Justus Baron

Yann Ménière

Tim Pohlmann

Yann Meniere

Joint innovation in ICT standards: How consortia drive the volume of patent filings

The development of formal ICT standards is a loose form of collaborative innovation: firms first develop rival technologies, some of which are then eventually selected in the standard. Against this background, firms often use informal consortia to define a clearer technology roadmap ahead of the formal standard setting process. The paper aims to assess how such consortia influence the volume of patents filed around standards, and whether this is efficient. We show that their effect actually depends on the strength of firms' incentives to develop the standard. Consortium membership triggers a higher number of patent files when insufficient rewards for essential patents induce underinvestment in the standard. This effect is necessarily pro-efficient. In situations where excessive rewards induce patent races, consortium membership only moderately increases or even reduces their volume of patents. At least in the latter case, the effect of consortia membership is also pro-efficient.

We are grateful to Mark Schankerman, Andrew Updegrove and Stephan Gauch for helpful discussion and data.

Introduction

Over the past twenty years, the number of essential patents 1 claimed on ICT standards has strongly increased (Simcoe, 2007). This evolution firstly denotes the importance of these patents for firms: they can generate substantial licensing revenues, and be used as bargaining chips to obtain freedom to operate on rivals' patent portfolios (Rysman & Simcoe, 2008). Another explanation lies in the growing complexity of ICT standards. As compared with other sectors, standardization in ICT has indeed evolved from the definition of mere specifications enabling interoperability to the joint development of large technology platforms including critical technologies [START_REF] Bekkers | Standardizing Intellectual Property Disclosure Data[END_REF] . Consequently, they tend to embody a growing number of patented components.

While the conditions for licensing essential patents have been widely discussed (see e.g., Shapiro, 2001; Lerner & Tirole, 2004; Layne-Farrar & Lerner, 2011), the peculiar type of collaborative innovation they proceed from has received less attention so far. Formal ICT standards are developed in standard setting organizations (SSOs)-such as ETSI (telecommunications) or IEEE (electronics)-that are open to a broad range of stakeholders. Besides the large number of participants, the originality of this process is that it does not involve any ex ante contracting between the firms preparing to develop a standard (Ganglmair & Tarentino, 2011). The choice of standard specifications rather takes place ex post in ad hoc working groups, based on the merit of rival technologies available to solve a given technical problem. Firms thus compete in R&D ahead of the working group meetings, thereby generating a large volume of patented innovations of which only a fraction will eventually become essential.

This formal process generates costly R&D cost duplications and delays due to vested interests (Farrell & Simcoe, 2012; Simcoe, 2012). Firms therefore increasingly rely on informal consortia to take the lead in the standard setting process (Cargill, 2001; Lerner & Tirole, 2006). Such consortia are fora wherein a group of firms seek to agree on a common design that they will jointly push as a standard. While some of them substitute for the lack of formal SDOs and issue their own standards (e.g., Blu-Ray alliance or W3C for web protocols), most consortia actually accompany formal standardization [START_REF] Benner | Close to you? Bias and precision in patent-based measures of technological position[END_REF] . They are then a means for members to better focus their R&D investments on a common roadmap (Delcamp & Leiponen, 2012), thereby saving useless development costs while enhancing their chances to obtain essential patents (Pohlmann and Blind, 2012). Leiponen (2008) furthermore shows that participation in a consortium improves [START_REF] Baron | Patent Pools and Patent Inflation -The effects of patent pools on the number of essential patents in standards[END_REF] Patents are deemed essential to a standard if they cover technology that is necessary for any implementation of this standard. [START_REF] Bekkers | Standardizing Intellectual Property Disclosure Data[END_REF] As an example, the number of functionnalities and formats (e.g., email, video, internet) supported by the late wireless comunication standards (3G and 4G) considerably exceed those of the second generation (GSM, CDMA) that are limited to voice communication. [START_REF] Benner | Close to you? Bias and precision in patent-based measures of technological position[END_REF] These consortia can submit the joint technological proposals of their member committees to the SDO for approval as part of a formal standard. ISO has for instance a formal fast track agreement, the PAS (Publicly Available Specifications), which allows sponsoring organization to receive a formal accreditation of their specification within six and nine months. JTC1 has a similar policy of featuring Approved References Specifications (ARS).

the capacity of firms to influence the technological decisions taken at the formal SSO.

This paper aims to assess how such consortia influence the volume of patents filed around formal standards, and whether this is efficient. We show that their effect actually depends on the strength of firms' incentives to develop the standard. Consortium membership induces a higher number of patent files in situations where insufficient rewards for essential patents induce underinvestment in the standard. This effect is necessarily pro-efficient. In situations where excessive rewards induce patent races, consortium membership only moderately increases or even reduces their volume of patents. At least in the latter case, the effect of consortia membership is also pro-efficient.

The implications of these results are twofold. They first highlight the cost entailed by the loose coordination of R&D investments in formal SSOs. In this context, they also suggest that the creation of informal consortia can be an efficient way to supplement formal SSOs. Consortia are indeed an effective means to unlock the development of standards when firms have insufficient incentives to contribute technology, while they do not significantly amplify the race for essential patents when these incentives are strong.

The paper proceeds in two steps. We first develop a theoretical model to analyse the efficiency of distributed innovation into a standard. We then assess empirically the actual impact of consortia over a large panel of ICT standards.

Our model allows for some degree of rivalry between the firms' innovations, so that only a fraction of their patents eventually become essential. We firstly establish that the level and efficiency of firms' investments depend on the share of the standard's value that accrues to owners of essential patents. A public good pattern involving sub-optimal investment prevails in equilibrium when the licensing revenue of essential patents holders is not sufficient to cover their R&D costs. Conversely, firms engage in a wasteful patent race when licensing profits exceed total R&D costs.

Against this background, we introduce consortia as a means to mitigate technology rivalry between member firms. By joining a consortium, a firm may thus deflate its volume of patents by cutting irrelevant R&D investments, or inflate it by seeking to develop more relevant innovations. We show that consortium membership is always pro-efficient if the first effect dominates. A patent-inflating consortium is also pro-efficient in a public good equilibrium, but it may actually harm efficiency in a patent race equilibrium if it induces an excessive inflation of patents around the standard.

Drawing on this framework, we use a large panel of ICT standards to assess the actual effect of consortia empirically, respectively for standards entailing over-and underinvestment. For this purpose, we have developed an original dataset of standard-related patent applications at firm level, which we use as a proxy for firms' R&D investments. We also use information on the participation of pure R&D firms in the standard development process in order to identify overinvestment patterns. We find that firms entering a consortium strongly increase their patent files in most of the cases. This is however not true for standards featuring an over-investment pattern: in these cases, consortia membership has a smaller, and in some cases negative effect on firms' patent applications. These results thus suggest that consortia tend to enhance the efficiency of innovation in the development of standards.

The remainder of this article is organized as follows. We present the theoretical model and its implications in Section 2. Section 3 discusses the empirical strategy, the database and econometric results. We conclude in Section 4.

Theoretical framework

Value of the standard We consider a set N of n firms that take part in the development of a standard. The standard embodies x = i∈N x i essential patents contributed by the firms, and its implementation is expected to generate aggregate profits v (x) in the industry. These profits increase with the amount of embarked technology, but with decreasing returns: v (x) > 0 and v (x) < 04 .

There are two ways in which firms can derive revenues from the standard. Patent holders firstly appropriate a share r ∈ [0, 1] of the standard's value through the royalties they charge to implementors of the standards. Parameter r can thus be thought of as reflecting the IP licensing policy of the standard setting organisation (r = 0 denoting a royalty free policy). In line with common practices regarding ICT standard, we assume that the share of the licensing revenues that accrues to firm i ∈ N is proportionnal to its share of the essential patents (x i /x).

The remaining part of the revenues, (1r) v (x), accrue to the firms that implement the standard in their products. Let s i denote firm i's share of these revenues, which can be thought of as its share of the market for standardcompliant products. We assume that all firms with s i > 0 are involved in the standard setting process (so that s i = 1). Other firms (s j = 0) may also contribute patented inventions provided they have appropriate R&D capabilities, but they will get a return only through royalty revenues.

Taking into account both sources of profits, the expected benefit of firm i ∈ N is thus:

B i = v (x) r x i x + (1 -r) s i

R&D investments

The definition of a standard is the outcome of an open innovation process wherein firms submit innovations, some of which only will be included in the standard specifications. Assuming constant and symmetric per unit R&D costs c, the R&D cost function of firm i ∈ N is proportional to y i , the number of patents it develops for the standard:

C i = cy i
Equation (1) in turn posits that only a fraction of these patents enventually become essential.

x i

y i = γ i ∈ (0, 1) (1)
Firm i's selection rate γ i denotes the chance that one of its patented inventions be eventually included in the standard specifications. Conversely, γ -1 i measures the number of patents that firm i must develop in order to obtain one essential patent. We define technology rivalry between the firms as follows:

m = i∈N γ -1 i ≥ n (2)
This parameter can be interpreted as a measure of the degree of complementarity or substituability between the firms' innovations. Setting m = n implies in particular that the firms' innovations are perfect complements: each of them can be adopted without evicting another one. More generally, the ratio m/n provides us with a measure of the degree of rivalry between the different technology alternatives promoted by the firms. For instance, a ratio m/n = 10 means that only one out of ten innovations developed for the standard will become essential. At the firm level, observe finally that firm i has a relatively weak position vis-à-vis other firms if γ i < n/m.

Public good or patent race

We first highlight that two types of coordination failure that may prevail in this context. Each firm i ∈ N defined by {γ i , s i } makes its investment decision so as to maximize B icy i . Solving this problem over x i yields the first order condition below:

v (x) r x i x + (1 -r) s i + rv (x) x -x i x 2 = c γ i (3)
The term in brackets captures the public good nature of the standard. It implies that firm i's direct incentive to develop the standard is proportional to the share of the value it can appropriate. The second term captures a patent race effect: To appropriate part of the expected profit, firm i needs to invest more the higher the number of essential patents held by its R&D competitors. It is easy to check that the LHS of equation ( 3) is decreasing in x, so that the firms' decisions are strategic substitutes.

Summing the FOC of all firms i = 1, n, we derive the joint R&D investment x * in equilibrium.

1 n v (x * ) + rv (x * ) n -1 x * = c m n (4)
The aggregate marginal profits (LHS) again combine the properties of a public good investment (marginal benefits are diluted when the number of firm increases) and a patent race (when r > 0, extra incentives are stronger the larger the number of competitors). On the RHS, the aggregate marginal cost of essential patents is higher when technology rivalry is strong (large m/n).

Observe also that the aggregate marginal cost does depend on the distribution of the γ i between the firms, but only on the degree of technology rivalry at the aggregate level (m/n). We use this property to study how the structure of the incentives affects the efficiency of firms' investments. Let us consider a social program wherein a unique representative firm with selection rate γ = m n -1

maximizes aggregate profits:

max x Ω = v (x) -cx/γ
Comparing the outcome of this program with the equilibrium outcome, we can establish the following result.

Proposition 1 Aggregate investment in equilibrium is efficient if the licensing revenues rv (x * ) equals the total R&D cost cx * /γ. Firms invest in excess if licensing revenues exceed total cost and they underinvest in the reverse case.

Firms' incentices to innovate can induce either too much (patent race pattern) or too little (public good pattern) investment. Which one prevails in equilibrium depends on the balance between total licensing profit and the total R&D cost at equilibrium. Firms engage a patent race if

rv (x * ) > cx * γ (5)
Intuitively, a patent race takes place when licensing is profitable per se, so that firms will compete in R&D in order to preempt the essential patents. Conversely, the public good equilibrium emerges when firms' incentives are primarily driven by the possibility to use the standard.

Observe that condition (5) also implies that the participation of a pure R&D firm i (s i = 0) with average sucess rate γ i = γ is profitable only in a patent race equilibrium:

(5) ⇔ x * i x * rv (x * ) -cγx * i > 0 (6)
Corollary 2 The participation of pure R&D firms signals a patent race pattern in equilibrium.

We will use this result in the empirical section to infer the existence of a patent race equilibrium from the participation of pure R&D firms. We can finally observe that the number of firms does not determine the type of equilibrium that prevails, but its magnitude. Hence Proposition 1 and its corrollary are robust to allowing free entry of firms in the standardisation game.

Corollary 3

The inefficiency pattern prevailing in equilibrium does not depend on the number of firms, and is thus robust to free entry.

Efficiency of consortium membership

Recall that the consortia we are interested in do not involve any formal contracting or joint R&D decisions. They rather function as fora wherein participating firms seek to agree on a mutually acceptable roadmap for specifications that they will jointly push in the SDO. Accordingly, we posit that consortium members can better focus their R&D effort, thereby saving useless investments and enhancing their chances of obtaining essential patents. Assuming that a subset of firms K ⊂ N have created a consortium to support the standard setting process, members thus benefit from a higher selection rate5 : γ k∈K > γ k∈N \L where L = K\ {k}.

We focus on the consequences of firm k's decision to join the consortium [START_REF] Blundell | Individual Effects and Dynamic Feedback in Count Data Models[END_REF] . Formally, this firstly translates into a positive shock on the new member's selection rate (dγ k > 0). Since firm k can better screen irrelevant innovation opportunities, this in turn induces a fall in the degree technology rivalry at the aggregate level: dm/dγ k = -γ -2 k < 0. It thus follows directly from ( 4) that the number of essential patents embodied in the standard increases in equilibrium. Since the firm's decisions are strategic substitutes, it is moreover clear from (3) that firm k develops more essential patents while the other firms react by developing less of them. Lemma 4 summarizes these results.

Lemma 4 Joining the consortium enables the new member to develop more essential patents in equilibrium, while the other firms develop less essential patents. The net effect is positive, and thus induces an increase of the equilibrium value of the standard v (x * ). This result does not necessarily imply that an enlarged consortium coalition is efficient, since it does not take into account the induced variation of firms' R&D costs. Indeed, deriving firms' aggregate profits Ω = v (x * )c i x * i /γ i wrt γ k and rearranging makes it possible to highlight the following three effects:

∂Ω ∂γ k = cx * k γ 2 k A + ∂x * ∂γ k v (x * ) - c γ B + c i ∂x * i ∂γ k 1 γ - 1 γ i C (7)
The first effect corresponds to R&D costs savings induced by firm k's ability to reduce the volume of non-essential patents (A). It is clearly positive. The second one is the net (cost/benefit) value of adding new essential patents to the standard (B). It is clear from the term in brackets that it is positive in a public good equilibrium. Indeed new patents can then mitigate firms' lack of investment in the standard. By contrast, developing more essential patents reduces joint profits in a patent race equilibrium. Finally, the third effect captures the cost or benefit of reallocating the development of essential patents between the firms (C). Its sign may be positive of negative, depending on the selection rate of firm k as compared with the other firms. Lemma 5 summarizes these findings.

Lemma 5 A firm's entry in the consortium deflates the volume of non-essential patents, which is clearly efficient. By contrast, the inflated volume of essential patents may be inefficient if i) a patent race pattern prevails in equilibrium and/or ii) it entails a reallocation of R&D effort from efficient to inefficient firms.

In order to carry further the analysis, we now focus on the direct effects of firm k's patenting strategy on joint profits, aside from the other firms' reactions [START_REF] Branstetter | When Do Research Consortia Work Well and Why? Evidence from Japanese Panel Data[END_REF] . We are especially interested in relating joint profits with the (empirically obervable) total volume of patents filed by firm k. Assuming that firm k has average selection rate (γ k = γ), we can establish that

cx * k γ 2 k + ∂x * k ∂γ k v (x * ) - c γ > 0 ⇔ dy * k < Δ dx * k γ (8)
where

dy * k = dx * k γ -x * k dγ γ 2
is the variation of the total number of patents filed by firm k (that is, the difference between the volumes of spared patents and new essential patents) and Δ = γv (x * ) /c. Since Δ > 0, condition (8) clearly holds if the total volume of firm k's patents is deflated. This is quite intuitive, since firm k then develops more essential patents and saves at the same time the R&D cost of an even larger volume of useless patents. The effect of firm k's move is more ambiguous if joining the standard has a patent inflating effect. Indeed the benefit of enhancing the standard's value must then be balanced with the cost of a larger volume of patents. As stated in Proposition 6, the new member still invests more efficiently provided the public good pattern prevails in equilibrium. Indeed, it thereby provides more of the missing essential patents, and it does so at a lower cost thanks to consortium membership. By contrast, and inflated volume of patents filed by the new member may harm efficiency in a patent race pattern, unless the volume of extra non-essential patents remains sufficiently small to be compensated by the benefit of new essential patents.

Proposition 6 Assume that a firm with average success rate joins the consortium:

• A deflated volume of patents filed by the new member is efficient whatever the inefficiency pattern prevailing in equilibium.

• A inflated volume of patents filed by the new member is efficient in a public good equilibirum. It becomes inefficient in a patent race equilibrium when it exceeds a positive threshold T ∈ (0, dx * k /γ).

Proof. Observe also that Δ > 1 ⇔ v (x * )v (x * )c/γ > 0, which is the condition for the public good pattern to prevail in equilibrium. Since dy * k < dx * k /γ, it directly follows that condition ( 8) is also verified in a public good equilibrium when firm k inflates its volume of patents. By contrast, the patent race pattern prevails when 0 < Δ < 1. Hence joint profits can increase only if the inflation of firm k's patents remains moderate, that is if dy * k < T ∈ (0, dx * k /γ). Otherwise, a strong inflating effects induces a fall of joint profits.

Empirical analysis

This section in turn presents an empirical analysis of patent filings around a large panel of ICT standards. Our purpose is to assess whether joining a consortium changes the volume of patents filed by firms involved in standard development, and what is the direction of this change. Drawing on the results of our theoretical analysis, we assess this effect separately for standards corresponding respectively to a public good or patent race pattern.

Data and indicators

Our empirical analysis draws on a comprehensive dataset of technological standards including essential patents [START_REF] Cargill | Consortia in the Standards Development Process[END_REF] . Our sample includes all ICT standards issued between 1992 and 2009 by one of the major formal SSOs which operate on an international level [START_REF] Cargill | Intellectual Property Rights and Standards Setting Organizations: An Overview of failed evolution[END_REF] . Since we aim to focus on the interaction between formal standardization and companion consortia, we exclude standards that are exclusively developed by informal standards consortia (e.g. BluRay).

We furthermore restrict the analysis to standards including essential patents of at least two different companies, thereby limiting the sample to 578 standards. Companies that own IPRs which are essential to a standard provide this information to the respective SSO. We downloaded these patent declarations at the websites of the above-mentioned SSOs in March 2010. From the PERINORM [START_REF] Chiao | The Rules of Standard Setting Organizations: an Empirical Analysis[END_REF] database we retrieve information on the date of first release, releases of further versions and amendments, number of pages from the standard document such as the technical classification of the standard.

Our sample includes 242 different companies declaring essential patents, observed over the whole period. For each firm, we collect yearly information on the amount of sales, R&D expenditure, employees and market to book ratio (Tobin's Q [START_REF] David | Formal standards-setting for global telecommunications and information services. Towards an institutional regime transformation?[END_REF] ). In addition we distinguish between pure R&D firms, manufacturer and net provider [START_REF] Delcamp | Innovating Standards Through Informal Consortia: The Case of Wireless Telecommunications[END_REF] and classify our sample by main active industry using SIC codes.

We connect the firm level data to the specific standard information and built up a panel of 1,720 company-standard pairs observed over a time span of 18 years (1992-2009). For each company-standard pair, we observe the amount of patents filed by the respective company in the technological field for the respective standard, and include a dummy variable indicating whether the company takes part in a consortium supporting the development of this standard. Other time-variant control variables are either company-or standard-specific. Timeinvariant factors affecting the firm, the standard or the relationship between both are captured by company-standard pair fixed effects.

Matching between informal consortia and formal standards

To identify informal consortia accompanying the formal standardization process, we use data from 15 editions of the CEN survey of ICT consortia and a list of consortia provided by Andrew Updegrove. We identify approximately 250 active ICT consortia [START_REF] Egyedi | Consortium Problem Redefined: Negotiating 'Democracy' in the Actor Network on Standardization[END_REF] . We categorize these consortia as to industry, function (spec producer, promoter) and years of activity (see Appendix 1). The connection to a standard in our sample is analyzed by using liaison agreements and information from consortia and SSO web pages. For instance, a connection was identified, when a consortium explicitly references a formal standard, or when a standard has been submitted to the formal SSO by an informal consortium. We are conservative in establishing the connections, resulting in a narrow list of 54 consortia. We use supplementary information for the selected consortia and further restrict the list to 21 consortia that technologically (spec producer) and significantly contribute to this specific standard (excluding pure promoting consortia) [START_REF] Farrell | Choosing the Rules for Consensus Standardization[END_REF] . Using information on the websites of the consortia as well as internet archives (www.archive.org) and internet databases (www.consortiuminfo.org), we inform consortium membership over time and connect this information with the company standard pairs of our sample.

Standard-specific patents

The most intuitive approach to track firms' R&D investments in standards is to count the patent declarations they state for these standards. However, former empirical analyses have shown that the timing of declaration is not connected to the dynamics of standardization (Baron and Pohlmann, 2010). Moroever essential patents only represent a very small amount of patenting around standards (Bekkers et al., 2012). To avoid these shortcomings, we thus build up a new measure of firms' standard-specific R&D investment. In a first step we count patents filed from 1992 to 2009 by the companies in our sample at the three major patent offices (USPTO, JPO and EPO), using the PatStat database and the company assignee merging methods of Thoma et al. (2010). We restrict the count of patent files to IPC classes in the relevant technological field of each standard, identified by using the IPC classification of declared essential patents [START_REF] Fleming | Evidence on the Benefits to Startups Participating in Open Standards Development[END_REF] . We measure the dynamics of patenting over the standard lifecycle (details can be consulted in Appendix 3). Our mean value analysis shows a patenting increase before standard release and a decrease thereafter. This finding reassures us that our variable captures the innovation for a specific standard, which indeed is expected to culminate in the period immediately preceding standard release.

Public good and patent race patterns One contribution of our analysis is the comparison of over-and under investment in standardization. As shown in the theroretical model, the patent race pattern can be identified when pure R&D firms take part in the standard development. We use this prediction as our identification strategy for the empirical sampling of standards. By labeling over-and underinvestment as to the classification above, we compare the residual results of a regression of standard related patent files against technical characteristics of the standards(details can be consulted in Appendix 4). A t-test analysis suggests that our classification of overinvestment is an appropriate measure. Results show that residual values of the regression are in average positive for standards where pure R&D firms participate to a standard and in average negative for those where pure R&D firms are not involved.

Descriptive Statistics

Pairwise correlations In the following Table 1, we provide pairwise correlations of firm-specific, standard-specific and firm-standard-specific variables at the company-standard-pair level.

Insert Table 1 about here

The volume of patents around standards is negatively correlated with both consortium membership and the existence of a consortium on the standard. This could indicate that consortia attract companies with smaller standard-related patent portfolios. On the other hand, consortium membership is positively correlated with the value of sales and the number of employees. The existence of consortia is positively correlated with the number of firms per standard and with standard age. As to the correlation analysis effects are yet not strong enough to derive conclusive interpretations.

Difference in means In the following Table 2, we present differences in the volume of patents, the number of employees, the value of sales and the book-tomarket ratio between consortia member observations and the rest. Membership observation is associated with a lower volume of standard-specific patents, but a higher number of employees and a higher value of sales.

Insert Table 2 about here

Multivariate Analyses

Estimation methodology We use our panel dataset to estimate how consortium membership affects the volume of patents filed around the related standard. Our dependent variable is the number of patent priority filings by firm i for standard j in year t. Our first key explanatory variable, member ijt , is a dummy equal to one for years where the firm i participates in a consortium supporting standard j. Following the theoretical model, we expect its effect to depend upon whether the standard is initially characterized by over-or underinvestment. We therefore also interact the consortium membership dummy with the over_investment j variable, denoting the share of pure R&D firms involved in the develoment of standard j.

To account for unobserved heterogeneity of standards and companies, we systematically include fixed effects for company-standard pairs. As our dependant variable is a count variable with overdispersion with respect to a poisson distribution, we will use a poisson estimator with robust standard errors unless explicitly stated otherwise [START_REF] Ganglmair | Patent Disclosure in Standard Setting[END_REF] . We furthermore cluster standard errors by companies in order to exclude that unobserved shocks to a company's patenting level bias the standard errors and lead to an insufficiently restrictive confidence interval [START_REF] Gauch | Dynamics and effects of competing standards of recordable DVD-media Author(s)[END_REF] . Unsurprisingly, we found strong evidence for persistent effects of transitory shocks to our explained variable, as indicated by positive autocorrelation of standard errors. We therefore include the lagged dependent variable as explanatory variable in all models.

Our basic regression model has the following specification:

st_patents ijt = exp (α 1 .st_patents ijt-1 +β 1 .member ijt +β 2 .member ijt * over_investment j +β 3 .st_activity jt-1 +F it-1 β 4 + X t β 5 + c jt + ε ijt
where st_activity jt-1 counts version releases and amendments per year, F it-1 is a vector of firms specific change such as a measure of Sales and Tobins's Q, X jt-1 denotes other control variables for time trends such as the overall ICT patent files and the count of patent declarations, c jt are standard age dummies and ε ijt is an idiosyncratic error term. We use the standard age dummies, each indicating a one year period in the standard lifetime, to control for the timing of standardization. Downstream innovation and patenting (taking place after the first release of the standard) is indeed likely to peak around periodical revisions of standards. The release of new standard versions or amendments to existing versions is labeled as standard activity and included as a control variable. In order to exclude immediate feedback (amendments or version releases explained by prior innovation), we include this control variable with a one-year lag.

We furthermore wish to account for external shocks such as the business cycle or technology-related policy. As we already control for standard fixed effects and standard age, it is impossible to include year dummies as a further control because of a collinearity problem. We therefore control for external shocks by including the overall number of triadic patent priorities filed per year in the relevant technological category (respectively IPC class G for telecom and IPC class H for IT standards) and the overall number of patent declarations made to any formal ICT standard per year in order to capture policy shocks that are more specifically relevant to essential patents. Models 1-4 Consortia are more likely to be created for important or technologically complex standardization projects. Furthermore, the organization of R&D can be different if a consortium is created for a standard. For these reasons, the timing of standardization is likely to be affected by the existence of consortia. It is thus preferable to estimate all coefficients, including controls for standard timing, only on the sample of standards related to an informal consortium. This strategy could however bias downwards the estimated effects of consortia, if some of these effects are systematically captured by control variables. We therefore present results based upon the whole sample in model M1. As expected, the coefficients on consortia variables are higher in the larger sample, but the fit of the model is much lower. This indicates that heterogeneity between standards with consortia and other standards is large. We therefore only estimate standard with accompanying consortia in all following models (M2-M4), while acknowledging a potential downward bias on our consortia coefficients.

In our second model (M2), consortium membership has a significant positive effect on the volume of standard-specific patents, but the level of this effect decreases with the level of overinvestment. This result is however potentially subject to an endogeneity bias. Unobservable variables, such as changes in the strategic importance of the standard for the specific company, may have an impact on both standard specific patents and consortium membership. External factors jointly affecting consortium membership and related patenting are particularly likely to occur in periods of turmoil, like the internet bubble in 2001. While desirable in order to reduce within-groups bias on weakly endogenous variables (Nickell, 1981; Bloom et al., 2005), the long period of observation (relatively to the fast-evolving world of ICT standards) increases the vulnerability to this type of biases.

Insert Table 3 about here

In order to deal with these concerns we restrict the observation period to 8 years from 2002 to 2009. Furthermore, we also reduce the cross-section dimension of the panel, by restricting the sample to stock-market listed companies. These companies are more likely to react in a similar fashion to external events. Finally, we identify positive or negative shocks to the number of employees in a one year period [START_REF] Hawkins | The rise of consortia in the information and communication technology industries: emerging implications for policy[END_REF] , indicating mergers, acquisitions, restructuring etc. If this shock takes place after 2005, all observations after the shock are dropped for this company, if the shock takes place earlier, we drop all previous observations. Companies with more than one shock are dropped altogether for our third model (M3), reducing the sample to 174 groups and 999 observations.

In our last model M4 we furthermore tackle endogeneity more directly by including time-varying firm characteristics as control variables. We choose to include the value of sales, and Tobin's Q as a measure of expected profits (both lagged by one year to exclude immediate feedback). We opt for not including employees, which is highly correlated with sales in the within dimension (both reflecting company growth). Furthermore, the number of employees, with respect to the value of sales, is likely to be more important for determining whether a company has the possibility to participate in a consortium, but less important in independently determining the evolution of patenting [START_REF] Layne-Farrar | To join or not to join: Examining patent pool participation and rent sharing rules[END_REF] . By including the value of sales as a control, we nevertheless face the risk to bias downwards the estimates of the consortia effects for smaller companies refraining from joining an expensive consortium. We therefore divide the level of consortia member fees [START_REF] Leiponen | Competing Through Cooperation: The Organization of Standard Setting in Wireless Telecommunications[END_REF] by the value of sales of the company at the time of consortium creation. The first percentile of observations according to this value (the companies-standard pairs characterized by the highest consortia fees relative to the value of sales) is most at risk to be affected by this effect. We therefore decide to exclude these observations, leaving us with 158 company-standard pairs and 884 observations in model 4.

M1-M4 show robust results. The magnitude of the coefficients decreases but the effects are yet more significant, and the signs of the coefficients are unchanged.

Further robustness checks

We check for robustness of our results to a correlation of our main explanatory variables with past outcomes of the dependent variable. It is plausible that a company's decision to join a consortium depends upon its stock of related patents. In this case, the regressors are predetermined, and the poisson fixed effect estimator yields inconsistent results (Blundell et al., 1999). In order to account for this problem, we take advantage of the fact that we have information on pre-sample levels of our dependent variable and adopt the methodology suggested in Blundell et al. (1999), substituting presample means for fixed effects. The results displayed in Appendix 5 are mainly consistent with the results from the fixed effect analysis.

Effect of consortium member share So far we have estimated the effect of consortium membership on the volume of patents of the respective company. In this section, we will estimate the effect of the consortium member share (indicating how many of the firms contributing to the standard are member of the consortium) on the volume of patents filed by members and outsiders. Finally, by estimating the effect of consortium member share on patents filed by all companies, we obtain a measure of the net effect of consortia.

As compared to the previous analysis, this method is less prone to endogeneity biases, as the decisions of other companies to join a consortium are probably relatively unrelated to a firm's own current or expected future R&D efforts. We are therefore less restrictive regarding the sample, and only drop observations for 2001 or earlier and of standards with no consortium within the observation period. On the other hand, the member share is sensitive to the membership decision of the firm itself, especially if the number of firms on the standard is low [START_REF] Lerner | Efficient Patent Pools[END_REF] . In order to check for robustness to this sensitivity, we present all results for a narrower subsample of standards including at least 6 contributing firms.

We estimate the effects of consortium member share separately for consortium members and non-members and for both. For the purpose of this analysis, a firm is labeled as a member over the whole period of observation, if it is consortium member at least once within this period. It is labeled consortium outsider if it has never been consortium member over the period of observation. We control for time-variant firm characteristics, standard-company fixed effects, the lagged dependent variable and external shocks. Results are displayed in Table 4.

Consortium members react to increasing consortium member share by inflating their patent filings, but this effect decreases with the level of overinvestment (model 5). Consortium outsiders do not react in a statistically significant way to changes in consortium member share (model 6). The overall effect (the effect indistinctly for members or outsiders) of increasing consortium member share on the volume of standard-specific patents is positive and significant, but this effect decreases significantly with the level of over-investment (model 7).

Insert Table 4 about here Net effects Our results suggest that nearly all effects of consortia depend upon the initial level of overinvestment. In order to be able to discuss the effect of consortia on patenting, one should therefore relate the estimated coefficients to the sample values of the overinvestment indicator. We calculate the net effects from the results of model 5 (for the effect of consortium membership) and model 7 (the overall effect of consortium member share in the whole sample). We find that the effect of consortia membership is positive for any share of non-practicing entities not exceeding 6 %. This is the case for 92,12% of the observations. The effect of consortia member share on overall volume of patents is positive for any share of non-practicing entities below 9 %. This is the case for 94,13% of the observations. These results indicate that the effects of consortia membership and consortia member share on standard-specific R&D are positive in a broad majority of standards [START_REF] Lerner | A Model of Forum Shopping[END_REF] . However, they also suggest that consortia can have a deflating effect in a minority of standards that are characterized by a particularly strong patent race pattern.

Conclusion

The purpose of the paper is to assess how consortia influence the volume of patents filed around formal standards, and whether this is efficient. In the first theory section, we defined consortia as a means to reduce the degree of rivalry between the firms' innovations. Accordingly, consortium members can obtain essential patents at a lower average cost, by better targeting R&D investments. The effect on the volume of patents filed around the standard is however ambiguous. By joining a consortium, a firm may indeed file less patents by cutting irrelevant R&D investments, or more of them if it seeks to develop more technology inputs for the standard. We have established that consortium membership is always pro-efficient if the first effect dominates. A patent-inflating consortium is also pro-efficient in a public good equilibrium, but it may actually harm efficiency in a patent race equilibrium if it induces an excessive inflation of patents around the standard.

Our empirical analysis makes it possible to assess which effect actually dominates, depending on the investment pattern -public good or patent race -prevailing for a given standard. When joint investments are suboptimal (public good pattern), the observed rise in patent files indicates that consortium membership induces firms to develop more innovations, rather than saving R&D costs. Since royalty-based incentives are weak in this case, this suggests that their reaction is chiefly driven by the opportunity of enhancing the value of the standard by developing more essential components. Consortia are thus an efficient way to supplement the lack of R&D investments when incentives to develop the standards ar not sufficient.

Empirical results differ when the patent race pattern prevails. For most standards, new consortium members still increase their patent applications, but in significantly lesser proportions than in the public good cases. Since firms have strong strategic incentives to develop essential patents, this suggests that there are few opportunities left for developing innovations that are relevant to the standard. For some standards featuring strong overinvestment, we even oberve that consortium members reduce their investments -consortia being then used to save R&D costs by eliminating irrelevant R&D investments. These results thus indicate that the creation of consortia does not significantly accentuate patent races, and rather has a proefficient deflating effect for at least a minority of standards around which overinvestment is particularly strong.

APPENDIX

Table 1 :

 1 Pairwise correlations on the company-standard level

		1	2	3	4	5	6	7	8
	1 St. R&D	1.00
	Invest.
	2 Member	-0.10 ***	1.00
	3 Consortia	-0.14 ***	0.67 ***	1.00
	Exists
	4 Standard	-0.07 ***	0.39 ***	0.58 ***	1.00
	Event
	5 Tobin's Q	0.02	0.01	-0.04 *	-0.05 *	1.00
	6 Sales	0.11 ***	0.06 ***	0.01	-0.01	-0.25 ***	1.00
	7 Em-	0.10 ***	0.06 **	0.01	0.02	-0.33 ***	0.87 *** 1.00
	ployees
	8 Number	0.05 **	0.34 ***	0.60 ***	0.62 ***	-0.09 ***	-0.02	0.00	1.00
	of Firms
	9 Standard	-0.07 ***	0.17 ***	0.29 ***	0.32 ***	-0.20 ***	0.00	0.05 ** 0.25 **
	Age

Table 2 :

 2 Differences in variable means between consortia members and others

	t = 4.1256			Standard Specific Patent Files
	Group	Obs	Mean	Std. Err. Std. Dev.	[95% Conf. Interval]
	consortium members	261	2,238.6	190.8	3,081.9	1,862.9	2,614.2
	not consortium members 1,571	12,092.8	972.8	38,559.2	10,184.6	14,001.0
	t = -2.4585				Employees
	Group	Obs	Mean	Std. Err. Std. Dev.	[95% Conf. Interval]
	consortium members	272	125,635.0 6,929.8 114,289.8	111,991.9 139,278.2
	not consortium members 1,645	106,528.7 2,945.1 119,448.5	100,752.2 112,305.2
	t = -2.6035				Sales
	Group	Obs	Mean	Std. Err. Std. Dev.	[95% Conf. Interval]
	consortium members	272	40,119.1	1,774.0 29,257.4	36,626.5	43,611.6
	not consortium members 1,644	35,211.2	708.4	28,721.6	33,821.8	36,600.6
	t = -0.2502			Book-To-Market Ratio
	Group	Obs	Mean	Std. Err. Std. Dev.	[95% Conf. Interval]
	consortium members	243	1.7	0.1	1.5	1.5	1.9
	not consortium members 1,240	1.7	0.0	1.4	1.6	1.8

Table 3 :

 3 Results of the multivariate analysis -testing consortia membership (firm level) All models are estimated with the conditional fixed-effects poisson estimator with robust clustered standard errors (reported in parentheses). Standard errors are robust to arbitrary heteroskedacity and allow for serial correlation through clustering by firm. Model 2-4 are restricted to a limited time period 2002-2009., ,and imply significance at the 99%, 95%, and 90% levels of confidence, respectively. 1 Coefficient multiplied by 1,000 to make effects visible. 2

	Unit of Observation = Company Standard Pair DV = Standard Specific R&D Investment (Patent Files)	M1 M2 M3 M4 M5	Coef. Coef. Coef. Coef. Coef.	Member 0.470 *** 0.208 ** 0.188 * 0.193 ** 0.194 **	(0.175) (0.108) (0.105) (0.098) (0.077)	Member * Over Investment -1.746 *** -1.135 * -1.172 * -1.203 * -1.349 ***	(0.981) (0.636) (0.705) (0.685) (0.506)	Lag1 Standard Activity -0.061 * -0.022 *** -0.022 -0.021 **	(0.032) (0.008) (0.008) ** (0.009)	Lag1 Patent Files 1 0.002 *** 0.072 *** 0.044 ** 0.04 * 0.022 **	(0.001) (0.017) (0.021) (0.022) (0.004)	ICT Patent Files 1 0.003 ** 0.007 *** 0.006 ** 0.007 ** 0.008 ***	(0.002) (0.001) (0.003) (0.003) (0.003)	Patent Declarations 1 -0.001 -0.003 0.002 *** 0.004 0.008	(0.006) (0.006) (0.009) (0.01) (0.009)	Lag1 Tobin's Q 0.088	(0.059)	Lag1 Sales 1 -0.011 ***	(0.003)	Standard Year Dummies Incl. Incl. Incl. Incl. Incl.	Log Likelihood 2 -17,820 -490.82 -68.55 -59.35 -114.06	AIC 2 35,600 981 137 118 228	BIC 2 35,600 981 138 118 228	Observations 16,390 4,181 999 884 884	Groups 1,046 298 174 158 158	Note: Values are reported in	thousand.

Table 4 :

 4 Results of the multivariate analysis -testing consortia member share (consortia net effect) All models are estimated with the conditional fixed-effects poisson estimator with robust clustered standard errors (reported in parentheses). Standard errors are robust to arbitrary heteroskedacity and allow for serial correlation through clustering by firm., ,and imply significance at the 99%, 95%, and 90% levels of confidence, respectively. 1 Coefficient multiplied by 1,000 to make effects visible.

					***		***		***				***
		M8	Marg.	Effekt	*** 0.903	(0.233)	*** -5.532	(1.346)	*** -0.027	(0.009)	0.022	(0.021)	*** 0.007	(0.002)	0.007	(0.005)	-0.002	(0.003)	Incl.	Both	-175	351	352	2041	276
				Coef.	0.903	(0.233)	-5.532	(1.346)	** -0.027	(0.009)	*** 0.022	(0.021)	0.007	(0.002)	0.007	(0.005)	-0.002	(0.003)
		M7	Marg.	Effekt	0.337	(0.445)	-3.65	(2.177)	** -0.035	(0.012)	*** 0.078	(0.028)	0.004	(0.003)	0.009	(0.017)	0.003	(0.003)	Incl.	Outsider	-29	58	57	735	107
	Unit of Observation = Year DV = Standard Specific R&D Investment (Patent Files)	M6	Marg.	Coef. Effekt Coef.	0.884 *** 0.884 *** 0.337 Member_share	(0.328) (0.328) (0.445)	-5.489 *** -5.489 *** -3.65	(1.923) (1.923) (2.177) Member_share * Over Investment	-0.022 ** -0.022 ** -0.035	(0.011) (0.011) (0.012) Lag1 Standard Activity	0.013 0.013 0.078 Lag1 Patent Files 1	(0.018) (0.018) (0.028)	0.008 *** 0.008 *** 0.004 ICT Patent Files 1	(0.002) (0.002) (0.003)	0.009 * 0.009 * 0.008	(0.005) (0.005) (0.017) Patent Declarations 1	-0.003 -0.003 0.003	(0.004) (0.004) (0.003) Lag1 Sales 1	Incl. Standard Year Dummies Consortium Member Log Likelihood 2 -140.39 AIC 2 280 BIC 2 281 Observations 1,288	169 Groups	Notes:

2

Values are reported in thousand.

Table 6 :

 6 Robustness analysis with mean scaling and negative binominal estimation

		M11-1	M11-2	M12-1	M12-2
		Coef. (SE)	Coef. (SE)	Coef. (SE)	Coef. (SE)
	Member	0.474***	0.186*
		(0.094)	(0.101)
	Member *	-1.969***	-1.273**
	Over Investment	(0.62)	(0.635)
	Member_share			1.162***	1.947***
				(0.212)	(0.269)
	Member_share *			-5.931***	-12.757***
	Over Investment			(1.418)	(1.823)
	Lag1 Patent Files 1	0.117***	0.105***	0.117***	0.103***
		(0.006)	(0.007)	(0.005)	(0.006)
	ICT Patent Files 1	0.002***	0.006***	0.002***	0.006***
		(0.001)	(0.001)	(0.001)	(0.001)
	Patent Declarations 1	0.001	0.011***	0.006	0.011***
		(0.001)	(0.003)	(0.001)	(0.003)
	Pre Sample Means	0.162***	0.427***	0.173***	0.457***
	(1982-1992)	(0.055)	(0.089)	(0.052)	(0.081)
	Lag1 Sales 1		-0.007***		-0.007***
			(0.001)		(0.001)
	Constant	-0.730***	-1.014***	-0.908***
		(0.158)	(0.298)	(0.162)

These assumptions account for various possible specifications. The standard's value v (.) can in particular reflect a dynamic innovation process, if we define it as the expected outcome λxπ/ (δ + λx) of a Poisson process whith hit rate λx, discount rate δ, and aggregate profits π.

We implicitely assume here that the size of the consortium coalition does not change the success rate of former members or consortium outsiders. In other words, the only effect of consortium membership is a better access to information of future specifications. The entry of a new member in the coalition nevertheless indirectly affects former members and outsiders through the new member's stronger ability to preempt essential patents in the standard.

In practice, firms have to pay significant membership fees to join consortia, and therefore decide to do so only if they have significant stakes in the standard. The benefits in terms of information and influence strongly depend on idiosyncratic factors such as the degree of compatibility between the firms' technology profiles and strategic agenda.

This can also be interpreted as an approximation of the full effects when the reactions of the other firms are negligible. We will see in the next section that this interpretation is actually supported by empirical evidence.

A summary of all relevant variables with description and sample statistics can be consulted in Appendix 1

ISO, IEC, JTC1 -a joint committee of ISO and IEC -, CEN/CENELEC, ITU-T, ITU-R, ETSI, and IEEE.

PERINORM is the world's biggest standard database with bibliographic information on formal standards and is regularly updated by the SDOs DIN, BSI and AFNOR.

We used the Thomson one Banker database to match the respective firm level data.

We used the extended business model description in the Thomson One Banker database and compared our classification to the list of companies identified by Layne-Farrar and Lerner (2010).

This is coherent with the identification of the CEN survey which reports approximately 250 standards consortia in ICT.

Assisting this rather broad distinction we conduct a word count analysis on the consortia self-description abstracts, kindly provided by Andrew Updegrove. We use keywords such as "developing", "creates", "set standard" or "standardizes". Appendix 1 provides a list of those consortia and standards for which a link could be established, as well as the narrower list of consortia contributing technologically.

This method is a novel way of measuring standard-specific R&D investment. We apply tests of timing, estimate technological positions of standards as well several test of size measures to prove our proposed variable to be a sufficient indicator of standard-related R&D investment. The methodology and the various tests have been presented at the Patent Statistics for Decision Makers Conference 2011 at the USPTO and can be reviewed in Appendix 3.

We prefer the poisson estimator with robust standard errors over a negative binomial estimator with fixed effects, because the negative binomial estimator cannot totally control for fixed effects and thus account for unobserved heterogeneity.

All presented results are robust to clustering standard errors by standard instead of by company.

distribution, the lower 5% are labeld as negative shocks.

The primary cost of consortium participation is workload, while the cost of patenting is primarily financial

Since our goal is to estimate the financial burden to join a consortium we use the low range of membership fees (find an overview of highest and lowest membership fees in the appendix 1).

If we substracted the company itself from the consortium size variable, this count would be nevertheless sensitive to company membership, as we estimate the effects separately for consortium members and non-members.

The negative effect of consortia membership and relative consortia size on R&D investment in situations of overinvestment is however stronger than this positive effect.

We change our poisson specification to a liner regression, since residual values of poisson estimators will not produce conclusive results. We log transform our count variable of patent files and run a linear OLS fixed effect regression model to then predict the linear residual values in a post estimation analysis.

Additionally including the closer pre-sample information (1992 to 2002) does not alter significantly the reported results.

Appendix 3: Empirical Methodology for measuring standard-related R&D

We identified the relevant technological field for each standard by using the 7-digit IPC 1 classification of the declared standard essential patents, to then count patents filed by each company in the identified IPC classes. We counted all patents filed from 1992 to 2009 by the companies in our sample at the three major patent offices (USPTO, JPO and EPO), using the PatStat database and company assignee merging methods of Thoma et al. (2010).

This merging yields 13 million patent files. We aggregated these patents to INPADOC patent families and informed the IPC classification and the year of priority. To create our explained variable, we computed for each company-standard pair and year the number of patents filed in the relevant IPC classes for the standard of observation.

This method is a novel way of measuring standard-specific R&D investment, and we therefore have to conduct a reliability analysis. We compute for each company-standard pair the mean number of patents filed in one year periods before and after standard release (t=0) and report the standard derivation for high and low values (figure1). The resulting pattern is a convincing description of the innovation process around standardization:

the number of patents filed is highest in the years immediately preceding standard release, and sharply decreases after the release of the standard. The further we move away from the development phase of the standard, the lower are the calculated numbers of relevant patents. We believe that these findings are important arguments corroborating our methodology. Using this classification, we create two sub samples, one where pure R&D firms contribute to the standard and one where pure R&D firms are not at place. We test over-and underinvestment by predicting the residual values of our specification. We run a linear fixed effect regression of our firmstandard pairs explaining patent files per year, controlling for standard dynamics and year trends and estimate the linear residual values 2 . We then compare the means of our residual values in both subsamples (pure R&D firms participate or not) conducting a t-test analysis.

The result of the t-test analysis in table 5 shows that in the case of overinvestment (pure R&D firms contribute), the mean residual value is positive and significantly higher compared to the subsample of underinvestment (pure R&D firms do not contribute). The estimated residual values indicate the level of patenting predicted upon our estimation equation. heterogeneity (closer pre-sample values are a better approximation of the sample fixed effect than more remote pre sample information). As this model is intended to complement a fixed effect analysis, we choose the average of the period from 1982 to 1992 as pre-sample values [START_REF] Benner | Close to you? Bias and precision in patent-based measures of technological position[END_REF] . We control for the same variables and operate the same sample restrictions as in the main models of our empirical tests. As our dependent variable is overdispersed with respect to a poisson distribution and we no longer include group fixed effects, we now opt for a negative binomial regression. This allows us to further add standard dummies. The results are displayed in table 6. The coefficients of the consortia membership variables of models 11-1 and 11-2 as well as 12-1 and 12-2 are similar to our previous poisson fixed effect analysis with clustered standard errors. Models 11-1 and 11-2 estimate the firm level membership effect, while models 12-1 and 12-2 estimate the overall membership net effect. We run two models including and excluding the lagged sales variable and restricting the observations to 2002-2009. Our estimations provide significant results for the consortia variables in all models. Furthermore the coefficients of the pre-sample means are positive and significant in all specifications, which indicates that controlling for unobserved heterogeneity of the patent behavior is important.


J Vogel

M Bonfim

N Rougemaille

O Boulle

I M Miron

S Auffret

B Rodmacq

G Gaudin

J C Cezar

F Sirotti

S Pizzini

Direct Observation of Massless Domain Wall Dynamics in Nanostripes with Perpendicular Magnetic Anisotropy

Domain wall motion induced by nanosecond current pulses in nanostripes with perpendicular magnetic anisotropy (Pt/Co/AlOx) is shown to exhibit negligible inertia. Time-resolved magnetic microscopy during current pulses reveals that the domain walls start moving, with a constant speed, as soon as the current reaches a constant amplitude, and no or little motion takes place after the end of the pulse. The very low 'mass' of these domain walls is attributed to the combination of their narrow width and high damping parameter α. Such a small inertia should allow accurate control of domain wall motion, by tuning the duration and amplitude of the current pulses.

The interaction between conduction electron spins and local magnetization leads to a wealth of fascinating phenomena that have been extensively studied over the last fifteen years. This interaction allows, for instance, manipulating magnetic domain walls in nanostructures using current pulses [START_REF] Thomas | Handbook of Magnetism and Advanced Magnetic Materials[END_REF][START_REF] Boulle | [END_REF]. The temporal response of domain walls to the exciting current pulse is a key point for a better understanding of the interactions. It was recently shown that important transient effects can exist for domain walls in in-plane magnetized nanostripes, leading to a delayed domain wall motion with respect to the current pulse [3,4]. These transient effects, giving rise to domain wall 'inertia' or an effective domain wall 'mass' [5], are caused by deformations of the domain wall internal structure when a current or magnetic field is applied [6][7][8]. Thomas et al. [4] have shown that in the case of vortex domain walls these deformations can lead to a delay of several nanoseconds of the domain wall motion with respect to the current pulse and transient displacements of the order of 1.5 µm. Besides fundamental interest, such inertial effects potentially limit the use of domain walls in fast logic or memory devices, and transient times give an upper value of the excitation frequency. In this sense, domain walls with no inertia, i.e. that react instantaneously to an excitation, are highly desirable. Massless domain walls have been predicted theoretically in cylindrical magnetic nanowires with small diameter (below 50 nm) [9]. The cylindrical symmetry should allow the magnetization direction inside the domain wall to rotate around the wire axis without changing the demagnetizing energy and without deformation of the domain wall structure. However, fabrication and experimental studies of such nanowires are difficult. In this paper, we will show that a very good approximation of massless domain walls can be obtained in more conventional magnetic nanostripes with perpendicular magnetic anisotropy and Bloch-type domain walls. Using time-resolved magnetic imaging, we show that in Pt/Co/AlO x nanostripes the domain walls move with constant velocity, without transient effects at both the beginning and the end of the pulses. We attribute this absence of inertial effects to the combination of a narrow domain wall width and a high damping parameter α, leading to a large decrease of domain wall deformations with respect to Néel-type walls in nanostripes with a planar magnetization.

Current-induced domain wall motion (CIDM) has been studied by magnetic microscopy and electrical measurements [10][11][12][13][14][15][16], which have allowed determining the position and the internal structure of domain walls before and after the application of current pulses. Direct, microscopic observations of domain wall motion during current pulses have been largely elusive until now. These observations are, however, essential for an unambiguous determination of inertial effects in domain wall motion. In this paper, we use time-resolved photoemission electron microscopy combined with x-ray magnetic circular dichroism (XMCD-PEEM) [17,[START_REF] Schönhense | Advances in Imaging and Electron Physics[END_REF] to study current-induced motion of domain walls in Pt/Co/AlO x nanostripes with perpendicular anisotropy. The domain wall position was imaged during the application of 10-100 nanoseconds long current pulses. Our measurements show, in a direct way, that in these nanostripes the transient motion of the domain walls, which are expected to be of Bloch type in this material, is smaller than about 20 nm both at the beginning and at the end of the pulses, and thus much smaller than the displacements observed for Néel-type walls [3,4].

Nanostructures based on asymmetric stacks of Pt/Co/AlO x are promising for new spintronic devices based on the manipulation of magnetization using current pulses [START_REF] Moore | [END_REF][20][21][22]. The Rashba interaction, induced by the structural inversion asymmetry, leads to a high spintorque efficiency and very high domain wall mobilities in this system [21].

Pt(3nm)/Co(0.6nm)/AlO In order to obtain a well-defined, reproducible initial domain wall position before each current pulse, the following procedure was used : i) starting from a saturated state, a 10 µs field pulse was applied perpendicular to the sample plane to create a domain wall in several nanostripes; ii) using a sequence of current pulses, the domain walls were driven to the top exit of the nanostripes, where the increasing cross section inhibits further motion in the up direction; iii) bipolar current pulses with the same positive and negative amplitudes but a longer positive pulse were then applied for the stroboscopic mea-surements. The domain wall motion was studied during the negative part of the bipolar pulses, which drive the domain walls into the stripes, while the longer positive part of the pulses was used to reset the domain walls to their initial position. The measurements were carried out for several time delays, before, during and after the negative driving pulse, with time steps of 5-20 ns. Measurements were performed for current densities J 1 = 7.7 × 10 11 A/m 2 and J 2 = 1.3 × 10 12 A/m 2 . The driving (reset) current pulse was 120 ns (160 ns) for J 1 and 30 ns (40 ns) for J 2 . The risetime was of the order of 4 ns for all pulses.

In a PEEM microscope, the image of the sample is formed using the photoelectrons extracted from the sample surface. In order to obtain a sharp image, the potential between the focussing lens and the sample has to be adjusted accurately. Since the sample potential is modified during the current (voltage) pulses, upon scanning the delay between photon and current pulses it can be easily detected when they arrive on the sample at the same time, with an accuracy of about 100 ps. During the current pulses a potential drop is present between the extremities of the stripes (about 3 V for the images of Fig. 2). This implies that the image cannot be wellfocussed over the whole length of the stripes. This potential drop, and thus the image deformation, increases with increasing current density. ns and 100 ns after the onset of the drive current pulse. The images are corrected for the deformations induced by the voltage drop over the stripe length. In three of the four stripes shown in Fig. 2 the domain wall positions are well-defined for each delay, and the domain walls move reproducibly from up to down [24] in the direction opposite to the electron flow [25]. The behavior of the domain wall in the left stripe is much more stochastic, probably due to some strong pinning sites in the middle of the stripe, where the DW sometimes stays blocked for a certain time. This anomalous behavior was observed only in this stripe, while the dynamical behavior of the other lines was very similar, allowing data averaging to improve data quality. The domain wall position for each time delay was obtained from the linescans of the XMCD intensity along each nanostripe. The domain wall displacement was defined with respect to the domain wall position before the driving pulse, corresponding to the top entrance of the stripes. The line scans averaged over the three rightmost stripes in Fig. 2(a)-(c) are given in Fig. 2(d). The corresponding domain wall displacements for all measured delays, with time steps of 5-10 ns, are given in Fig. 3. The driving current pulse is shown in the same figure. The first important information provided by the timeresolved measurements is that the averaged domain wall displacement during the current pulse is linear in time, i.e. the DWs move at a constant average velocity. The velocity, obtained from a linear fit to the data, is 7 ± 1 m/s. Inertial effects should show up as a 'delay' of the beginning of the constant velocity regime with respect to the beginning of the pulse [4]. The fit crosses y = 0 at 4.4 ± 2.9 ns from the beginning of the pulse. If we consider that the motion during the 4 ns risetime of the pulse is negligible, the motion starts thus within 0.4 ± 2.9 ns from the onset of the 'plateau' of constant current density. The maximum time delay (including the error bar) of about 3 ns corresponds to a maximum displacement delay of 3 ns × 7 m/s = 21 nm [26].

We also measured the DW displacements for a 30 ns driving pulse with current density J 2 = 1.3 × 10 12 A/m 2 . Due to the higher voltage drop on the sample, the deformation of the images used to obtain these data was larger, leading to larger error bars. The average DW velocity obtained from the linear fit of the data points taken during the pulse is 45 ± 10 m/s, with a delay with respect to the beginning of the current pulse of 0.8±5 ns. Transient effects are therefore small also for this higher current density.

In our previous work [21], we have shown that for current densities smaller than 2 × 10 12 A/m 2 the domain wall motion in Pt/Co/AlO x nanostripes is influenced by thermally activated depinning and can be described by the so-called creep law. Note that this thermally assisted depinning does not influence the domain wall speed averaged over a large number of displacements, but it leads to a distribution of domain wall positions that becomes wider when the average displacement is larger [START_REF] Moore | [END_REF]. This is reflected in the increase of the error bar as a function of time in Fig. 3. The domain velocities of 7 ± 1 m/s for J 1 and 45 ± 10 m/s for J 2 obtained here are in good agreement with the ones we obtained on similar samples with Kerr microscopy [START_REF] Moore | [END_REF]21], where the average domain wall velocities were extracted from the slope of the displacement versus pulse duration.

Our data directly show that the transient motion of the domain walls is very small both at the onset and at the end of the current pulses, corresponding to a very small effective domain wall mass. According to Thiaville et al. [8], the domain wall internal structure is modified under the action of a field or current pulse, and the transient displacement depends on the change of generalized angle, δφ : δq = -∆ α (1 -β α )δφ. In this formula, δq is the change in domain wall position, ∆ the domain wall width at rest, α the damping parameter and β the non-adiabatic parameter [7,27]. For a Bloch wall in a nanostripe, φ corresponds to the tilt angle of the magnetization in the center of the wall with respect to the wall plane, in the direction parallel to the nanostripe. Above an angle φ of 45 • , the DW transforms into a Néel wall, then in a Bloch wall with opposite chirality (the so-called Walker limit). For the current densities used here, we have shown previously that the domain wall motion in our samples should be in the regime below the Walker breakdown [21], and the maximum value φ can take during domain wall propagation is thus 45 • .

One situation possibly leading to negligible transient effects (δq ≈ 0) is when β ≈ α. However, previous experiments have shown that β α ≈ 2 in our samples [28], with α ≈ 0.5 and β ≈ 1, leading to (1 -β α ) ≈ -1. The maximum transient displacement, for φ = 45 • , would thus be 0.25π α × 5 nm ≈ 8 nm, where 5 nm is the approximate DW width ∆ [21]. This is in good agreement with our experiments. Since the transient motion is proportional to ∆, it is expected to be smaller in systems with perpendicular anisotropy with Bloch-type domain walls, which are in general a factor ten to hundred narrower than Néel-type domain walls in in-plane systems. However, the small transient motion in our system is favored also by the relatively large value of α : for a damping parameter α = 0.02 (typical for permalloy) and β α = 2, the maximum transient motion would be about 200 nm, much larger than our experimental observation. Finally, the angle φ and thus the transient motion should be reduced by the s-d mediated Rashba field [21].

In conclusion, we have used time-resolved magnetic imaging to directly reveal the absence of transient effects during current-induced domain wall motion in Pt/Co/AlO x nanostripes with perpendicular anisotropy. We attribute the negligible domain wall mass to the combination of a narrow domain wall width, a large value of the damping parameter α and the s-d mediated Rashba field transverse to the nanostripes. Added to the large domain wall velocities obtained in these systems [21] and the good reproducibility of the domain wall displacements, such a small domain wall inertia should allow a fast and accurate control of domain wall motion at high repetition rate, by tuning the duration, frequency and amplitude of the current pulses. Our measurements also show the extreme robustness of these Pt/Co/AlO x nanostripes, since many billions of pulses with current densities higher than 1 × 10 12 A/m 2 could be applied at high frequencies without changing their physical properties.

  x layers, deposited by mag-netron sputtering on resistive Si, were patterned into twenty parallel 500 nm wide and 10 µm long stripes by ebeam lithography and Ion Beam Etching. Ti/Au electrical contacts were fabricated by UV lithography. A Scanning Electron Microscopy image of the sample is shown in Fig.1. XMCD-PEEM measurements were performed at the TEMPO beamline of the SOLEIL synchrotron, using a Focus IS-PEEM. The magnetic contrast in the Co layer was optimized by subtracting two consecutive images collected at the Co L 3 absorption edge (778.1 eV) with 100% left and right circularly polarized x-rays respectively. For each circular polarization, 60 images of 0.5 s were averaged, after correcting for possible image drifts. Temporal resolution was obtained by synchronizing the nanosecond current pulses applied to the sample with the x-ray pulses of the synchrotron single-bunch mode, where photon bunches reach the sample at a repetition rate of 846 kHz. The temporal evolution of the domain wall position in the nanostripes was obtained by recording images for different delays between the current and photon pulses[17,23]. If events are reproducible for each current pulse, the temporal resolution of this pump-probe technique is limited only by the duration of the photon pulses (about 50 ps) and the jitter between pump and probe (about 100 ps). The total acquisition time of 1 minute for each XMCD image implies that sequences of about 5 × 10 7 current (pump) and photon (probe) pulses were averaged.

FIG. 1 .

 1 FIG. 1. Scanning Electron Microscopy image showing part of the twenty nanostripes connected in parallel to a pulsed voltage source. The Pt/Co/AlOx pads and lines show up in light grey, while the silicon substrate is dark grey. The gold contacts for current injection are schematically indicated with the dashed boxes.

FIG. 2 .

 2 FIG. 2. Time-resolved XMCD-PEEM images taken during current pulses with a current density of 7.7 × 10 11 A/m 2 , for delays of 20 ns (a), 60 ns (b) and 100 ns (c) after the beginning of the pulse. Line scans of the XMCD intensity averaged over the three stripes on the right are given in (d). The zero position in this graph corresponds to the initial position of the domain walls at the top entrance of the stripes.

Figure 2

 2 Figure 2 shows XMCD-PEEM images for a selection of the twenty nanostripes present in our sample. The three images were taken during current pulses with a current density of J 1 = 7.7 × 10 11 A/m 2 , for delays of 20 ns, 60

FIG. 3 .

 3 FIG. 3. (color online)The domain wall displacements, averaged over the three stripes on the right of the images in Fig.2, as a function of time (black squares, left axis). The driving pulse with a current density of 7.7 × 10 11 A/m 2 is also shown (continuous line, right axis). The dashed line is a linear fit to the data points taken during the current pulse. The slope gives a domain wall velocity of 7 ± 1 m/s. The error bars are determined by the spread in displacement values for the three stripes, the error bar on the time is less than the width of the points.

We acknowledge the invaluable technical and experimental help of E. Wagner, D. Lepoittevin, L. Delrey, Z. Ishaque and A. Hrabec, as well as O. Fruchart for discussions. Nanofabrication was performed at the Institut Néel/CNRS 'Nanofab' facility in Grenoble. This work was partially supported by the Agence National de la Recherche through projects ANR-07-NANO-034 'Voice' and ANR-11-BS10-008 'Esperado', and by the Fondation Nanosciences.