility isto consider the conditional maximum likelihood estimator developed by HHG (1984). However,this ®xed e�ects approach relies on the assumption of strong exogeneity of the right-hand-sidevariables. As will be discussed below, this assumption is hard to maintain in the patent±R&Drelationship and hence a more general approach allowing for both correlated e�ects andpredetermined variables is also estimated. Finally, some issues related to the speci®cation of theexplanatory variables are examined. In particular, it is ascertained that these variables are notre¯ecting neglected serial correlation and dynamic misspeci®cation.

The paper is organized as follows. Section 2 presents the speci®cation of the patent±R&Drelationship to be estimated as well as some econometric count models for panel data and theirproperties. To begin, the basic Poisson model is introduced as a benchmark model. Then, themore General Event Count model and a semi-parametric estimator both based on a randome�ects speci®cation of the unobservables are presented. In order to allow for correlated ®rm-speci®c e�ects, a conditional maximum likelihood estimator and a non-linear GMM estimatorare discussed. These estimators are based on ®xed e�ects speci®cations and later model relaxesthe strict-exogeneity assumption of the regressors. Finally, the speci®cation issues raised aboveare investigated by imposing restrictions on serial correlation in the previous GMM estimatorand by considering an alternative one based on a dynamic speci®cation of the patenting process.The construction of some variables and the main characteristics of the data sample are exposed inSection 3. Section 4 summarizes the main empirical ®ndings. Section 5 concludes with theeconomic and methodological implications of the paper.

2 For a review, see Griliches (1992). It should be noted that with the exception of CreÂ pon and Duguet (1993) whoestimated the impact of technological spillovers on patents with a simpler model (no distributed lag in R&D andspillovers), none of the cited papers above consider this additional variable.3 For a discussion of count data models, see GourieÂ roux, Monfort and Trognon, henceforth GMT, (1984b), Cameronand Trivedi (1986) and Winkelmann and Zimmermann (1991, 1995).4 See Hsiao (p. 41, 1986).

266 M. CINCERA

J. Appl. Econ., 12, 265±280 (1997) # 1997 by John Wiley & Sons, Ltd.

2. PATENT±R&D SPECIFICATION AND COUNT MODELS FOR PANEL DATA

2.1. The Knowledge Production Function and the Basic Poisson Model

In order to investigate the dynamics of the ®rms' patenting process, I adopt a speci®cation alongthe lines of Pakes and Griliches (1984), HHG (1984, 1986), Montalvo (1993), and BGW (1995).These authors consider that patents, the dependent variable, is a function of contemporary andlagged ¯ow of the ®rms' annual R&D expenditures. In this paper, three additional technologicaldeterminants are included in the knowledge-production function. These variables are the annual¯ow of technological spillovers and the technological and geographical opportunities.

Technological opportunity and spillovers have often been described as technology-push forces,i.e. the exogenous technological factors which exercise pressures on the innovative activity(Rosenberg, 1983; Griliches, 1979, 1992). The technological opportunity represents the costs orthe di�culties linked with technological activity. Such di�culties vary with technological areasbecause of the physical properties inherent to technology and the stock of scienti®c knowledgeavailable at a certain time. Also, if the costs of doing R&D vary among countries, then thegeographical opportunities can be expected to be important. Important variations in techno-logical and geographical opportunity e�ects should be re¯ected in di�erent propensities to patentamong technological areas and countries. The technological spillovers are also an importantdeterminant of R&D activities. Technological spillovers are often divided into competitive anddi�usion spillovers. In the theoretical literature of patent races models (Loury, 1979), competitivespillovers have a negative rivalry e�ect on a ®rm's likelihood to apply for a patent to the extentthat the more competitors invest in R&D, the less a ®rm is likely to invent a new product ®rst.Following Griliches (1992), di�usion spillovers can be de®ned as the potential bene®ts of theresearch activity of other ®rms for a particular ®rm. Because the returns of R&D are not entirelyappropriable, the fruits of a ®rm's research activity may bene®t or spill over to other ®rms.Hence, di�usion spillovers have a positive impact on own R&D and, as a result, on patenting.

In order to assess the impacts of these determinants on the number of patent applications, thediscreteness of this variable has to be taken into account. For instance, because of di�culties anduncertainty inherent to R&D activities, ®rms do not always apply for patents and hence a zerovalue is a natural outcome of this variable. Because of this property, the use of conventionallinear regression models may be inappropriate. The reasons are that some basic assumptions suchas the normality of residuals or the linear adjustment of data are no longer ful®lled. The usualway to deal with the discrete non-negative nature of the patent dependent variable is to considerthe simple Poisson regression model. Let Pit be this variable which represents the number ofpatent applications by ®rm i at time t where i � 1; . . . ;N indexes ®rms and t � 1; . . . ;T indexestime periods. The Pit are assumed to be independent and have Poisson distributions withparameters lit. Parameters lit depend on a set of explanatory variables which are in this case thedeterminants of the knowledge production function:

lit � exp�xitb� � exp b0 �X4t�0

b1tÿt log�kitÿt� �X4t�0

b2tÿt log�sitÿt� �X

dmTDm �X

gnGDn

!�1�

where xit5 represents the set of explanatory variables, b is the vector of parameters to be

estimated, kit is the annual ¯ow of R&D investment, sit is the annual ¯ow of spillovers, TD and

5 Because of data constraints and in order to allow for comparison with previous studies, a four-lag period has beenconsidered for explanatory variables.

PATENTS, R&D, AND TECHNOLOGICAL SPILLOVERS 267

# 1997 by John Wiley & Sons, Ltd. J. Appl. Econ., 12, 265±280 (1997)

GD are respectively technological and geographical time-invariant dummies which are intendedto pick up technological and geographical opportunities.6 The dependent patent variable isrelated to this function through the conditional mean of the Poisson model. An importantproperty of the Poisson model is the equality between its ®rst two conditional moments:

E�Pit jxit;b� � V�Pit j xit;b� � lit �2�For panel data such as patents, the failure to include individual speci®c e�ects may lead to`overdispersion', i.e. conditional variance exceeds conditional mean, when estimating a cross-section model such as Poisson. For instance, in the patent±R&D relationship the presence of®rms unobserved e�ects like the uncertainty inherent to R&D activities, the ability of engineersto discover new products or the commercial risk of selling an invention, ®nd expression in the factthat only a few successful ®rms are likely to apply for a large number of patents in a given timeperiod while for a majority of ®rms the importance of patenting may be limited or even nil. AsWinkelmann and Zimmermann (1995) stressed, overdispersion can arise for reasons such asunobserved heterogeneity and this situation is not well suited by the Poisson model given theproperty of equality between its two ®rst conditional moments. Therefore, more generaleconometric models have to be considered.

2.2. Negative Binomial and QGPML Models

In order to take into account the unobserved heterogeneity, one possible extension of the Poissonmodel is to include a ®rm unobserved speci®c e�ect ei into the lit parameters. This ®rm-speci®ce�ect which is assumed to be invariant over time can be treated as random or as ®xed. In the caseof random e�ects, the Poisson's parameters become:

~lit � exp�xitb � ei� �3�The random terms ei take into account possible speci®cation errors of ~lit. The precise form of thedistribution of the compound Poisson model depends upon the speci®c choice of the probabilitydistribution of exp�ei�. In fact, di�erent negative binomial models can be generated according tothe way the parameters of the gamma distribution are linked to the xit. For instance, in theformulation of Winkelmann and Zimmermann (1991), the variance±mean relationship of thenegative binomial model7 is de®ned as:

V�Pit j xit� � �s2 ÿ 1�E�Pit j xit�k�1 � E�Pit j xit� �4�where s2 and k, which are independent of b, represent, respectively, the dispersion parameter andthe non-linearity in the variance±mean relationship. This more general full parametric speci®ca-tion allows for overdispersion. Furthermore, it embraces the Poisson model (for s2 � 1) andnegative binomial models such as the so-called Negbin I (for s2 > 1 and k � 0) and Negbin II8

(for s2 > 1 and k � 1) as special cases. Using the estimated value of s2 and k, it is possible to

6 The construction of these variables is discussed in Section 3.7 The authors call this model the General Event Count (GEC) model. A similar variance function is given by Cameronand Trivedi (1986, p. 33).8 For a discussion of these models, see Cameron and Trivedi (1986).

268 M. CINCERA


discriminate between the Poisson and both negative binomial models or to reject them ratherthan to choose one of them a priori.

The models presented so far can all be estimated by maximum likelihood (ML) techniques.However, the knowledge production function (1) has also been estimated by a Quasi-GeneralizedPseudo Maximum Likelihood (QGPML) estimator developed by GMT (1984a,b). The mainadvantage of such a semi-parametric approach is that it requires fewer distributional assumptionsregarding exp�ei�. However, it leads generally to less accurate estimates than those obtained bythe ML method if the chosen model is the true one.

2.3. CML and GMM Estimators

In the previous models, ®rm-speci®c e�ects are introduced into the Poisson parameter lit in orderto take into account the heterogeneity arising from the panel structure of data. Assuming thatthese speci®c e�ects are random, the compounded Poisson model leads to more general modelssuch as the negative binomial and the QGPML ones. Nevertheless, as stressed by BGVR (1995),this way of introducing the heterogeneity relies on the strong assumption that the ®rms'unobserved e�ects are independent of the explanatory variables. If this assumption is notsatis®ed, the previous estimators are not consistent and we know, from panel data analysis, thatin this case the ®xed e�ect speci®cation has to be used. In order to allow for ®xed e�ects to becorrelated with regressors, I consider two alternative econometric approaches, the conditionalmaximum likelihood estimator developed by HHG (1984) and a non-linear GMM estimatorproposed by Montalvo (1993) following Chamberlain (1992) and applied by BGVR (1995),BGW (1995) and CreÂ pon and Duguet (1997). Both approaches rely on a ®xed e�ect speci®cationof the ®rm unobserved heterogeneity. Finally, the `robustness' of the spillover speci®cation isinvestigated by imposing stronger assumptions on the residuals of the previous GMM estimatorand by considering an alternative one based on a linear feedback model.

HHG (1984) developed ®xed-e�ects Poisson and negative binomial models based on theconditional maximum likelihood approach of Anderson (1970). The key point of this approachconsists of conditioning on the sum over time of patents for a given ®rm. This allows removal ofthe ®rms' speci®c e�ects from the distribution of the dependent patent variable conditionally tothe sum of patents over the whole period. Moreover, the authors showed that the derivation ofthe Poisson ®xed-e�ect model leads to a multinomial logit distribution while a negative multi-variate hypergeometric distribution is obtained from the negative binomial ®xed-e�ect model. Itshould be noted that although these CML estimators allow one to get around the problem ofcorrelated ®rm-speci®c e�ects, their consistency relies on the crucial assumption of strictexogeneity of explanatory variables (Montalvo, 1993; BGVR, 1995). This assumption is hard tojustify in the patent±R&D relationship where the patenting of an innovation is likely to call forfurther R&D. For instance, activities such as developing, testing, or improving a new product arein many cases undertaken after the patent application itself. Hence the technological deter-minants of the patenting process should be considered more as weakly exogeneous or predeter-mined rather than strictly exogeneous.

The last approach investigated in this paper still allows for correlated ®xed e�ects but relaxesthe strict exogeneity assumption of the regressors. This approach departs from the multiplicative®xed-e�ects model (MFEM):

Pit � exp�xitb � ei� � uit �5�



From this expression, the generalized method of moments (GMM) framework of Hansen (1982)can be implemented by forming the following set of conditional mean restrictions:

E�Pit j zis;ei� � exp�xitb � ei�; 8s4 t �6�where zis represents any set of instruments such that equation (6) holds. This raises the questionof the choice of the optimal instruments set. As in Montalvo (1993) and BGVR (1995), I considerthe following instruments:

zis � �1; ki1; . . . ; kis; si1; . . . ; sis� �7�though e�ciency gains of the GMM estimator could be achieved by considering additionalinstruments.9

Conditions (6) cannot be used directly because they depend on the unobserved ®xed e�ects.However, these e�ects can be removed by the following quasi-di�erenced transformationproposed by Chamberlain (1992):

EfPit ÿ Pit�1 exp��xit ÿ xit�1�b� j zisg � 0; 8s4 t �8�Since the conditioning set is dated at period s, these orthogonality conditions remain valid underweak exogeneity of the regressors. Moreover, if the instruments are strictly exogeneous, thenobservations for all periods become valid instruments and this implies additional orthogonalityconditions in equation (8).10 Following Arellano and Bond (1991) and Mairesse and Hall (1996),the validity of these additional conditions can be tested by performing Sargan di�erence tests in asequential way.

The GMM method based on equation (8) has several advantages with respect to the fullparametric Poisson ®xed-e�ect model. First, it does not impose the equality of the ®rst twoconditional moments. Second, it allows for heteroscedasticity and any serial correlation patternof the error terms. Finally, it relaxes the strict exogeneity assumption of the regressors. However,this greater ¯exibility comes at the price of less e�cient estimators in general. However, followingCreÂ pon and Duguet (1997) more structure can be put on the GMM estimator, in particular interms of restricted serial correlation, by imposing additional conditions in equation (8) whosevalidity can in turn be tested using Sargan di�erence tests.11

Besides the question of e�ciency gains, CreÂ pon and Duguet put forward an economicmotivation for testing restrictions on residual correlation as well. On the one hand, once the ®xede�ects are accounted for, the estimates of current and past values of R&D and spillovers couldre¯ect the existence of correlated random shocks in the knowledge-production function due to

9 See CreÂ pon and Duguet (1997) for an application.10 Given equations (1), (7) and (8), there are 2T � 1 instruments (including the constant term) and �T ÿ 5� quasi-di�erences, where T � 9. Two cases have to be distinguished. First, in the case of weak exogeneity of the zis, the numberof orthogonality conditions as in equation (8) is �T ÿ 5��2�T ÿ 4�=2 � 2�T ÿ 4 ÿ t� � 1�, where t represents the extent towhich the zis are weakly exogeneous, i.e. t � 1�t � 2; . . .� means that s � t �t ÿ 1; . . .� in equation (8). Second, if the zisare strictly exogeneous, then equation (8) implies �T ÿ 5��2T � 1� orthogonality conditions, that is, �T ÿ 5��2T � 1�ÿ2�T ÿ 4�=2 � 2�T ÿ 4 ÿ t� � 1� additional conditions.11 In order to restrict serial correlation, the authors suggest two methods, one of which consists of adding past values ofthe dependent variable in the set of instruments:

z�is � �1; xi1; . . . ; xis;Pi1; . . . ;Pisÿ1� �9�This implies �T ÿ 5��T ÿ 4�=2 � �T ÿ 5 ÿ t�� additional orthogonality conditions in the case of weakly exogeneous zis.

270 M. CINCERA


the presence of serially correlated residuals. On the other hand, if the hypothesis of no serialcorrelation cannot be rejected, then this function should rather be viewed as a steady process.This argument is actually more crucial than it may appear at ®rst because of the presence ofcurrent and lagged values of technological spillovers in the knowledge-production function.Indeed, these variables are characterized by outside R&D, and hence, they might re¯ect neglectedserial correlation to the extent that the total amount of R&D performed outside a given ®rm atdi�erent time periods picks up such random innovation shocks.

Furthermore, the presence of serial correlation may also be viewed as an issue of dynamicmisspeci®cation. For instance, if the past patenting activity is an important determinant ofcurrent outcomes, then the omission of this determinant may be re¯ected in correlated residuals.Here also, if no restriction is imposed on serial correlation, these e�ects may again be picked upby the spillover variables. In order to investigate this last issue, an alternative dynamic speci®ca-tion of the knowledge production function has been estimated in line with BGVR (1995). Theauthors propose a linear feedback model (LFM) which leads to the following quasi-di�erencedorthogonality conditions:

E �Pit ÿ P�itÿ1r� � ÿ Pit�1 ÿ P�itr�exp x��it ÿ x��it�1

ÿ �b�

� � j z�isÿ � 0; 8s4 t �10�where P�it � �Pit;Pitÿ1;Pitÿ2�; r0 � �r1; r2; r3�; x��it � �kit; sit� and b0� � �bk; bs�.The speci®cation on which equation (10) is based is characterized by the presence of lagged

values of the patent variable among the regressors. In this particular case, we know from theliterature of panel data that if the ®xed e�ects are removed by ®rst (or quasi) di�erencing and ift ÿ 2 lagged and higher values of Pit are used as instrument for DPitÿ1, then consistent estimatescan be obtained as long as the residuals are not serially correlated. Using the same GMMframework as before, it is possible to test nested hypotheses regarding serial correlation byperforming Sargan di�erence test statistics. Finally performing a non-nested J test aÁ laDavidson±MacKinnon, it is possible to compare this last model with the previous one.

3. DATA SOURCES AND DESCRIPTIVE STATISTICS

In this paper, the annual R&D expenditures, the technological spillovers as well as technologicaland geographical opportunities are assumed to be the relevant explanatory variables of patent-ing. The next section presents the main empirical ®ndings regarding the patent±R&D relation-ship. These estimates are based on the di�erent econometric models that have been discussed inthe previous section. Before presenting the results, I detail the construction and the properties ofthe sample of ®rms used in this paper.

The data sample was constructed in order to constitute a representative sample of the mostimportant international ®rms conducting R&D over the period 1983±91. The size of the sampleis 181 ®rms for which information is available for at least nine consecutive years. For each ®rm,besides its corporate name and the country of its registered o�ce, three kinds of variables werecollected. These variables are the annual R&D investment expenditures, the industrial sectors ofactivity, and the total number of patent applications for each year. The sources of R&D areStandard & Poor's Compustat Services and the ®rm's annual reports. Fifteen manufacturingsectors were considered according to the Standard Industrial Classi®cation. The source for thisinformation is Dun & Bradstreet International. Given the international nature of the sample,four geographical areas, i.e. the EU, Japan, the USA, and the Rest of the world, were alsodistinguished. The number of ®rms in each area is, respectively, 28, 12, 140 and 1.



The source for patent applications is the European Patent O�ce database. Total nationalR&D expenditures at the manufacturing sector-based level were also collected from the OECD'sAnberd database. The R&D investment has been de¯ated by gross domestic product price indicesof the countries. They have also been converted to constant 1990 dollars.

According to Mohnen (1991), ®ve approaches can be distinguished for constructing a measureof technological spillovers. In the present work, for each ®rm, the spillovers are constructed as themanufacturing sector-based amount of R&D reported in the Anberd database less its own R&Dinvestment. It should be noted that this approach considers only intra-sector spillovers. Thisapproach also gives an identical weight for the R&D of all other ®rms. Ja�e (1986, 1988)developed a more sophisticated methodology in which the R&D spillovers are constructed bypositioning the ®rms in the technological space. The distribution of the ®rm's patents over patentclasses are used to characterize their positions in the technological space. The more two ®rms areclose in such a space, the more the potential spillovers are assumed to be important. The maindrawback of this methodology is that it can only be applied for ®rms that apply for patents. Thetechnological and geographical dummies have been constructed by assigning each ®rm to itsmain industrial sector and to the geographical area the ®rm is domiciled respectively.

Table AI in the Appendix indicates the representativeness of the whole sample compared to theAnnual National Business Enterprise R&D published by OECD. It appears that 45% of thewhole R&D for the six major countries is covered by the ®rm's sample in 1990. Table AII in theAppendix exhibits the R&D distribution of ®rms among manufacturing sectors. Some descript-ive statistics are given in Table I. On average, there were 60.8 annual patent applications over theperiod 1983±91. The standard deviation is quite high. This observation is to be related to theoverdispersion associated with this sort of variable. For 19.0% of the sample, at most one patenthas been applied. The bottom-right corner of Table I shows a high correlation between the laggedR&D investments.12 Such high multicollinearity of data may lead to some estimation problems.An alternative speci®cation based on polynomial R&D lagged structure (Almon-type weightedvariables) has been tested but the results did not improve signi®cantly.

4. EMPIRICAL FINDINGS

Table II presents the estimation results of the patent±R&D relationship for alternative countpanel data econometric models. The patent±R&D speci®cation allows us to examine the timepattern of the lag between R&D investment and technological spillovers on patenting activity. Ascan be observed, the results are quite sensitive to the selected econometric model, especiallyamong the four last models. The General Event Count and the QGPML models lead one toconclude that the estimates relative to the lag of the R&D investment are characterized bypositive and large coe�cients in the ®rst and last years and by imprecisely estimated coe�cientsin the intermediate years. It is worth noting that this `U-shaped' lag distribution has already beenbrought to the fore in previous studies (Pakes and Griliches, 1984; HHG, 1984, 1986) usingdi�erent data sets and speci®cations relating patents to R&D. These authors concluded to apossible lag-truncation bias because of the neglect of pre-sample R&D investment. Anothertelling argument put forward by HHG (1986) is the possible correlation of the ®rms' speci®ce�ects with the right-hand-side variables. The estimates related to the lag of technological

12 Such high correlation has also been encountered in others studies. For instance, HHG (1986) found a correlationgreater than 0�97 for their lagged R&D variables.

272 M. CINCERA


spillovers are from an economic point of view somewhat disturbing. The estimated coe�cientsare not only unstable across the models but they are also characterized by low signi®cance levels.Such a phenomenon associated with jointly highly signi®cant coe�cients is symptomatic ofmulticollinearity.13 The high signi®cance of technological and geographical dummies which aresupposed to pick up the technological and geographical opportunities indicates that patentingbehaviours vary substantially across countries and sectors.

From a methodological point of view, the estimated value of the GEC parameter s2 indicatesthat the basic Poisson model has to be rejected (H0: s2 � 1; t � 8�0). The rejection of this modelis due to the situation of overdispersion which is associated with unobserved heterogeneity.Therefore, more general models which allow for ®rms' unobservables have to be considered. Thedata sample is consistent with the hypothesis that s2 is higher than one (H0: s2 > 1; t � 7�9)and that k is not di�erent from one (H0: k � 1; t � 0�5). These hypotheses vindicate the use ofthe so-called Negbin II model and QGPML estimation technique. Although the QGPMLestimation is less restrictive in regard to the shape of the probability distribution, the estimatedparameters of these two models are very similar.

Column (3) of Table II presents the results for the conditional Poisson model. These resultsappear to be substantially di�erent from those observed in the two previous models. Indeed, weknow from the analysis of panel data that if the ®rms' speci®c e�ects are correlated with theexplanatory variables then neither the GEC model nor the QGPML estimator are consistent.This is due to the fact that these models rely on random speci®cations of their speci®c e�ects. Onthe other hand, the conditional ®xed-e�ect Poisson model leads to consistent e�ects even inpresence of correlated ®xed e�ects. Hence, the di�erent estimates obtained from this model giveclues for the presence of such a correlation. Using a Hausman test and comparing the Negbin IIand conditional Poisson estimates, it is possible to test whether the ®rms' speci®c e�ects arecorrelated or not. The value of the test's statistic (H0: random effects; X2�10� � 171�0) leads oneto conclude that the random e�ect model has to be rejected. The estimates of the conditionalPoisson model show that the U-shaped structure of the R&D coe�cients is to a large extentattenuated. In fact, the coe�cients associated with the current and last lagged R&D still exhibitthe largest estimates, but in this case only the current R&D is signi®cant. However, the estimated

Table I. Characteristics of the sample

Mean Standard error Minimum value Maximum value

Pit 60.8 121.6 0 925ln�kit� 5.3 1.3 3 8.7ln�sit� 9.5 0.9 6.9 10.8

CorrelationPit ln�kit� ln�kitÿ1� ln�kitÿ2� ln�kitÿ3�

ln�kit� 0.55ln�kitÿ1� 0.55 0.99ln�kitÿ2� 0.55 0.98 0.99ln�kitÿ3� 0.55 0.97 0.98 0.99ln�kitÿ4� 0.55 0.95 0.96 0.97 0.99

13 Correlation between the lagged ¯ow of spillovers is close to unity.



elasticities concerning the technological spillovers are not convincing. The current and laggedvalues of this variable are still marked by a sign change from one year to another. In addition, thesigni®cant positive elasticity of the current spillovers variable is puzzling. Indeed, these e�ectstake time to show up in new patents and, consequently, it is doubtful that they are immediate.Because of the way the conditional Poisson is constructed, the time-invariant individualtechnological and geographical opportunities can no longer be estimated. More fundamentally,the consistency of the parameters in this model relies on the assumption of strict exogeneity of theexplanatory variables. As has already been discussed, such an assumption is hard to maintain inthe context of the patent±R&D relationship.

In order to overcome this last issue, an alternative non-linear GMM estimator is considered inthe fourth column of Table II. This estimator still allows for correlated e�ects but relaxes thestrict exogeneity condition of the right-hand-side variables. The exogeneity assumption ofinstruments has been tested systematically by estimating any combination of both predeterminedand strictly exogeneous explanatory variables. As can be seen in Table AIII in the Appendix, theweak exogeneity hypothesis of R&D is always rejected (at the 5% level and whatever hypothesisis made regarding the exogeneity of the spillover variables) in favour of lag 1 and higher values ofinstruments associated with this variable, while for the technological spillovers, the hypothesis ofstrict exogeneity is never rejected (again, whatever exogeneity hypothesis is made for R&D).These ®ndings corroborate the idea that, on the one hand, patents are induced by R&Dexpenditures but also patents themselves lead to future R&D activities. On the other hand,accepting the strict exogeneity of technological spillovers supports the view that they are a resultof exogenous technological factors on the supply side of innovation.

The result of the test for restricted serial correlation is displayed in Table AIV in the Appendix.The statistic associated with this test leads to the conclusion that the hypothesis of no serialcorrelation cannot be rejected. Hence, we cannot conclude for the presence of correlated randomshocks in the knowledge production function and therefore such e�ects should not be re¯ected inthe explanatory variables.

Column (4) of Table II presents the results of the GMMmodel with restricted serial correlationimposed. The estimated value of the chi-square statistic of the overidenti®cation test shows noclear indication of misspeci®cation. The rejection of the weak exogeneity assumption shows thatthe previously estimated models are no longer valid. Indeed, the estimated elasticities of theGMM model lead to di�erent economic conclusions. The U-shaped structure has disappearedsince strong returns on R&D investment are now observed for the current and one-year-laggedcoe�cients while for the t-2 and t-4 lagged value of R&D small but negative and signi®cantimpacts are found. This result con®rms the ®ndings of previous studies and leads one to concludethat patenting occurs at an early stage of the R&D sequence. Indeed, the estimated elasticities ofpatents with respect to current and ®rst lag R&D variables say that when a ®rm spends 10%moreR&D in t-1, it applies for 6%more patents in t, while an increase of 10% of current R&D impliesan increase of 3.5% of patent applications in the same year.

The interpretation of the timing of technological spillovers indicates that only the t-3 laggedvalue of this variable is not statistically di�erent from zero. An important impact of this variableis observed for its current and t-2 lagged values (estimated elasticities of 1.2 and 0.85, respect-ively). It should be noted that the lag structure of spillovers is relatively similar in both theConditional Poisson and GMM models while this is clearly not the case for R&D. Oneexplanation could be that the hypothesis of strict exogeneity has been accepted for spillovers butnot for R&D. Hence, only the former variables satisfy the strict exogeneity hypothesis required

274 M. CINCERA


for consistency of the Conditional Poisson model. However, considering the sum of thecoe�cients related to this variable, an important stimulating e�ect favourable to patentingactivities is observed (estimated elasticity of 2.6) while negative e�ects were characterized in thetwo ®rst models. This empirical result supports the view that di�usion spillovers are moreimportant than competitive ones to the extent that the former exercise a positive impact onpatenting while the second are characterized by a negative e�ect on the output of the techno-logical production function. Interestingly is the opposite ®ndings of CreÂ pon and Duguet (1993).These authors estimate an elasticity of the spillovers variable of ÿ0�2. Two arguments can be putforward to explain this di�erent result. On the one hand, the dataset of this study consists of a

Table II. Parameter estimates of the knowledge-production function (t-statistics in parentheses)

(2) (3) (4) (5)Econometric (1) QGPML- Conditional GMMc- GMMc-model GEC gamma Poisson MFEMd LFMd

log�kt� 0.44 (3.5)a 0.44 (4.3) 0.29 (1.6) 0.35 (6.9) 0.31 (5.8)log�ktÿ1� 0.14 (1.1) 0.11 (0.8) 0.06 (0.8) 0.62 (15.0)log�ktÿ2� 0.04 (0.4) 0.03 (0.2) 0.07 (0.5) ÿ0�27 �ÿ4�5�log�ktÿ3� ÿ0�23 �ÿ2�4� ÿ0�23 �ÿ1�7� ÿ0�18 �ÿ1�4� ÿ0�06 �ÿ1�5�log�ktÿ4� 0.51 (4.7) 0.54 (5.3) 0.11 (0.8) ÿ0�16 �ÿ5�8�Sum of k 0.90 (26.2)b 0.89 (53.7) 0.35 (6.3) 0.48 (4.8)

log�st� 0.70 (6.6) 0.66 (1.2) 1.2 (2.8) 1.2 (9.9) 2.5 (9.7)log�stÿ1� ÿ0�39 �ÿ0�7� ÿ0�55 �ÿ0�9� ÿ0�11 �ÿ0�3� 0.26 (2.7)log�stÿ2� 0.00 (0.0) 0.22 (0.4) 0.83 (2.9) 0.85 (10.8)log�stÿ3� ÿ0�76 �ÿ1�1� ÿ0�70 �ÿ1�3� ÿ0�73 �ÿ2�3� 0.03 (0.4)log�stÿ4� 0.13 (0.4) 0.19 (0.5) 0.24 (0.9) 0.22 (3.2)

Sum of s ÿ0�32 (5.5) ÿ0�18 (11.0) 1.5 (14.5) 2.6 (14.0)

Ptÿ1 0.10 (4.8)Ptÿ2 0.07 (4.0)Ptÿ3 0.16 (5.0)

Sum of P 0.34 (6.3)

s2 1.42 (26.9)k 1.02 (25.3)

loglikelihood ÿ4047 ÿ6237 ÿ3493LR test techn. 212 313dummies

LR test geogr. 32 67dummies

Hausman test 171.0Overidenti®cation teste 69.0 (73) [0.61] 87.8 (78) [0.21]J-test:f a 1.02 (455) ÿ0�02 �ÿ8�6�a Heteroscedastic-consistent t-statistic.b t-statistics performed by means of the `delta method'.c Two-step GMM estimator, z� is used as instruments.d Restricted serial correlation imposed.e Chi-square statistic, degree of freedom in parentheses, signi®cance level in square brackets.f Davidson±MacKinnon non-nested test (OLS on: �Pit ÿ Pit�4�� a��Pit�5� ÿ Pit�4�� in column (4), �Pit ÿ Pit�5�� a��Pit�4� ÿ Pit�5�� in column (5)).



larger number of ®rms (451 French manufacturing ®rms) operating in a single domestic marketso that higher levels of competition can be expected among these ®rms. On the other hand, theconstruction of the spillovers variable rests on an industry-sector-based stock of R&D and onlythe current impact of this stock on patents is considered. Two more comments are worthmentioning when we compare R&D and spillovers e�ects. First, the positive and signi®cant e�ectof total spillovers reveal that social rates of return of knowledge is above private rates. Second,these e�ects appear to take more time to materialize than own R&D returns.The last GMM estimator investigated in this paper rests on a dynamic speci®cation of the

knowledge-production function. The statistic of the Sargan di�erence test reported in Table AVin the Appendix indicates that the hypothesis of serially uncorrelated residuals cannot berejected. Hence, all current and past values of Pitÿ1 can be used to implement the GMM-LFMestimator. However, as can be seen in column (5) of Table II, all lags of the patent variable arefound to be signi®cant with an overall e�ect of 0.34. Though the J-test statistic indicates that themodel of column (5) is preferred to the GMM-MFEM one, no contradiction appears whencomparing the elasticities of R&D and spillovers of both models. One interpretation of this®nding could be that the lag speci®cation of our explanatory variables is not inappropriate totake into account the dynamics of the patenting process.

Finally, considering the sum of all R&D coe�cients for each model, it is possible to comparethe results of this paper with those found in other empirical studies examining the patent±R&Drelationship. In the Pakes and Griliches (1984) study, the sum of R&D coe�cients is equal to 0.6,while HHG (1984, 1986) estimate elasticities varying from 0.29 to 0.6 according to the regressionmodel and to the number of lags. Montalvo (1993) and BGVR (1995) ®nd evidence of correlated(®xed) e�ects and weak exogeneity of regressors. They estimate by GMM a similar total R&Delasticity of 0.56 which is close to the value of 0.48 obtained in this paper. CreÂ pon and Duguet(1997) do not reject the hypothesis of strict exogeneity which might explain their lower elasticityof 0.26.

5. CONCLUSION

This paper has attempted to measure the impact of the technological factors on patenting activityat the ®rm level. The main determinants of this activity, i.e. R&D expenditures, technologicalspillovers, as well as technological and geographical opportunities, come from an original repre-sentative sample of 181 international large R&D ®rms over the 1983±91 period. The speci®cationof the patent±R&D relationship relies on a lagged structure of the explanatory variables andattempts to explain the patenting behaviour of ®rms over time.

In order to deal with some econometric problems arising from the panel data structure andfrom the discrete nature of the dependent variable, alternative econometric models for countpanel data were investigated. The General Event Count model allows for a more ¯exibleconditional mean±variance relationship than the Poisson and the negative binomial. TheQGPML estimator provides consistent estimates with less restrictive assumptions regarding thedistribution of the random ®rms' speci®c e�ects. However, these models are only valid if therandom e�ects are not correlated with the right-hand-side variables. In order to allow forcorrelated speci®c e�ects, a conditional Poisson model and two non-linear GMM estimatorswere considered as well. The last two estimators are more general since they relax the strictexogeneity assumption of the regressors which is hard to maintain in the patent±R&Drelationship.

276 M. CINCERA


The main ®ndings of the empirical analysis are a high sensitivity of the results among thedi�erent econometric models. Returns to scale in research activity are characterized by a`U-shaped' structure in the random e�ects speci®cations and to some extent in the ®xed-e�ectconditional Poisson model. This pattern of the R&D lag structure is no more present in theGMM-MFEM estimates. Furthermore, Sargan di�erence tests have been performed in asequential way in order to examine the exogeneity hypothesis of both R&D and spilloversvariables as well as the presence of serially correlated residuals. The conclusion is that the strictexogeneity of spillovers is not rejected, which is not the case for R&D. This last result invalidatesthe conditional Poisson model. Regarding the serial correlation assumption, no evidence ofcorrelated residuals is found in the knowledge-production function. The GMM-MFEMestimates suggest an important contemporaneous and one-year-lagged e�ects of R&D, indicat-ing that the bulk of such activity is performed during the two years before the patent application.Also, this result leads one to conclude that patenting activity occurs in an early stage of theknowledge-production process. As far as technological spillovers are concerned, the results revealan important positive impact when the sum of lagged e�ects is considered, i.e. outside R&D givesan incentive to patent. The positive elasticity of total spillovers indicates that social returns ofknowledge are more important than the private ones. Moreover, when the timing of such e�ectsis examined, it appears that the impacts of technological spillovers are less immediate than thecorresponding ®ndings for R&D. Finally, the last GMM-LFM estimator investigated in thispaper indicates that ®rst, the hypothesis of no serial correlation is not rejected, second, theestimated elasticities of R&D and spillovers are not inconsistent with the GMM-MFEMcorresponding estimates, and third, the feedback e�ects of past patents on current outcomes arepositive and signi®cant.

APPENDIX

Table AI. Representatives of the sample: proportion of Annual National Business Enterprises R&Drealized by ®rms of the samplea

1983 1984 1985 1986 1987 1988 1989 1990 1991

France 42.2 45.2 46.4 45.9 50.5 51.8 51.0 52.4Germany 42.5 43.3 46.8 48.5 50.4 52.2 60.5 57.6Italy 16.3 14.0 13.4 12.7 15.4 15.2 16.8 17.9Japan 26.6 28.1 28.6 29.9 29.8 29.8 29.7 29.7UK 3.3 3.0 3.0 3.2 3.8 3.8 3.9 4.1USA 47.4 51.2 50.0 52.2 52.7 55.2 59.5 61.2

Total 35.4 37.8 40.0 39.9 41.6 43.7 45.6 45.0 42.3

a based on OECD's ANBERD database.

Table AII. Manufacturing sector-based distribution of ®rms included in the sample

Aerospace Chemistry Computers Drugs Electricity Food Fuel and Mining Glass12 28 20 13 29 9 11 3

Instruments Machinery Metals Other Paper Software Vehicles TOTAL13 10 3 8 5 2 15 181



Table AIII. Strict versus weak exogeneity of instruments

Model and exogeneityof instruments (kit; sit)

a Overidenti®cation testb Sargan di�erence testc

(0, 0) 74.5 (65) [0.20] (0, 0)±(0, 1) 7.4 (10) [0.62] (0, 0)±(1, 0) 10.5 (10) [0.40](0, 1) 67.1 (55) [0.13] (0, 1)±(0, 2) 1.9 (4) [0.07] (1, 0)±(2, 0) 14 (4) [0.01](0, 2) 65.2 (51) [0.09] (0, 2)±(0, 3) 8.6 (4) [0.76] (2, 0)±(3, 0) 0.7 (4) [0.95](0, 3) 56.7 (47) [0.16] (0, 3)±(0, 4) 2.7 (4) [0.68] (3, 0)±(4, 0) 8.9 (4) [0.06](0, 4) 54.0 (43) [0.12]

(1, 0) 64.0 (55) [0.19] (1, 0)±(1, 1) 7.6 (10) [0.67] (0, 1)±(1, 1) 10.6 (10) [0.39](1, 1) 56.5 (45) [0.12] (1, 1)±(1, 2) 1.7 (4) [0.80] (1, 1)±(2, 1) 10.8 (4) [0.03](1, 2) 54.8 (41) [0.07] (1, 2)±(1, 3) 4.8 (4) [0.30] (2, 1)±(3, 1) 0.9 (4) [0.92](1, 3) 50.0 (37) [0.08] (1, 3)±(1, 4) 5.0 (4) [0.29] (3, 1)±(4, 1) 7.6 (4) [0.11](1, 4) 44.9 (33) [0.08]

(2, 0) 50.0 (51) [0.51] (2, 0)±(2, 1) 4.3 (10) [0.93] (0, 2)±(1, 2) 10.4 (10) [0.41](2, 1) 45.7 (41) [0.28] (2, 1)±(2, 2) 3.9 (4) [0.41] (1, 2)±(2, 2) 13.1 (4) [0.01](2, 2) 41.7 (37) [0.27] (2, 2)±(2, 3) 4.9 (4) [0.30] (2, 2)±(3, 2) 0.8 (4) [0.94](2, 3) 36.8 (33) [0.30] (2, 3)±(2, 4) 2.9 (4) [0.58] (3, 2)±(4, 2) 9.6 (4) [0.05](2, 4) 33.9 (29) [0.24]

(3, 0) 49.3 (47) [0.38] (3, 0)±(3, 1) 4.5 (10) [0.92] (0,3)±(1,3) 6.7 (10) [0.75](3, 1) 44.8 (37) [0.18] (3, 1)±(3, 2) 4.0 (4) [0.41] (1,3)±(2,3) 13.2 (4) [0.01](3, 2) 40.9 (33) [0.16] (3, 2)±(3, 3) 5.2 (4) [0.27] (2,3)±(3,3) 1.1 (4) [0.89](3, 3) 35.7 (29) [0.18] (3, 3)±(3, 4) 2.9 (4) [0.57] (3,3)±(4,3) 6.9 (4) [0.14](3, 4) 32.8 (25) [0.14]

(4, 0) 40.4 (43) [0.59] (4, 0)±(4, 1) 3.2 (10) [0.98] (0, 4)±(1, 4) 9.1 (10) [0.52](4, 1) 37.2 (33) [0.28] (4, 1)±(4, 2) 5.9 (4) [0.21] (1, 4)±(2, 4) 11.0 (4) [0.03](4, 2) 31.3 (29) [0.35] (4, 2)±(4, 3) 2.6 (4) [0.63] (2, 4)±(3, 4) 1.1 (4) [0.89](4, 3) 28.8 (25) [0.27] (4, 3)±(4, 4) 0 (4) [1.00] (3, 4)±(4, 4) 4 (4) [0.41](4, 4) 28.8 (21) [0.12]

a �t; t0� represents the extent to which kit and sit are strictly �t; t0 � 0� or weakly exogeneous �t; t0 � 1; . . . ; 4�. Forinstance t � 2 and t0 � 0 indicates that only one-year-lag and higher lags of kit are valid instruments and thatobservations for all periods are valid instruments for sit.b Chi-square statistic, degree of freedom in parentheses, signi®cance level in square brackets.c �t1; t01� ÿ �t2; t02� represents the additional orthogonality conditions when we go from set of instruments implied by�t2; t02� to the one implied by �t1; t01�. Under the null that all additional conditions hold, the test statistic is chi-squaredistributed with degree of freedom and signi®cance level in parentheses and square brackets.

Table AIV. Restricted versus non-restricted serial correlation

Model Overidenti®cation testb Sargan di�erence testc

Restricted serial correlation (RSC) 69.0 (73) [0.61] (RSC)±(USC) 19.0 (22) [0.65]Unrestricted serial correlation (USC) 50.0 (51) [0.51]

b±c See Table AIII.

278 M. CINCERA


Table AV. LFM model: serial correlation test

Model and exogeneity of Pita Overidenti®cation testb Sargan di�erence testc

(1) 87.8 (78) [0.21] (1)±(2) 6.2 (4) [0.19](2) 81.6 (71) [0.25] (2)±(3) ÿ2�0 (4) [1.00](3) 83.6 (70) [0.13] (3)±(4) 5.1 (4) [0.28](4) 78.6 (60) [0.14]

a �t� means that E�DuitPitÿtÿ1� � 0, t � 1; . . . ;T and t � 1; . . . ; 4.b See Table AIII.c �t� ÿ �t � 1� represents the additional orthogonality conditions when we go from the set of instruments implied by�t � 1� to the one implied by �t�.

ACKNOWLEDGEMENTS

I am indebted to Henri Capron, Renato FloÃ res, Bronwyn H. Hall, Lars Muus, Pravin Trivedi,Bruno Van Pottelsberghe, and two anonymous referees for valuable suggestions. Helpfulcomments were received from participants of the 7th ESWC and the 6th Biennial InternationalConference on Panel Data as well as seminars at University of Aahrus and Hong KongUniversity of Science and Technology. Financial support of UniversiteÂ Libre de Bruxelles isgratefully acknowledged. All opinions and remaining errors are my own.

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