Gauging a Firm’s Innovative Performance Using an Integrated Structural Index for Patents

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Abstract

Purpose

In this contribution we try to find new indicators to measure characteristics of a firm’s patents and their influence on a company’s profits.

Design/methodology/approach

We realize that patent evaluation and influence on a company’s profits is a complicated issue requiring different perspectives. For this reason we design two types of structural h-indices, derived from the International Patent Classification (IPC). In a case study we apply not only basic statistics but also a nested case-control methodology.

Findings

The resulting indicator values based on a large dataset (19,080 patents in total) from the pharmaceutical industry show that the new structural indices are significantly correlated with a firm’s profits.

Research limitations

The new structural index and the synthetic structural index have just been applied in one case study in the pharmaceutical industry.

Practical implications

Our study suggests useful implications for patentometric studies and leads to suggestions for different sized firms to include a healthy research and development (R&D) policy management. The structural h-index can be used to gauge the profits resulting from the innovative performance of a firm’s patent portfolio.

Originality/value

Traditionally, the breadth and depth of patents of a firm and their citations are considered separately. This approach, however, does not provide an integrated insight in the major characteristics of a firm’s patents. The Sh(Y) index, proposed in our investigation, can reflect a firm’s innovation activities, its technological breadth, and its influence in an integrated way.

Abstract

Purpose

In this contribution we try to find new indicators to measure characteristics of a firm’s patents and their influence on a company’s profits.

Design/methodology/approach

We realize that patent evaluation and influence on a company’s profits is a complicated issue requiring different perspectives. For this reason we design two types of structural h-indices, derived from the International Patent Classification (IPC). In a case study we apply not only basic statistics but also a nested case-control methodology.

Findings

The resulting indicator values based on a large dataset (19,080 patents in total) from the pharmaceutical industry show that the new structural indices are significantly correlated with a firm’s profits.

Research limitations

The new structural index and the synthetic structural index have just been applied in one case study in the pharmaceutical industry.

Practical implications

Our study suggests useful implications for patentometric studies and leads to suggestions for different sized firms to include a healthy research and development (R&D) policy management. The structural h-index can be used to gauge the profits resulting from the innovative performance of a firm’s patent portfolio.

Originality/value

Traditionally, the breadth and depth of patents of a firm and their citations are considered separately. This approach, however, does not provide an integrated insight in the major characteristics of a firm’s patents. The Sh(Y) index, proposed in our investigation, can reflect a firm’s innovation activities, its technological breadth, and its influence in an integrated way.

1 Introduction

The technological scope of a firm’s patents, as expressed by the number and nature of the classes to which these patents are assigned, is an important element to describe the relation between a company’s technological diversity and its profits (Chen, Jang, & Wen, 2010; Chiu, et al., 2010; Olivo et al., 2011). Indeed, research suggests that the scope of patents owned by a firm has a strong impact on performance and is, as such, an economically significant variable (Lerner, 1994; Reitzig, 2003).

As we want to take an international point of view we use the International Patent Classification (IPC) codes, but not American or European patent codes. Moreover, IPC codes have already been used in several other investigations (Chen, Jang, & Wen, 2010; Chiu et al., 2010; Lerner, 1994; Sapsalis, van Pottelsberghe de la Potterie, & Navon, 2006). Following these colleagues we use the number of 3- or 4-digit IPC codes assigned to a patent as a proxy of its technological breadth. Besides, the depth of a patent is also a structural element involved in a patent portfolio. Consider, for example, an IPC code such as “A61K-037”: the head 3 to 4 digits refer to a technological class and subclass (A61K), and the tail digits reflect the technological depth of the patent involved (037). This suggests that at the structural level, the breadth of patent is the primary structure, and the depth of a patent is the secondary one.

The ratio between the total number of codes (7- or 8-digit codes) used to describe patent p and the number of classes and subclasses, reflected by 3- or 4-digit codes, is called its technological depth, denoted as d(p). It is at least one and usually strictly larger than one. This indicator is not very precise because the number of 7- and 8-digit IPC codes is quite different per class (Lodh & Battaggion, 2014; Zhang, Chen, & Niu, 2012).

Generally, the broader the scope of a patent, the larger the number of competing products and processes that might infringe on the patent (Merges & Nelson, 1990). In this context, these authors pointed out that excessively broad patents may lead to use by other parties. Yet, Gilbert and Shapiro (1990) claimed that broader patents provide inventors with a greater ability to earn profits. As the competitive strength of a firm’s patents is an aspect of their market value, technological value, and social value, finding the optimal depth and breadth of a patent is a complex as well as a controversial topic (Guan & Gao, 2009; Hu & Rousseau, 2015; Hu, Rousseau, & Chen, 2012; Klemperer, 1990; Lee, 2009; Palokangas, 2011; Reitzig, 2003). We recall that, according to Gilbert and Shapiro (1990), the breadth of a patent is related to the flow of profits available to the patentee as well as to the minimum improvements that another inventor has to make in order to obtain a non-infringing patent. According to Lerner (1994) the market value of patents, sometimes even of a single patent, can have a major effect on the value of a firm. Exploring the optimal depth and breadth of a patent, researchers have increasingly recognized the importance to focus on the breadth of a patent (Denocolò, 1996; Kanniainen & Stenbacka, 2000; Merges & Nelson, 1990; Palokangas, 2011).

Continuing our research on the characteristics of the IPCh indicator (Hu & Rousseau, 2015) (its definition is recalled further on), the purpose of this contribution is:

  1. To show, using a large dataset, how the IPCh indicator for patents is able to provide information on a company’s innovative activities;

  2. To provide convincing evidence that the IPCh and the yearly h-index of patents are closely related to a firm’s innovative performance, and compare this with a synthetic indicator including the depth of a patent, based on companies in the pharmaceutical industry; and

  3. To provide a simple way to gauge a firm’s patent performance by jointly taking two h-type indices into account, each reflecting another aspect of the h-core in the lists of technological breadth and citations (reflecting market value and technological value).

As we are aware of the shortcomings of all h-type indices (Bouyssou & Marchant, 2011; Waltman & van Eck, 2012), we nevertheless claim that our approach is a useful addition to the patent toolbox. Moreover, no indicator on its own can provide information from all possible perspectives at the same time. Borrowing the terminology of Valiant (2013), proposed by him in the context of machine learning, the information provided by such an indicator is at best Probably Approximately Correct (PAC).

2 A Short Literature Review Related to the Concepts Used in This Contribution

2.1 The General h-index Idea

Hirsch (2005) proposed the h-index as an author-level indicator combining productivity (published articles) and impact (received citations). Soon his idea was applied to other source-items relations such as journal publications and citations (Braun, Glänzel, & Schubert, 2005), a company’s patent assignments and their citations in other patents (Guan & Gao, 2009), publications and citations of topics, restricted to recent years (Banks, 2006) or availability of books and their loans according to a library classification (Liu & Rousseau, 2009). We first recall the basic mechanism for calculating the h-index of an actor (author, company, or a journal). One considers a two-dimensional table of sources and items, where sources, e.g. publications or patents, are ranked according to items, e.g. received citations. Sources with the same number of items are given different rankings, but the exact order does not matter. Then actor A’s h-index is equal to the number h if the first h sources have each at least h items, while the source ranked h+1 has strictly less than h+1 items.

2.2 Patent Analysis

The relation between the breadth and depth of its patents on the one hand, and the health of a firm on the other, has been studied for several decades (Denicolò, 1996; O’Donoghue, Scotchmer, & Thisse, 1998; Palokangas, 2011; Prencipe, 2000; Wang & von Tunzelmann, 2000). Yet, no final answer about the optimal breadth and depth of patents has been found (Ozman, 2007; Zhang, Chen, & Niu, 2012; Lodh & Battaggion, 2014; Breschi, Lissoni, & Malerba, 2003). When using diversity indexes to measure the technological breadth and depth of a firm, it may happen that results are biased downwards for small and medium-sized firms for which the scale of technological activities is small (Chen, Jang, & Wen, 2010; Hu & Rousseau, 2015; Miller, 2006; Palokangas, 2011). Moreover, diversity indices such as the Rao-Stirling index may show cyclical patterns that are not related to a company’s profits but are rather related to the number of inventors (Leydesdorff, 2015). This suggests that if one wants to understand the optimal breadth and depth of patents, an approach different from the “complexity and diversity” might be worth investigating (Lodh & Battaggion, 2014; Wang & von Tunzelmann, 2000).

Traditionally, the breadth and depth of patents of a firm and their citations are considered separately. This approach, however, does not provide an integrated insight in the major characteristics of a firm’s patents. It has been observed that return on investment of a patent depends largely on a firm’s market value and its technological value, while the competitive strength of a firm’s patents bears a close relation to market value, technological value, social value of patents, and healthy management styles (Guan & Gao, 2009; Hu & Rousseau, 2015; Lee, 2009; Palokangas, 2011).

3 Methodology

We develop a new approach to gauge a firm’s innovative performance based on the following insights.

3.1 Potential Applications of Patents

We claim that one of the most important elements affecting the potential applications of a patent is its breadth, operationalized by codes, such as the IPC, the U.S. Patent Classification System (USPC), Cooperative Patent Classification (CPC) or the European Patent Office (EPO) codes assigned to it. This set of codes forms a basic aspect to grant its owner either a very limited right to exclusive use or a more general right covering a variety of different realizations of the invention (Reitzig, 2003). This fact implies that patents can differ with respect to the degree of protection afforded to an invention (Gilbert & Shapiro, 1990; Klemperer, 1990). In this context we note that accrediting codes to a patent is an arena in which patent examiners exercise wide discretion. In general, the broader the patent, the higher the chance to be applied in different practical fields and the larger the potential profits to the firm or a purchaser of the firm’s patent (Palokangas, 2011). This leads to the claim that the optimal breadth of patents should focus on a firm’s performance. Excessively broad patent claims increase the patentees’ non-market related risks from rivals and provide them with little flexibility to face unexpected situations (Merges & Nelson, 1990). However, the narrower a patent’s claims, the more the patentee may be victim of imitation as very similar products may lie outside the original patent’s claims (Denicolò, 1996; Kanniainen & Stenbacka, 2000).

A firm which focuses on excessively broad patents would overspend its research and development (R&D) capital by developing or buying an overly large number of patents. And, vice versa, if most of the firm’s patents are of narrow breadth, the firm reduces its chance to earn larger profits than competitors. Obviously, these two extreme cases do not lead to healthy management styles in a competitive industry. Therefore, it is very important to measure the competitive strength of patents and hence the “weight” of a firm’s patent portfolio. Such an investigation must include the number of patents, their impact and their breadth.

3.2 The Structure of Patents and Their Influence Must Jointly Be Taken into Account

It is well known that the received number of patent citations is an important indicator to measure the influence of a patent. Moreover, patent citations have a positive relation with the profits of the patent owner (Hu, Rousseau, & Chen, 2012; Trajtenberg, 1990).

Many investigations point out that, compared to the breadth of a patent (the primary dimension), it is less meaningful to focus on the depth of a patent because the determination of a patent’s depth is just approximate and no positive relation between a patent’s performance and its depth has been found (Gilbert & Shapiro, 1990; Kanniainen & Stenbacka, 2000; Klemperer, 1990; Lodh & Battaggion, 2014; Ozman, 2007; Palokangas, 2011; Reitzig, 2003; Zhang, Chen, & Niu, 2012).

Grönqvist (2009) argues that broader patents are not necessarily more valuable than narrower ones. Concretely, patents described with many codes do not necessarily lead to a larger profit for the firm. Therefore, neither the breath of patents nor the number of received citations on their own are clear-cut indicators for the value of a company’s patent portfolio. If we want to understand the competitive strength of a firm from the perspective of patent performance, the primary structure of patents (patent breadth), the secondary structure (patent depth), and their influence should jointly be taken into account in a multi-layered approach (Denicolò, 1996; Hu, Rousseau, & Chen, 2012; Palokangas, 2011). Abstractly, their relationships can be described with Equation (1):

SP=f(p,bp,dp,cp),
where SP denotes the competitive strength of patent-related performance of a firm, and p is the number of patents; bp denotes their breadth, dp their depth and cp the number of received citations.

3.3 The Structural h-index for Patents

To reveal the relation between the essential structure of patents and their competitive strength, e.g. profit performance, in the real world, and clarify the controversy on the influence of depth on a patent’s profit, we propose two types of structural h-indices for patents: (1) the structural h-index, a primary one, combining the number of patents with the primary structure (breadth of patent) and with forward, i.e. received, citations; (2) the synthetic structural h-index, using the number of patents, the breadth and depth of these patents, and the number of forward citations.

Hence, we hypothesize that the primary structure of patents (patent breadth) and their influence on a firm can be measured by a structural h-type index, combining different aspects in a dynamic way.

3.4 Definitions of IPCh and Yearly h-index

A firm’s innovation activities are operationalized as the number of patents, while their technological breadth is operationalized by the number of 3- or 4-digit IPC codes. Consider a set of patents granted to a firm in a certain year Y, ranked in decreasing order of the number of 3- or 4-digit IPC codes assigned to them. Then the IPC h-index of this firm in the year Y is equal to q if q is the highest rank such that the first q patents are assigned to at least q IPC codes (Hu & Rousseau, 2015). The resulting indicator is denoted as IPCh3 or IPCh4 depending on the number of digits that have been used.

Next, we define a yearly h-index slightly modified from the original meaning of Hirsch (2005) to map a firm’s innovation activities and influence in the year Y. The yearly h-index of a firm in the year Y, denoted as hY, is equal to h if h is the largest rank such that the first h patents receive each at least h citations within a given citation window. In the examples investigated below the citation windows always end on May 20, 2014.

3.5 Definition of the Patent Depth Yearly h-index (DhY)

Next, we define the yearly h-index of patent depth in the year Y, denoted as DhY as follows. Consider the set of patents granted to a firm in the year Y, ranked in decreasing order of their technological depth index, d(p). The DhY index of this firm in the year Y is equal to k if k is the highest rank such that the first k patents have at least a technological depth equal to k.

3.6 The Structural h-index for Patents

We define the structural h-index for patents granted in the year Y, denoted as Sh(Y), as a combination, actually a multiplication, of the IPCh and the yearly patent h-index. Hence Sh(Y) can be calculated with Equation (2):

Sh(Y)=IPChs×hY,

where s = 3 or 4. Moreover, although not indicated in the notation, Sh(Y) is time dependent, i.e. depends on the citation window, which in our examples ends on May 20, 2014. The Sh(Y) sequence shows a firm’s innovation activities and their technological breadth, as well as the influence of patents (by citations) in each year. As such we claim that it can be used to gauge the “primary weight” of a firm’s patents. This claim is investigated in the next section.

3.7 The Synthetic Structural h-index for Patents

Finally, we define the synthetic structural h-index for patents granted in the year Y, denoted as SSh(Y), as a summary indicator constructed from the IPCh, the yearly patent h-index (hy), and the patent depth yearly h-index and it can be calculated with Equation (3):

SSh(Y)=w1IPChs+w2hy+w3Dhy,

where w1, w2 and w3 are positive weights such that w1 + w2 + w3 = 1.

4 An Application and an Empirical Study in the Pharmaceutical Industry

We recall that the pharmaceutical industry is a high-tech industry in which a firm’s performance (and profit) is closely connected to the market value of its patents (Hu, Rousseau, & Chen, 2012; Chen, Shih, & Chang, 2013). Therefore, the pharmaceutical field is a good test bed to study the practical value of the new indicators Sh(Y) and SSh(Y). We intend to find out if these two indicators are indeed able, as we hypothesize, to detect the “weight” of a firm’s patents through their relation to a firm’s profits.

4.1 Choice of Firms

The general range of firms acceptable for our purposes contains those pharmaceutical companies listed in Fortune 500 2006–2010 issued by the CNNMoney website. These companies are the primary focus of our investigation, because yearly ranks for “pharmaceutical industry” are available during these years.

As there are many invisible factors affecting the performance of patents, we try to control for external variables by considering the following criteria for inclusion in our case study.

  1. Firm location: Different countries have different regulations for patents which may influence realized profits (Chen, Shih, & Chang, 2013). For this reason only US companies were selected.

  2. Firm internationality: Prior literature has found that there is a significant effect of firm scale on profits (Chen, Jang, & Wen, 2010). Accordingly, only US-based multinational firms included in Fortune 500 qualify.

  3. Firm age: It has been shown that, in terms of innovation activities, older firms have a stronger foundation than younger ones. Hence, a firm’s age influences the outcome of its patents’ performance. For this reason we included only firms founded before the year 1990 (Banerjee & Cole, 2010; McMillan & Thomas, 2005).

  4. Patent age: As the time between applying for a pharmaceutical patent and its return on investment is generally between 8 and 12 years, with 5 years as a strict minimum (ISTIS, 2003), and the protection period given by a patent is at most 20 years (WIPO, 2000), care must be exerted to take these facts into account (Chen, Jang, & Wen, 2010; Hu, Rousseau, & Chen, 2012). For this reason, we included only patents granted during the period 1990–2005, and considered profits reported by Fortune 500 for the period 2006–2010.

Taking all these requirements into account resulted in eight US-based multinational pharmaceutical companies meeting all the criteria, namely Johnson & Johnson, Pfizer, Merck, Bristol-Myers Squibb, Amgen, Genzyme, Allergan and Biogen Idec.

4.2 Data Collection and Processing

We extracted from the Derwent Innovations Index (DII) all patents granted to these eight companies during the period 1990 – 2005. For each record we downloaded all fields, including IPC-codes and citations received (so-called forward citations). Data were extracted on 20/05/2014. This led to a total of 19,080 patents for the eight firms. Next, we collected the yearly profits for each company as reported by Fortune 500 2006–2010.

For the dataset of a company’s patents, we first counted the number of 4-digit IPC codes for each record via a simple program written by ourselves, and determined the yearly IPCh and yearly h-index during 1990–2005 for each company (Appendix Tables A1A3). Then, we calculated the yearly Sh(Y) and yearly SSh(Y) for each firm according to Equations (2) and (3). As the breadth of a patent is a primary structure while its depth is a secondary one, and because research suggests that both breadth and number of citations have positive relations with the profits of the patent owner, we take all these factors into account. Moreover, as previous research pointed out that 4-digit codes and citation-weighted counts can be taken as “patent-equivalents” (Miller, 2006), we – tentatively – weighted them higher than DhY according to a weight of 0.4 for IPCh and for hY, and a weight of 0.2 for Dhy in Equation (3) (Appendix Table A4).

To compare results based on 3-digit IPC codes with those based on 4-digit codes, we also collected the number of 3-digit codes for each patent (Appendix Tables A2 and A3), and calculated the corresponding Sh index.

4.3 Statistical Methods

To observe the relationship between the Sh(Y) and a firm’s profits, we use two different statistical methods:

  1. We calculated the Spearman rank correlation coefficient between the eight companies, mean Sh(Y) and mean SSh(Y) values and total profits over the period from 2006 to 2010.

  2. A nested case-control (NCC) study. This type of study is an observational study whereby a case-control approach is employed within an established cohort (Bornehag et al., 2004). This is a popular and valid approach in medical studies for small-sample investigations. As such we consider it also suitable to our study. The nested case control model as applied in medical investigations is less expensive, but less efficient than a full-cohort analysis. However, it has been shown that with four controls per case and/or stratified sampling of controls, relatively little efficiency may be lost (Goldstein & Zhang, 2009).

To apply the NCC method, the eight companies are grouped according to their profits: Group H (high profit) consists of the four companies with the highest profit; Group L (low profit) consists of the four companies with the lowest profits. For each group, we re-rank companies by their profits in a descending way and denote them GHR1, GHR2, GHR3, GHR4, GLR1, GLR2, GLR3, and GLR4 (Table 1). In this way, case-control is performed between four control-pairs of companies with the same rank order in the respective groups (such as GHR1 vs GLR1), and the nested control is designed by a sequence of time points, that is, yearly Sh and yearly SSh among controlled cases between two groups during the period 1990–2005. Hence, 16 time points in total are used as observations. We recall that the Sh(Y) indicator is time dependent. For example, in our case, the Sh(Y) of the year 1990 has a citation window from the year 1990 to May 20, 2014, and the Sh(Y) in the year 1991 has a citation window from the year 1991 to May 20, 2014, and so on. As pointed out above, such a stratified sampling of controls can lead to an efficient result.

Table 1

Controlled cases design for companies included in NCC study.

Note. Profits 2006–2010 in millions of US dollars (average per year).

Group HGroup L


CompanyCodeProfitsRankCompanyCodeProfitsRank
Johnson & JohnsonGHR111,451.001AmgenGLR13,718.201
PfizerGHR210,461.002Biogen IdecGLR2554.102
MerckGHR36,610.023AllerganGLR3395.243
Bristol-Myers SquibbGHR44,521.804GenzymeGLR4349.724

Then, we compare the yearly Sh and yearly SSh for each company during the period 1990–2005 between two groups using a Paired Samples Test, where pairs consist of a company from GH and a corresponding company from GL, as a so-called ‘control.’

4.4 Results

In this section, we present the results obtained from our analysis of the 19,080 patents. We will show that the two types of structural h-indices Sh(Y) and SSh(Y) have significant correlations with a firm’s profits as given by Fortune 500 2006–2010. Moreover, the Sh(Y) index has more significance than SSh(Y).

4.4.1 Yearly Values of Sh for Eight Companies during 1990–2005

Tables 2 and 3 show the resulting yearly Sh values. We would like to point out that the rank order of these eight companies is different from those obtained from the IPCh and from the h-indices separately (Appendix Tables A1A3). We consider Sh to represent the primary competitive strength of a firm’s patents.

Table 2

Yearly Sh indices of eight companies during the period 1990–2005 (using IPCh4).

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
1990192161150853214412
199117414418613872010012
199214516222410040110020
19932241322561253517612
199421715024018278308535
19952401082401628449235
19963281202801568448484
1997312140264138128309570
1998280174280174120667090
199924019627219278355696
200020324020020398706490
20011892082081861206013078
20022732522402081409111560
20032341753331891365610860
2004210132296189105669066
2005288108270114915610230
Mean234.31162.63246.19158.8190.0635.6988.1953.13
Rank23145867

Table 3

Yearly Sh indices of eight companies during the period 1990–2005 (using IPCh3).

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
19901609210068241338
1991145120155923608012
1992116108160803018015
199316088192100211578
199415510018010439185121
1995150541501085646921
1996246961751045646356
1997234801989264245756
199820011617511675444260
199916011220412852214264
200014515015011670564860
200113510413012460407852
200219514018013070526940
200315610022213585407240
20041508822210860447244
2005216722109565406815
Mean170.19101.25175.19106.2553.9424.37561.3135.75
Rank24136857

4.4.2 Yearly Values of SSh for Eight Companies during 1990–2005

Table 4 shows the yearly values of the synthetic structural h-indices for eight companies. Note that SSh(Y) combines the IPCh, the yearly patent h-index, and the yearly h-index of patent depth. Therefore, it reflects the first ranked patents in three essential dimensions. We may say that SSh(Y) represents the essential competitive strength of a firm’s patents. It turns out that the ranks of the mean SSh(Y) for eight companies are very similar to those according to Sh(Y). Only the first and the second company change places.

Table 4

Yearly SSh indices of eight companies during the period 1990–2005 (using IPCh4).

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
199015.811.39613.49.45.41.06.43.2
199114.811.81215.812.47.80.010.83.2
199214.412.74016.810.66.41.010.64.2
199316.210.83617.212.85.61.010.03.2
199415.812.18817.214.08.44.89.45.4
199516.08.80416.414.28.61.811.65.4
199620.411.85218.413.68.81.810.68.8
199719.610.04417.612.810.85.010.48.4
199820.414.00418.214.810.47.48.29.4
199920.213.54417.816.48.65.28.010.0
200016.214.65614.415.69.68.48.69.8
200115.613.36415.016.010.47.213.08.8
200219.214.02416.615.611.29.012.07.4
200315.012.87620.015.011.66.610.47.6
200416.011.34419.615.010.27.610.08.0
200518.89.86817.211.29.66.810.05.2
Mean17.1512.08516.97513.7138.9634.663106.75
Rank14236857

4.4.3 Correlations between Sh and SSh and a Firm’s Profits

Table 5 shows the rank correlations between yearly Sh(Y) and yearly SSh(Y) and firms’ profits for the eight pharmaceutical companies under study. The Sh and SSh values refer to the years 1990–2005, and firms’ profits refer to the period, 2006–2010. The Spearman rank correlation coefficient between the yearly Sh and a firm’s profits is 0.857 (p = 0.007) when using IPCh4, and is 0.762 (p = 0.028) calculated by IPCh3. These results mean that the correlations can be described as “very strong”. We note that Sh(Y) based on IPCh4 has the higher correlation with profits. Moreover, the Spearman rank correlation coefficient between the yearly SSh (using IPCh4) and a firm’s profits is 0.810 (p = 0.015). This value can also be described as “very strong”.

Table 5

Correlations among yearly Sh and yearly SSh on the one hand and a firm’s profits on the other.

Note.

CompanyProfits 2006–2010 millions of US dollars (Average)Rank profits 2006–2010Yearly ShYearly SSh

Using IPCh4Using IPCh3



Yearly Sh (Mean)Rank ShYearly Sh (Mean)Rank ShYearly SSh (Mean)Rank SSh
Johnson & Johnson11,451.001234.312170.19217.151
Pfizer10,461.002162.633101.25412.094
Merck6,610.023246.191175.19116.982
Bristol-Myers Squibb4,521.804158.814106.25313.713
Amgen3,718.20590.06653.9468.966
Biogen Idec554.10635.69824.3684.668
Allergan395.24788.19561.31510.005
Genzyme349.72853.13735.7576.757
Spearman correlation0.857**0.762*0.810*

4.4.4 Differences of Yearly Sh and SSh Indices of Firms between Two Different Profit Groups

Tables 6 and 7 present the results of a longitudinal observation combined with a nested case-control design. Obviously, the yearly Sh and SSh indices of firms in Group HP are much bigger than those in Group LP during the period 1990–2005; these differences are significant. We note that the same statistical significances of paired differences are valid for results of Sh indices as well as for SSh indices.

Table 6

Results of paired differences tests of firms’ yearly Sh between Group H and Group L (based on IPCh4).

Paired differences95% confidence interval of the difference


Pairs-ShMeanStd. DeviationLowerUppert-valuedfSig. (2-tailed)
GHR1 - GLR1144.25045.918119.782168.71812.566150.000
GHR2 - GLR2126.93834.555108.524145.35114.694150.000
GHR3 - GLR3158.00046.286133.336182.66413.654150.000
GHR4 - GLP4105.68826.63091.497119.87815.875150.000

Table 7

Results of paired differences tests of firms’ yearly SSh between Group H and Group L (based on IPCh4).

Paired differences95% confidence interval of the difference


Pairs-SShMeanStd. DeviationLowerUppert-valuedfSig. (2-tailed)
GHR1 - GLR18.1882.3316.945609.42914.052150.000
GHR2 - GLR27.4222.7005.983298.86110.996150.000
GHR3 - GLR36.9752.2135.796028.15412.610150.000
GHR4 - GLR46.9631.5706.125867.79917.738150.000

Figure 1 shows average profit values as a function of average Sh(Y) values (using IPCh4). As the Pearson correlation R is about 0.83, the rank correlation of Table 2 as well as the results shown in Table 5 are logical consequences of this relation. Note that, although this figure consists of just eight points, each of them is the result of thousands of values.

Figure 1

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Figure 1

Functional relation between the Sh(Y) values and profits.

Citation: Journal of Data and Information Science 1, 1; 10.20309/jdis.201603

5 Discussion and Conclusions

In many scientific fields, it is difficult to collect large samples to perform an “ideal” real-world investigation. Therefore, special approaches are developed and carefully designed for small samples. In this contribution we included a nested case-control approach, a method often used in the medical sciences, and applied it to improve the methodology used in patent research. By way of discussion we address the following issues.

5.1 The New Sh(Y) Index Indicates the Primary Competitive Strength of a Firm’s Patent Portfolio

Compared to the case of IPCh3, Sh based on IPCh4 can better indicate a firm’s innovative activities, measured through patents, as well as their technological breadth, and map the potential market value of patents. Instead of the yearly h-indices which may represent a firm’s innovation activities and their influence, the Sh(Y) index, proposed in our investigation, can reflect a firm’s innovation activities, its technological breadth, and its influence in an integrated way. As such the new index reflects the primary structure of a firm’s patents and their influence and is an indicator for the “weight” related to primary competitive strength of a firm’s patent portfolio (with significant correlation to a firm’s profits).

5.2 The Breadth of Patent is a Primary Structure Affecting Its Performance

Although SSh(Y) is a comprehensive indicator for the “weight” of the essential, competitive strength of a firm’s patent portfolio (including the depth of patents), and although the relation between SSh(Y) and a firm’s profits is also significant, it does not have the same “strong” correlation as the Sh(Y) index does, which suggests that the breadth of a patent is the primary structure affecting a patent performance. The depth of a patent plays a smaller role in a firm’s profit. The Spearman rank correlation coefficient between the yearly Dh and a firm’s profits is 0.690 (p = 0.058), while this correlation between the yearly average depth of patents and a firm’s profits is -0.024, and hence is not significant (Appendix Tables A5 and A7).

5.3 The h-core Reflects Market Value and Technological Value

The first h items in a firm’s patent list, known as its h-core, reflect market value and technological value. These core patents are closely related to the competitive strength of a company. Although there are multiple dimensions involved in the innovative performance of a firm, the core competitive strength of a company is highly dependent on the performance of patents (Hagedoorn & Cloodt, 2003), one aspect being that patents are transferable, so that the patent assignee benefits in monetary terms from their purchase (Lee, 2009; Palokangas, 2011).

Our work further leads to the suggestion to different sized firms to include policymaking on technological innovation in its management. This is because there is always a limited R&D capital in a company. Indeed, we also found out that the Spearman correlation coefficient between the yearly average number of 4-digit codes of patents and a firm’s profits is even negative (namely –0.310, Appendix Tables A6 and A7), suggesting that a firm’s profits are highly dependent on the first h items of a firm’s patents rather than the “average patent” (Palokangas, 2011; Reitzig, 2003). The fact that a small group of patents essentially determines the competitive strength of a company is yet another example of the law of the vital few, also known as the 80–20 rule. In this sense, we claim that the structural h-index proposed in this study will be beneficial for modelling an optimal patent system.

Patent evaluation is a complicated issue which requires taking a full picture from different perspectives. This preliminary study proposes a new and simple indicator for gauging a company’s patent portfolio. Positive results are backed by evidence based on a large dataset from the pharmaceutical industry. Of course, we are aware that this is just a case study and, moreover, that any R&D indicator is at best PAC, as put forward in the case of citation indicators by Rousseau (2016). We are convinced though that the structural h-index is a useful addition to the field of patentometrics.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos: 71173185 and 71573225). The authors thank Jiancheng Guan (Professor in innovation policy at the University of the Chinese Academy of Sciences) and Yi Shen (Professor in medical statistics at Zhejiang University) for helpful discussions. We also thank Chaoyang Zhu for programming and Hui Jiang for help in data collection. Finally, we thank the reviewers for helpful suggestions leading to an improved manuscript.

Author Contributions: X. J. Hu (xjhu@zju.edu.cn) proposed the research idea, planned and designed the outline, carried out the data collection and data analysis, and wrote the first draft. R. Rousseau (ronald.rousseau@kuleuven.be, corresponding author) revised the plan and outline, joined discussion of the findings and contributed to writing the paper and its revision after review.

References

  • Banerjee, P.M., & Cole, B. M. (2010). Breadth-of-impact frontier: How firm-level decisions and selection environment dynamics generate boundary-spanning inventions. Technovation, 30(7), 411–419.

  • Banks, M.G. (2006). An extension of the Hirsch index: Indexing scientific topics and compounds. Scientometrics, 69(1), 161–168.

  • Bornehag, C.G., Sundell, J., Weschler, C.J., Sigsgaard, T., Lundgren, B., Hasselgren, M., & Hägerhed-Engman, L. (2004). The association between asthma and allergic symptoms in children and phthalates in house dust: A nested case-control study. Environmental Health Perspectives, 112(14), 1393–1397.

  • Bouyssou, D., & Marchant, T. (2011). Ranking scientists and departments in a consistent manner. Journal of the American Society for Information Science and Technology, 62(9), 1761–1769.

  • Braun, T., Glänzel, W., & Schubert, A. (2005). A Hirsch-type index for journals. The Scientist, 19(22), 8.

  • Breschi, S., Lissoni, F., & Malerba, F. (2003). Knowledge-relatedness in firm technological diversification. Research Policy, 32(1), 69–87.

  • Chen, J.H., Jang, S.L., & Wen, S.H. (2010). Measuring technological diversification: Identifying the effects of patent scale and patent scope. Scientometrics, 84(1), 265–275.

  • Chen, Y.S., Shih, C.Y., & Chang, C.H. (2013). Patents and market value in the U.S. pharmaceutical industry: new evidence from threshold regression. Scientometrics, 97(2), 161–176.

  • Chiu, Y.C., Lai, H.C., Liaw, Y.C., & Lee, T.Y. (2010). Technological scope: Diversified or specialized. Scientometrics, 82(1), 37–58.

  • Denicolò, V. (1996). Patent races and optimal patent breadth and length. Journal of Industrial Economics, 44(3), 249–265.

  • Gilbert, R., & Shapiro, C. (1990). Optimal patent length and breadth. RAND Journal of Economics, 21(1), 106–112.

  • Goldstein, L., & Zhang, H.M. (2009). Efficiency of the maximum partial likelihood estimator for nested case control sampling. Bernoulli, 15(2), 569–597.

  • Grönqvist, C. (2009). The private value of patents by patent characteristics: Evidence from Finland. Journal of Technology Transfer, 34(2), 159–168.

  • Guan, J.C., & Gao, X. (2009). Exploring the h-index at patent level. Journal of the American Society for Information Science and Technology, 60(1), 35–40.

  • Hagedoorn, J., & Cloodt, M. (2003). Measuring innovative performance: Is there an advantage in using multiple indicators? Research Policy, 32(8), 1365–1379.

  • Hirsch, J.E. (2005). An index to quantify an individual’s scientific research output. Proceedings of the National Academy Sciences of the United States of America, 102(46), 16569–16572.

  • Hu, X.J., & Rousseau, R. (2015). A simple approach to describe a company’s innovative activities and their technological breadth. Scientometrics, 102(1), 1401–1411.

  • Hu, X.J., Rousseau, R., & Chen, J. (2012). A new approach for measuring the value of patents based on structural indicators for ego patent citation networks. Journal of the American Society for Information Science and Technology, 63(9), 1834–1842.

  • ISTIS: Institute of Scientific & Technical Information of Shanghai (2003). Feature analysis on global pharmaceutical industry 2002–2003, small change in the periodic R&D. Retrieved on August 20, 2012, from http://www.istis.sh.cn/list/list.aspx?id=3958 (in Chinese).

  • Kanniainen, V., & Stenbacka, R. (2000). Endogenous imitation and implications for technology policy. Journal of Institutional and Theoretical Economics, 156(2), 360–381.

  • Klemperer, P. (1990). How broad should the scope of patent protection be? RAND Journal of Economics, 21(1), 113–130.

  • Lee, Y.G. (2009). What affects a patent’s value? An analysis of variables that affect technological, direct economic, and indirect economic value: An exploratory conceptual approach. Scientometrics, 79(3), 627–637.

  • Lerner, J. (1994). The importance of patent scope: an empirical analysis. RAND Journal of Economics, 25(2), 319–333.

  • Leydesdorff, L. (2015). Can technology life-cycles be indicated by diversity in patent classifications? The crucial role of variety. Scientometrics, 105(3), 1441–1451.

  • Liu, Y.X., & Rousseau, R. (2009). Properties of Hirsch-type indices: The case of library classification categories. Scientometrics, 79(2), 235–248.

  • Lodh, S., & Battaggion, M.R. (2014). Technological breadth and depth of knowledge in innovation: The role of mergers and acquisitions in biotech. Industrial and Corporate Change, 24(2), 383–415.

  • McMillan, G.S., & Thomas, P. (2005). Financial success in biotechnology: Company age versus company science. Technovation, 25(5), 463–468.

  • Merges, R.P., & Nelson, R.R. (1990). On the complex economics of patent scope. Columbia Law Review, 90(4), 839–916.

  • Miller, D.J. (2006). Technological diversity, related diversification, and firm performance. Strategic Management Journal, 27(7), 601–619.

  • O’Donoghue, T., Scotchmer, S., & Thisse, J.F. (1998). Patent breadth, patent life, and the pace of technological progress. Journal of Economics & Management Strategy, 7(1), 1–32.

  • Olivo, C., Lebedeva, I., Chu, C.Y., Lin, C.Y., & Wu, S.Y. (2011). A patent analysis on advanced biohydrogen technology development and commercialisation: Scope and competitiveness. International Journal of Hydrogen Energy, 36(21), 14103–14110.

  • Ozman, M. (2007). Breadth and depth of main technology fields: An empirical investigation using patent data. Middle East Technical University Working Paper, 2007.

  • Palokangas, T. (2011). Optimal patent length and breadth in an economy with creative destruction and non-diversifiable risk. Journal of Economics, 102(1), 1–27.

  • Prencipe, A. (2000). Breadth and depth of technological capabilities in CoPS: The case of the aircraft engine control system. Research Policy, 29(7–8), 895–911.

  • Reitzig, M. (2003). What determines patent value? Insights from the semiconductor industry. Research Policy, 32(1), 13–16.

  • Rousseau, R. (2016). Citation data as a proxy for quality or scientific influence are at best PAC (Probably Approximately Correct). Journal of the Association for Information Science and Technology (to appear); DOI: 10.1002/asi.23525.

  • Sapsalis, E, van Pottelsberghe de la Potterie, B., & Navon, R. (2006). Academic versus industry patenting: An in-depth analysis of what determines patent value. Research Policy, 35(10), 1631–1645.

  • Trajtenberg, M. (1990). A penny for your quotes: Patent citations and the value of inventions. Rand Journal of Economics, 21(1), 172–187.

  • Valiant, L. (2013). Probably Approximately Correct. New York: Basic Books.

  • Waltman, L., & van Eck, N.J. (2012). The inconsistency of the h-index. Journal of the American Society for Information Science and Technology, 63(2), 406–415.

  • Wang, Q., & von Tunzelmann, N. (2000). Complexity and the functions of the firm: Breadth and depth. Research Policy, 29(7–8), 805–818.

  • WIPO (2000). Patent law treaty, available at http://www.wipo.int/treaties/en/ip/plt/ (last visited on 2016, February 20).

  • Zhang, G.P., Chen, X.D., & Niu, X. (2012). The technology complexity based on patent width and depth (in Chinese). Science Research Management, 33(3), 113–135.

Appendix A

Table A1

Yearly h-indices for eight companies during the period 1990–2005.

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
19903223251781114
199129243123120204
199229273220101205
19933222322571194
199431253026136177
199530183027142237
1996412435261422114
1997392033231661914
19984029352915111415
1999402834321371416
20002930252914141615
20012726263112102613
20023928302614132310
2003262537271781810
20043022372715111811
200536183019138175

Table A2

Yearly IPCh4 for eight companies during the period 1990–2005.

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
199067654143
199166666053
199256754154
199376855143
199476876555
199586866245
199685866246
199787868555
199876868656
199967866546
200078877546
2001788610656
2002798810756
200397978766
200476877656
200586967766

Table A3

Yearly IPCh3 for eight companies during the period 1990–2005.

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
199054443132
199155543043
199244543143
199354643132
199454643333
199553544233
199664544234
199764644434
199854545434
199944644334
200055645434
200154545434
200255655434
200364655544
200454644444
200564755543

Table A4

The yearly h-index of patent depth (Dhy) for eight companies during the period 1990–2005.

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
199036533122
199146543042
199245634133
199335644142
1994361044233
199544653143
199646644134
199745666344
199886546335
199996565246
200097666437
2001108768436
2002487108545
200358878346
200467877446
200568868444

Table A5

Yearly average depth of patents (average dad) for eight companies during the period 1990–2005.

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
19901.502.491.791.772.044.221.442.29
19911.722.531.671.762.810.001.802.13
19921.592.351.931.672.862.831.482.39
19931.632.591.861.793.942.281.792.52
19941.522.472.581.703.712.531.622.00
19951.802.012.012.042.101.661.742.01
19961.782.632.011.752.293.631.662.85
19971.672.611.951.822.652.892.072.40
19982.223.012.011.733.152.821.533.18
19992.242.862.082.122.892.412.172.72
20002.383.142.222.402.933.331.683.44
20012.743.412.262.562.473.541.683.05
20021.693.062.333.343.653.182.032.30
20031.773.192.462.733.502.421.812.69
20041.932.862.652.483.992.781.992.57
20052.0162.672.642.313.963.012.002.01
Mean1.8872.7432.1532.1233.0592.7211.7812.543
Rank72561384

Table A6

Yearly average number of 4-digit IPC codes (ave IPC-4 codes) of patents for eight companies during the period 1990–2005.

YearJohnson & JohnsonPfizerMerckBristol-Myers SquibbAmgenBiogen IdecAllerganGenzyme
19902.852.812.832.763.469.002.582.67
19913.142.922.952.864.470.002.514.00
19922.372.603.002.723.636.002.843.91
19932.992.862.752.754.087.001.972.55
19942.982.752.722.974.176.002.544.07
19953.192.893.063.024.397.502.503.50
19963.522.943.072.834.086.501.943.57
19973.433.502.942.744.926.602.503.67
19982.603.603.122.594.645.562.363.08
19992.333.623.312.613.884.362.433.23
20002.963.783.473.144.084.572.183.49
20013.073.783.523.085.624.722.163.17
20022.783.723.743.556.064.742.433.57
20032.263.423.673.334.995.912.713.12
20042.912.973.483.044.664.512.563.29
20052.912.703.763.023.934.822.763.42
Mean2.893.183.212.944.445.492.443.39
Rank75462183

Table A7

Correlations among yearly average IPC-4 codes and yearly average dad of patents and a firm’s profits.

CompanyRank profits 2006–2010Yearly average IPC-4 codesYearly average dad


MeanRankMeanRank
Johnson & Johnson12.8971.8877
Pfizer23.1852.7432
Merck33.2142.1535
Bristol-Myers Squibb42.9462.1236
Amgen54.4423.0591
Biogen Idec65.4912.7213
Allergan72.4481.7818
Genzyme83.3932.5434
Spearman correlation–0.310–0.024

Footnotes

http://money.cnn.com/magazines/fortune/fortune500/

**

Correlation is significant at the 0.01 level (2-tailed);

*

Correlation is significant at the 0.05 level (2-tailed).

*

Correlation is significant at the 0.05 level (2-tailed).

Banerjee, P.M., & Cole, B. M. (2010). Breadth-of-impact frontier: How firm-level decisions and selection environment dynamics generate boundary-spanning inventions. Technovation, 30(7), 411–419.

Banks, M.G. (2006). An extension of the Hirsch index: Indexing scientific topics and compounds. Scientometrics, 69(1), 161–168.

Bornehag, C.G., Sundell, J., Weschler, C.J., Sigsgaard, T., Lundgren, B., Hasselgren, M., & Hägerhed-Engman, L. (2004). The association between asthma and allergic symptoms in children and phthalates in house dust: A nested case-control study. Environmental Health Perspectives, 112(14), 1393–1397.

Bouyssou, D., & Marchant, T. (2011). Ranking scientists and departments in a consistent manner. Journal of the American Society for Information Science and Technology, 62(9), 1761–1769.

Braun, T., Glänzel, W., & Schubert, A. (2005). A Hirsch-type index for journals. The Scientist, 19(22), 8.

Breschi, S., Lissoni, F., & Malerba, F. (2003). Knowledge-relatedness in firm technological diversification. Research Policy, 32(1), 69–87.

Chen, J.H., Jang, S.L., & Wen, S.H. (2010). Measuring technological diversification: Identifying the effects of patent scale and patent scope. Scientometrics, 84(1), 265–275.

Chen, Y.S., Shih, C.Y., & Chang, C.H. (2013). Patents and market value in the U.S. pharmaceutical industry: new evidence from threshold regression. Scientometrics, 97(2), 161–176.

Chiu, Y.C., Lai, H.C., Liaw, Y.C., & Lee, T.Y. (2010). Technological scope: Diversified or specialized. Scientometrics, 82(1), 37–58.

Denicolò, V. (1996). Patent races and optimal patent breadth and length. Journal of Industrial Economics, 44(3), 249–265.

Gilbert, R., & Shapiro, C. (1990). Optimal patent length and breadth. RAND Journal of Economics, 21(1), 106–112.

Goldstein, L., & Zhang, H.M. (2009). Efficiency of the maximum partial likelihood estimator for nested case control sampling. Bernoulli, 15(2), 569–597.

Grönqvist, C. (2009). The private value of patents by patent characteristics: Evidence from Finland. Journal of Technology Transfer, 34(2), 159–168.

Guan, J.C., & Gao, X. (2009). Exploring the h-index at patent level. Journal of the American Society for Information Science and Technology, 60(1), 35–40.

Hagedoorn, J., & Cloodt, M. (2003). Measuring innovative performance: Is there an advantage in using multiple indicators? Research Policy, 32(8), 1365–1379.

Hirsch, J.E. (2005). An index to quantify an individual’s scientific research output. Proceedings of the National Academy Sciences of the United States of America, 102(46), 16569–16572.

Hu, X.J., & Rousseau, R. (2015). A simple approach to describe a company’s innovative activities and their technological breadth. Scientometrics, 102(1), 1401–1411.

Hu, X.J., Rousseau, R., & Chen, J. (2012). A new approach for measuring the value of patents based on structural indicators for ego patent citation networks. Journal of the American Society for Information Science and Technology, 63(9), 1834–1842.

ISTIS: Institute of Scientific & Technical Information of Shanghai (2003). Feature analysis on global pharmaceutical industry 2002–2003, small change in the periodic R&D. Retrieved on August 20, 2012, from http://www.istis.sh.cn/list/list.aspx?id=3958 (in Chinese).

Kanniainen, V., & Stenbacka, R. (2000). Endogenous imitation and implications for technology policy. Journal of Institutional and Theoretical Economics, 156(2), 360–381.

Klemperer, P. (1990). How broad should the scope of patent protection be? RAND Journal of Economics, 21(1), 113–130.

Lee, Y.G. (2009). What affects a patent’s value? An analysis of variables that affect technological, direct economic, and indirect economic value: An exploratory conceptual approach. Scientometrics, 79(3), 627–637.

Lerner, J. (1994). The importance of patent scope: an empirical analysis. RAND Journal of Economics, 25(2), 319–333.

Leydesdorff, L. (2015). Can technology life-cycles be indicated by diversity in patent classifications? The crucial role of variety. Scientometrics, 105(3), 1441–1451.

Liu, Y.X., & Rousseau, R. (2009). Properties of Hirsch-type indices: The case of library classification categories. Scientometrics, 79(2), 235–248.

Lodh, S., & Battaggion, M.R. (2014). Technological breadth and depth of knowledge in innovation: The role of mergers and acquisitions in biotech. Industrial and Corporate Change, 24(2), 383–415.

McMillan, G.S., & Thomas, P. (2005). Financial success in biotechnology: Company age versus company science. Technovation, 25(5), 463–468.

Merges, R.P., & Nelson, R.R. (1990). On the complex economics of patent scope. Columbia Law Review, 90(4), 839–916.

Miller, D.J. (2006). Technological diversity, related diversification, and firm performance. Strategic Management Journal, 27(7), 601–619.

O’Donoghue, T., Scotchmer, S., & Thisse, J.F. (1998). Patent breadth, patent life, and the pace of technological progress. Journal of Economics & Management Strategy, 7(1), 1–32.

Olivo, C., Lebedeva, I., Chu, C.Y., Lin, C.Y., & Wu, S.Y. (2011). A patent analysis on advanced biohydrogen technology development and commercialisation: Scope and competitiveness. International Journal of Hydrogen Energy, 36(21), 14103–14110.

Ozman, M. (2007). Breadth and depth of main technology fields: An empirical investigation using patent data. Middle East Technical University Working Paper, 2007.

Palokangas, T. (2011). Optimal patent length and breadth in an economy with creative destruction and non-diversifiable risk. Journal of Economics, 102(1), 1–27.

Prencipe, A. (2000). Breadth and depth of technological capabilities in CoPS: The case of the aircraft engine control system. Research Policy, 29(7–8), 895–911.

Reitzig, M. (2003). What determines patent value? Insights from the semiconductor industry. Research Policy, 32(1), 13–16.

Rousseau, R. (2016). Citation data as a proxy for quality or scientific influence are at best PAC (Probably Approximately Correct). Journal of the Association for Information Science and Technology (to appear); DOI: 10.1002/asi.23525.

Sapsalis, E, van Pottelsberghe de la Potterie, B., & Navon, R. (2006). Academic versus industry patenting: An in-depth analysis of what determines patent value. Research Policy, 35(10), 1631–1645.

Trajtenberg, M. (1990). A penny for your quotes: Patent citations and the value of inventions. Rand Journal of Economics, 21(1), 172–187.

Valiant, L. (2013). Probably Approximately Correct. New York: Basic Books.

Waltman, L., & van Eck, N.J. (2012). The inconsistency of the h-index. Journal of the American Society for Information Science and Technology, 63(2), 406–415.

Wang, Q., & von Tunzelmann, N. (2000). Complexity and the functions of the firm: Breadth and depth. Research Policy, 29(7–8), 805–818.

WIPO (2000). Patent law treaty, available at http://www.wipo.int/treaties/en/ip/plt/ (last visited on 2016, February 20).

Zhang, G.P., Chen, X.D., & Niu, X. (2012). The technology complexity based on patent width and depth (in Chinese). Science Research Management, 33(3), 113–135.

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    Functional relation between the Sh(Y) values and profits.

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