Lionel Nesta
email: lionel.nesta@ofce.sciences-po.fr

Knowledge and Productivity in the World's Largest Manufacturing Corporations

Keywords: JEL classification: O3, L2, D24 Keywords: Knowledge, Productivity, Relatedness

This paper develops a model linking firm knowledge with productivity. The model captures three characteristics of firm knowledge (capital, diversity and relatedness) that are tested on a sample of 156 of the world's largest corporations. Panel data regression models suggest that unlike knowledge diversity, knowledge capital and knowledge relatedness explain a substantial share of the variance of firm productivity. Relatedness matters because it lowers coordination costs between heterogeneous activities. Consequently, the traditional econometric specification has repeatedly underestimated by 15% the overall short-run contribution of intangible assets to firm productivity. This underestimation becomes fiercer in high technology sectors.

Introduction

The literature investigating the econometric relationship between R&D and productivity has produced a large amount of evidence of the positive contribution of knowledge capital to firm productivity [START_REF] Griliches | Productivity, R&D, and basic research at the firm level in the 1970s[END_REF][START_REF] Griliches | Comparing productivity growth: An exploration of the French and U.S. industrial and firm data[END_REF][START_REF] Griliches | Productivity growth and R&D at the business level: results from the PIMS data base[END_REF][START_REF] Griliches | Productivity and R&D at the firm level[END_REF]. Although convincing, these studies fail to address the issue of how firms cope with heterogeneous scientific and technical knowledge, the combination of which is likely to affect overall firm performance. The reasons for this is that knowledge is considered homogenous and that, as a consequence, firm knowledge capital equates with the sum of homogeneous pieces of knowledge.

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Instead, I argue that knowledge is intrinsically heterogeneous in nature because it refers to various scientific disciplines and is embodied in diverse technical devices. Such scientific and technical knowledge may yield a variety of services, the exploitation of which is far from given to firms. As argued by [START_REF] Penrose | The Theory of the Growth of the Firm[END_REF], firms must devote additional efforts to combine their resources, comprising their knowledge capital, in a non-random and non-obvious way. The combination of these heterogeneous scientific and technical resources gives rise to ad hoc, local arrangements, leading to a persistent heterogeneity amongst competing firms. [START_REF] Teece | Understanding corporate coherence: Theory and evidence[END_REF] argue that the non-random organisation of activities has its very roots in the firm's competencies. When entering into new business lines, firms move into activities with similar scientific and technical competencies and common complementary assets. The reason for this is that diversification comes at costs, stemming from increases in agency costs, sub-optimal choices in investments across divisions and imperfect internal capital market [START_REF] Rajan | The cost of diversity: The diversification discount and inefficient investment[END_REF][START_REF] Lamont | The diversification discount: Cash flows versus returns[END_REF][START_REF] Graham | Does corporate diversification destroy value[END_REF]). An additional cost is that diversification is likely to decrease momentarily the technological coherence at both the plant and conglomerate level, thereby disrupting existing coordinating mechanisms. Firms must then devote part of their focus towards integrating these new sets of activities, competencies and technological knowledge with pre-existing ones. Therefore, diversification inherently calls for some sort of integration to increase the relatedness of the firm's activities and the underlying knowledge base [START_REF] Breschi | Knowledge-relatedness in firm technological diversification[END_REF].

In fact, relatedness across productive activities has been shown to be tightly linked with firm performance. In one of the earliest examples [START_REF] Rumelt | Strategy, Structure, and Economic Performance[END_REF] showed that diversification is more likely to be successful within related activities 2 A c c e p t e d M a n u s c r i p t sharing similar business lines and production chains. Later, related diversification has been shown to be positively associated with higher profit rates [START_REF] Scott | Purposive diversification and economic performance[END_REF]) and higher growth rate of profits [START_REF] Palepu | Diversification strategy, profit performance and the entropy measure[END_REF]. [START_REF] Schoar | Effects of corporate diversification on productivity[END_REF] shows that although increases in diversification lead to a net reduction in total factor productivity, diversified firms enjoy higher productivity levels than single segment firms. The main justification for this lies in the presence of economies of scope, the benefit of which is likely to be a positive function of relatedness across business lines [START_REF] Montgomery | Diversification, market structure, and firm performance: An extension of Rumelt's work[END_REF][START_REF] Ramanujam | Research on corporate diversification: a synthesis[END_REF][START_REF] Montgomery | Diversified expansion by large established firms[END_REF][START_REF] Teece | Understanding corporate coherence: Theory and evidence[END_REF].

It is well recognised that economies of scope arise when similar productive sequences are shared among several business lines. Still, related diversification also stems from vertical diversification, where the productive activities across businesses integrate complementary activities and competencies. Arguably, the cost of coordinating a set of productive activities decreases as the knowledge used in these activities is being combined efficiently. For example, [START_REF] Scott | Purposive diversification of R&D in manufacturing[END_REF] demonstrate that R&D diversification in large U.S. manufacturing firms is found to be purposive (to exploit complementarities across research programmes that consolidate around related categories of products). Thus activities based on a set of related technological knowledge should prove more productive than activities based on a heterogeneous and unrelated set of activities. In other words, integrated knowledge bases should be positively linked with firm productivity.

This paper develops a model that analyses the contribution of firm knowledge. This model generalises the traditional econometric specification where only intangible capital is assumed to play a significant role. Instead, the model captures three characteristics of firm knowledge (knowledge capital, diversity and relatedness),

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showing that the traditional model is the specific case for firms with completely unrelated scientific and technical knowledge. A firm's knowledge base is considered related when all scientific and technological competencies are found to be statistically inter-dependent. The paper tests for the importance of these three characteristics (knowledge capital, diversity and relatedness) using financial and patent data from a sample of the 156 world's largest manufacturing firms between 1986 and 1996. The major finding is that unlike knowledge diversity, knowledge capital and relatedness are important sources of productivity at the firm level.

The paper is structured as follows. Section 2 develops the formal model. Sections 3 and 4 present the measures, data and econometric model used in this paper.

The results are discussed in Section 5, leading to the conclusion of Section 6.

The Model

Similar to [START_REF] Griliches | Issues in assessing the contribution of research and development to productivity growth[END_REF], I start by using an augmented Cobb-Douglas production function. Firm output is a function of firm traditional factor endowment of capital and labour and firm knowledge stock:

Q it = A • C β it • L α it • K δ it • exp(u it ), (1)
where subscripts i and t refer to the firm i and the current year t, Q is output measured by sales, A is a constant, C is the gross value of plant and equipment, and L is the number of employees. Traditionally in Eq.( 1), K is defined as the firm's stock of knowledge corrected for technical obsolescence:

K it = kit + (1 -δ) • K i,t-1 ,
where kit is new knowledge acquired by firm i at time t and δ represents the rate of knowledge obsolescence. There is no unique way of measuring k, but R&D

4

A c c e p t e d M a n u s c r i p t expenses and patents, either granted or applied for, have been by far the most widely used proxies to date.

This approach has received a lot of attention, due both to its simplicity and to the significant improvement it has brought to our understanding of the contribution of intangible assets to productivity. However, the above formulation fails to address the issue of heterogeneous scientific and technical knowledge. These encompass specific technical artefact, human capital, scientific principles guiding research activities as in the biopharmaceutical industry and so on, the combination of which is far from being given to firms. Assume for simplicity that firms are composed

K ≡ E • [1 + (D -1) • R]. ( 4
)
Eq.( 4) states that firm knowledge is a function of its total knowledge capital or expertise E, the number D of productive activities implemented within the firm, and relatedness R across activities.

The amendment of K as done traditionally leads to insert two supplementary properties of firm knowledge: knowledge diversity and knowledge relatedness. The existence of these properties is due to the collective nature of knowledge: in order to produce aggregate outcomes, diverse knowledge must be combined in a nonrandom and non-obvious way and integrated into a coherent base. Supposing for instance that firm i is composed of a set of activities with highly related knowledge (R > 0), knowledge base K increases with the number D of productive activities implemented inside the firm weighted by their average relatedness R. Conversely if firm i is composed of a set of activities with entirely unrelated technical knowledge, implying no spillovers across activities (R = 0), the knowledge base K is reduced to its knowledge stock E as measured traditionally. Thus this paper advances a more general formulation of firm intangible assets, where the traditional measure of K is the special and unlikely case where R = 0.

For the sake of simplicity, let us start by using the following approximation:

K ∼ = E • D • R. ( 5
)
Substituting ( 5) into (1), noting θ K = δ× K , where K is the weight attributed to each of the three properties K = {E, D, R} of firm knowledge base yields:

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Q it = A • C β it • L α it • [E E • D D • R R ] δ it • exp(u it ) (6) = A it • C β it • L α it • k k θ K it • exp(u it ),
or in the log form:

q it = a + β • c it + α • l it + k (θ k • k it ) + u it , ( 7
)
where k = {e, d, r} and β, α and θ k are the parameters of interest. Eq.( 7) can be estimated using ordinary least squares. The error term u it is decomposed into η i , λ t and ε it , where η i ∼ IID(0,σ 2 η ) is a 1×1 scalar constant capturing persistent but unobserved individual heterogeneity across firms such as managerial capabilities, firm propensity to collaborate, the type of economic environment, and so on, λ t ∼ IID(0,σ 2 λ ) is a 1×1 scalar constant representing the time fixed effect that would capture positive or negative trends common to all corporations, and ε it ∼ IID(0,σ 2 ε ) is the individual disturbance.

Measures of Firm Knowledge

Perhaps the starting point of any work on knowledge should simply state that unlike physical assets, it is impossible for all components of intangible capital to be accurately described. Therefore the observer can only find indirect traces of knowledge. For example, the contributions by Griliches have repeatedly used (the accumulation of past) R&D investments as a proxy for knowledge capital.

Patent data have also been used for similar purposes, and in what follows, I base the three measures of knowledge capital, diversity and relatedness on the use 7 A c c e p t e d M a n u s c r i p t of patent statistics. There are several pitfalls in using patent statistics, ranging from persistent sectoral differences in firm patenting to the quite heterogeneous economic value of patents [START_REF] Archibugi | Patenting as an indicator of technological innovation: A review[END_REF][START_REF] Pavitt | Uses and abuses of patent statistics[END_REF]). However, these critics lose their relevance when one uses patents statistics as a proxy for competencies, not as a proxy for innovative performance.

The other difficulty with the three knowledge variables is that one should expect them to be collinear, since empirical evidence suggests that firms diversify into related technologies [START_REF] Teece | Understanding corporate coherence: Theory and evidence[END_REF][START_REF] Breschi | Knowledge-relatedness in firm technological diversification[END_REF][START_REF] Fai | Corporate technological competence and the evolution of technological diversification[END_REF]. In this case, the decision to diversify is likely to be conditioned by issues regarding other knowledge variables. Typically, the decision to diversify will raise issues on the investments necessary to acquire any new technology, and on its complementarity with existing ones. As a consequence, processes of diversification will always increase knowledge stock E, but may or may not increase relatedness R, depending on the degree of complementarity between the newly acquired technology and those previously mastered by the firm. The question of the drivers of knowledge expertise, diversification and relatedness and of their interdependencies are important questions in their own rights, but they are beyond the scope of the present paper. Below, I deal with issues of multicollinearity from the statistical viewpoint only, to then consider all knowledge variables as independent predictors of the firm's productive efficiency.

Patent statistics provide information on technology classes in which firms develop technological competencies. This information is essential in experimenting for the expected positive role of knowledge diversity and knowledge relatedness.

First, I proxy knowledge capital using the so-called permanent inventory method and measure it as the cumulated stock of past patent grants using a rate of knowl-8 A c c e p t e d M a n u s c r i p t edge obsolescence of 15 percents per annum:

E it = ġit + (1 -δ) • E i,t-1
, where ġit is the number of patent grants of firm i in year t and δ represents the rate of knowledge obsolescence.

Second, I define knowledge diversity as the breadth of firm knowledge base. Let ġkit be the number of patents grants of firm i at time t in technology class k. In order to compensate for abrupt changes in firm learning strategies and introduce some rigidities in the technology portfolio of the firm, P kit sums patent grants over the past five years: It should be pointed out, however, that as the patent stock increases, the likelihood of developing competencies in auxiliary technologies increases correspondingly. Thus measures E and D, namely knowledge capital and knowledge diversity, are likely to be correlated, which may induce multicollinearity problems when estimating their associated elasticities. I correct for this by computing the difference between the observed diversity D and the expected diversity D, conditional on patent stocks:

P kit = 4 τ =0 ġki,
D it = D it -E[D it | E it ] = D it -Dit .
By its very construction, D it can be either negative or positive. A positive (negative) measure of knowledge diversity informs on the relatively high (low) degree of knowledge diversity, given firm knowledge capital.

Third, the measure of knowledge relatedness in two steps: in the first step, I quantify technological relatedness between any two technologies k and l; in the second step, I assume that technological relatedness is given to firms, so that firms first observe all τ 's and then choose their technology portfolio. Thus I use τ kl to 9 compute the weighted average relatedness of all technologies held within the firm.

In the first step, I estimate the relatedness measures τ kl between any two technologies k and l by comparing the observed frequency f kl with which the two technologies are jointly used with the expected frequency fkl of their co-use. The observed frequency f kl with which two technologies are used simultaneously is derived from patent documents. The computation of the expected frequency fkl may be grounded on several methods (parametric vs. non-parametric), but in any case it must be based on the hypothesis that the two technologies are randomly used together. In this paper, I calculate the expected frequency on the assumption that the distribution of random technological co-occurrences is hypergeometric (See Appendix A available on the website of the Journal). The outcome of the comparison between f kl and fkl produces the relatedness measures τ kl , as detailed in Appendix A, Eq.(A-5). Typically, τ kl is a real number that can be positive or negative and may be thought of as the strength of the technological relationship between technologies k and l, or relatedness.

In the second step, I compute the weighted average relatedness W AR k of technology k with respect to all other technologies within the firm. Similarly to [START_REF] Teece | Understanding corporate coherence: Theory and evidence[END_REF], the weighted average relatedness W AR k of technology k is defined as the degree to which technology k is related to all other technologies l = k present within the firm, weighted by patent count P lit :

W AR kit = l =k τ kl • P lit l =k P lit . ( 8
)
Measure W AR kit expresses the expected relatedness of technology k with respect to any given technologies randomly chosen within the firm. W AR kit may be either positive or negative, the former (latter) indicating that technology k is 10 A c c e p t e d M a n u s c r i p t closely (weakly) related to all other technologies within the firm. Consequently, knowledge relatedness is defined as the weighted average of the W AR kit measures:

R it = l =k W AR kit × P kit k P kit . ( 9
)
Eq.( 9) estimates the average relatedness of any technology randomly chosen within the firm with respect to any other technology. Again, this measure can be either negative or positive, the latter indicating that the firm's technologies are globally well related, while a negative value shows a poor average relatedness amongst the technologies in which the firm has developed competencies.

Applied to technology classes, the relatedness measure implies a different interpretation than when applied to activities, as done in [START_REF] Teece | Understanding corporate coherence: Theory and evidence[END_REF]. For

these authors, the prominent reason for related diversification lies in the similarity of activities amongst the firm's various production lines. Diversification is related when common competencies are shared in a (bounded) variety of business lines.

This differs from our own interpretation of relatedness as applied to technologies.

Technological relatedness τ kl assesses the statistical intensity of the joint use of two given technologies and thus indicates that the utilisation of technology k implies that of technology l in order to perform a specific set of activities. In other words, technologies are related when their combination leads to specific technological functions that are not reducible to their independent use. Hence a reasonable interpretation of technological relatedness is that it indicates primarily the complementarity of the services rendered by two technologies. In the remaining of the paper, I shall refer to relatedness as assessing the complementarity between two technologies1 .

Data

The dataset used in this study is a compilation of a patent data set crossed with a financial data set. Concerning the former, I used the US Patent and Trademark

Office (henceforth USPTO) patent dataset provided by the National Bureau of Economic Research [START_REF] Hall | The NBER patent citation data file: Lessons, insights and methodological tools[END_REF]. This dataset comprises more than 3 million US patent grants since 1963, but requires some additional manipulations to convert it into a workable tool. First, using the information on the company name and year of application2 , I selected the most abundantly patenting manufacturing firms using Fortune 500, August 1998 [START_REF] Fortune | The world's largest corporations August[END_REF]. Because many of the world's largest companies operate outside the manufacturing sectors, such as banking or insurance, the selection yielded a sample of 162 companies, meant to be the world's largest manufacturing corporations. Second, the lack of data on firm consolidation in the USPTO patent dataset was overcome using the Who Owns Whom 2000

Edition. The consolidation exercise proved extremely useful, inflating the number of patents held by the firms in the sample by more than 300,000 [Table 1 about here.]

The other data set, the 1997 edition of Worldscope Global Researcher, provides the financial variables needed. Firm sales are used as a proxy for output (Q), gross value of property plant and equipment proxies firm capital (C), and the number of employees is used to proxy labour (L). Ideally, one would like to measure value-added to measure output (Q) more accurately and control for labour quantity and quality by having data on the number of hours worked and on wages and compensation. Unfortunately, companies do not disclose such information systematically and the resulting figures proved too scarce to be of any use. We do not have information on value-added by firms, and information on the number of hours worked or on education is not systematically provided in the company SEC filings. Therefore, the variable on labour input can only be used in ratio, yielding the following functional form:

Q L it = A • C L β it • L ϕ it • k k θ K it • exp(u it ) (10)
where ϕ = α + β -1. The parameter ϕ is used as an assessment for constant returns to scale. If the parameter ϕ is not significantly different from nullity (i.e. ϕ = 0), the world's largest manufacturing firms are enjoying constant returns scale in production. However if ϕ is significantly different from zero, the production of the representative firm in the sample departs from an equilibrium of constant returns to scale, and leaves prospect for either downsizing (ϕ < 0) or expansion in the scale of productive activities (ϕ > 0). Taking logs yields

(q -l) it = a + β • (c -l) it + ϕ • l it + k (θ k • k it ) + u it , (11)
where k = {e, d, r}. The left hand side of Eq.( 11) is the logarithm of labour [Table 2 about here.]

Compiling data from both the patent and financial datasets produced an unbalanced panel dataset of 156 companies observed between 1986 and 1996, yielding 1,608 observations. Tables 1 and2 II), with more than 5 percent of their sales invested in research. Thus, our findings are likely to be biased towards more research-intensive sectors, which is in line with the selection procedure of selecting the most abundantly patenting firms in the set of the world's largest manufacturing corporations.

Consistent with Eq.( 11), all variables are entered in logs, and their correlation coefficients are displayed in Table 3.

[Table 3 about here.] 15 5 Results

Preliminary results

Several econometric specifications have been used to estimate Eq.( 11), and Table 4 reports the main results. In Column (1), the results of Ordinary Least Squares (OLS) on the pooled sample show that all explanatory variables have a significant effect on labour productivity. Not surprisingly, the effect of physical capital (c -l)

is large (0.690) and in line with previous findings that state that the omission of materials in the production function overestimates the effect of physical capital [START_REF] Griliches | Productivity and R&D at the firm level[END_REF]. The estimate for labour l is significant and negative (-0.197), which implies that the world's largest manufacturing corporations cope with decreasing returns to scale. This is hardly surprising, for the size of the world's largest corporations offers little scope for productivity gains related to increases in their scale of operations. The effect of the newness of capital (N C/C) is significant

(1.005), suggesting a positive contribution of embodied technical progress to firm productivity.

The effects related to firm knowledge are all significant. Consistent with the works of Griliches, knowledge capital contributes positively to firm productivity (0.035), although knowledge capital as measured here differs from measures of R&D stocks. The negative sign of knowledge diversity (-0.101) is in line with, but not identical to, the so-called "diversification discount". As product diversification, diversified knowledge bases impact negatively on firm productivity owing to increased agency costs and sub-optimal choices in investments across divisions.

By the latter, we mean that assimilating technologies unrelated to those already mastered by the firm increases initial investments. These sunk costs should presumably affect productivity negatively, at least in the short run.

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Knowledge relatedness is positive (0.894) with high significance. This conforms to the initial intuition that knowledge relatedness is related to coordination costs: firms diversifying in related activities are more productive because the cost of coordinating a heterogeneous set of related productive tasks is simply inferior to that combining unrelated activities. This is consistent with the proposition that effective knowledge combination lowers coordination costs across the productive activities within firms. This finding is particularly important because it also implies that the overall effect of firm knowledge is larger that the mere effect of knowledge capital. That is, the traditional econometric specification has repeatedly underestimated the overall contribution of intangible asset to firm performance.

Columns ( 2)-( 5) explore alternative specifications of Eq.( 11) in order to test the robustness of these preliminary findings. Column (2) controls for unobserved heterogeneity by converting all variables as differences from group (firm) means:

x it = x it -x i , where x is any of the dependent and independent variables. This wipes out the unobservable and persistent heterogeneity across firms that may alter the consistency of the estimates. The specification (Least Square Dummy Variable -LSDV) produces significant estimates for most explanatory variables: large corporation cope with decreasing returns to scale, and the effect of knowledge capital and relatedness remain highly significant whereas the effect of knowledge diversity to productivity becomes insignificant.

Eq.( 11) relies on the critical assumption that the error term e it is serially uncorrelated. One can relax this assumption by adopting a dynamic representation of Eq.( 11), converting all level variables into growth rates (log differences). This specification is robust to spurious regressions where significant estimates may be driven by their positive correlation with time. First in column (3), all variables

A c c e p t e d M a n u s c r i p t are expressed as differences from their value at time t -1 weighted by parameter ρ representing first order autocorrelation (AR1): x it -ρx it-1 . The estimated ρ has a standard value of slightly above 0.5. In the first difference model (FD, Column 4) where ρ is set to unity, knowledge capital and relatedness keep their high significance levels, although the latter becomes significant at the 5 % level.

This observation is quite satisfactory, as the autoregressive models with firm fixed effects is a fairly conservative method where a substantial share of the information available in the dataset is swept away before the actual estimation.

[Table 4 about here.]

The inclusion of a lagged dependent variable makes the standard panel estimation techniques, Ordinary Least Squares (OLS), inconsistent because the lagged dependent variable induces a correlation between the explanatory variables and the error term. A standard procedure for dealing with variables that are correlated with the error term is to instrument them using the Generalised Method of Moment (GMM) estimator along the lines suggested by [START_REF] Arellano | Some tests of specification for panel data: Monte carlo evidence and an application to unemployment equations[END_REF]. The GMM one-step estimates (Column 5) produce significant estimates for all variables, with the exception of knowledge diversity. They imply that from a dynamic perspective, positive changes in knowledge capital and relatedness lead to positive changes in firm productive efficiency. We also note that the significance of newness is low. Globally, these results are consistent with the idea that both knowledge capital and knowledge relatedness are significant drivers of productivity at the firm level.

One crucial question relates to the magnitude of the parameter estimates for both knowledge capital and knowledge relatedness. Fundamentally, these results

suggest that knowledge relatedness is economically valuable, the extent to which

Sample Decomposition

I deal with the first issue by decomposing the sample in several ways. The results are reported in Table 5. The parameter estimates reveal their usual robustness, but interesting insights emerge from the results. In column (6), I control for the possible contagion of results from outliers by excluding observations located in the top and bottom 5 percentiles of observations for the dependent variables.

The results are consistent with Table 4, although the estimated parameters, while keeping their significance levels, are all closer to zero (note the drop in the Rsquare). This suggests that a good deal of information on the relationship between tangible and intangible assets and firm productivity is found in the tails of the distribution. Interestingly, computing θ sd r θ sd e +θ sd r inflates the ratio to 19%, reinforcing the argument that knowledge relatedness must be accounted for when assessing the contribution of intangible assets to firm productivity.

In columns ( 7)-( 9), I control for the R&D intensity of sectors, where observations have been grouped according to the sectoral aggregate R&D intensity as displayed in In low-technology sectors, the source of superior productivity does not seem to rely on the characteristics of firm knowledge. In fact, one should be careful in rejecting the role of knowledge in low-technology sectors for two reasons. First, it may well be that these firms have all achieved a satisfactory level of knowledge capital and relatedness that is a pre-requisite for their productive operations.

Since knowledge is supposedly more stable, the knowledge variables are no more a discriminating criterion for high productivity, but remain a criterion for firm survival. Failure to accumulate and integrate knowledge in a productive fashion may lead to firm exit. Second, the method using patent statistics may be more [Table 5 about here.]

Last in columns ( 10) and ( 11), I investigate the effect of geography on the production function by grouping firms in two sets: America, including Canada (Column 10) and Europe (Column 11). Both groups have a peculiar production function. American firms conform mostly to the general results. The determinants of firm productivity in European corporations are similar with the exception of knowledge relatedness, whose parameter estimate, though positive, becomes non-significant. How should we interpret this? One can think of two competing interpretations. First, the observed regional differences reflect actual differences in production function, notably concerning the use of scientific knowledge and the way heterogeneous knowledge is combined. Second, these parameter differences are the outcome of differences in regional sector endowment. This second explanation implies that in Europe, knowledge relatedness should be a significant contributor to firm productivity in high technology sectors as well. To arbitrate between these two explanations, we ran an additional within regression for the sample of European firms in high-technology sectors. The results 7 show that indeed in high technology sectors, both knowledge capital and knowledge relatedness are active component of the production function in Europe.

7 The results are not reported here, but can be obtained upon request to the author.

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Using Alternative Measures of Firm Knowledge

One may object that our results are driven by the way with which we measure firm knowledge. This choice is important because it may affect the significance and signs of the relationships with productivity. In order to test the robustness of the results, table 6 provides the parameter estimates using alternative measures of firm knowledge. In column ( 12), I follow [START_REF] Griliches | Productivity growth and R&D at the business level: results from the PIMS data base[END_REF] and [START_REF] Griliches | Productivity and R&D at the firm level[END_REF] and use the ratio (R/Q) to proxy knowledge capital. The results are as expected, positive and significant, although the estimate for knowledge relatedness loses its significance due to its co-linearity with R&D investments.

In column (13), I introduce knowledge diversity computed as the dispersion of firm competencies across technological areas: D it = µ P,it ÷ σ 2 P,it . This measure is the inverse of the coefficient of variation and increases as firm competencies are distributed evenly across technologies ( lim

σ 2 P kit →∞ D it → +∞). Impor-
tantly, this measure is not based directly on the number of patents held by the firm over the past 5 years, but on its revealed technological advantage, defined as RT A it = (P it / k P kit ) ÷ ( i P kit / ki P kit ). The numerator is the share of patents in technology k in the total patent stock of firm i. Likewise, the denominator represents the share of patents in technology k in the total patent stock of all actors. Therefore for a given technology, if the share of patents of firm i exceeds that of all actors, RT A will be greater than unity and firm i will have a so-called Revealed Technological Advantage in technology k. 8 This measure has the advantage of re-scaling all patent grants to a measure accounting for heterogeneous firm propensities to patent by relying on a more accurate idea of the firm's distinctive skills.

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The results show a persistent non-significance of technological diversification with firm productivity, whereas the other estimates are consistent with previous results. I do not, however, rule out the significant role of technological diversity in firm activities. First, diversification has been depicted to be a major input for innovative activities, simply because new ideas are more likely to emerge from a stock of diversified knowledge [START_REF] Henderson | Scale, scope and spillovers: the determinants of research productivity in drug discovery[END_REF]. Switching the dependent variable with innovative output would certainly depict the positive and significant contribution of knowledge diversity to firm innovation. Second, technological diversification is being increasingly viewed as a major characteristic of modern productive activities: firms differ more on the basis of their product portfolio than they do in terms of their technological competencies, precisely because the share of scientific and technical knowledge in productive activities has increased substantially, keeping the number of productive activities constant [START_REF] Patel | The technological competencies of the world's largest firms: complex and path-dependent, but not much variety[END_REF]Pavitt 1997, Gambardella and[START_REF] Gambardella | Does technological convergence imply convergence in markets? Evidence from the electronics industry[END_REF]. Finally firms must develop technical competencies other than those they directly exploit in their very productive activities, first to benefit from technical spillovers from competitors (Jaffe), and second to cope with the technological development of their most direct partners [START_REF] Brusoni | Knowledge specialisation, organizational coupling, and the boundaries of the firm: Why do firms know more than they make[END_REF].

Last, I develop several measures of knowledge relatedness. Echoing Section 3, there are two main choices one must make when measuring knowledge relatedness within firms: the choice of a relatedness measure τ kl and the choice of how to measure knowledge relatedness within the firm, given technological relatedness.

Concerning the former, Appendix A suggests that there is no authoritative metrics for quantifying relatedness between technologies. Instead of relying on a parametric setting that produces relatedness τ P kl , one can also develop a non-parametric (1994) and [START_REF] Breschi | Knowledge-relatedness in firm technological diversification[END_REF] and include only the (m -1) strongest links that are needed to create a connected graph that comprises all firm competencies. This captures the strongest associations across technical areas k and l and is equivalent to depicting the maximum spanning tree from graph G = (K, R). I thus rewrite Eq.( 8) as follows:

W AR kit = l =k τ kl • P lit • λ kl l =k P lit • λ kl , ( 12
)
where λ kl = 1 is the link between technological competencies k and technological competence l is part of the tree. Because W AR only includes the strongest links within the firm, W AR is likely to produce measures of firm knowledge relatedness that are biased upwards, whereas conversely the previous measure is biased downwards.

[Table 6 about here.]

The results in Table 6 show that the measure of knowledge relatedness is generally robust. In column ( 14 Clearly, knowledge relatedness embodies a large firm-specific element that is not captured with the methodology developed in the paper and that goes beyond the means of the metrics suggested here.

In all instances, this measure is likely to embody quite a bit of noise, which in turn should bias the parameter estimate of knowledge relatedness θ R downwards with respect to its unknown true value θR . Thus globally, the positive and significant relation between knowledge relatedness and firm productivity is quite supportive for the theory that more integrated knowledge is associated with lower coordination costs, thereby increasing significantly firm productivity. Although the ratio θ sd r θ sd e +θ sd r drops to 12%, its level remains sufficiently large to motivate further research in this area.

The Non-Linear Specification

The last issue concerns the validity of the linear specification, relying on the sim-

plification that K ≡ E • D • R, whereas the original model implies that K = E + (1 + (D -1) • R).
Consistently with the previous results, I consider the estimate of knowledge diversity ω D as being a residual, so that

ω D = 1 -ω E -ω R .
Substituting (4) into (6) yields

26 Q L it = A • C L β it • E E it + [1 + (D it -1) 1-E -R • R R it ] δ • exp(u it ), ( 13
)
where the parameters E and R represent the weights associated with, respectively, knowledge capital and knowledge relatedness, whereas δ represents the overall effect of firm knowledge base on firm productivity. In the log form, Eq.( 13) becomes 14)

(q -l) it = a + β • (c -l) it + ϕ • l it + δ • log E E it [1 + (D it -1) 1-E -R • R R it ] + u it .(
All variables are expressed as deviations from firm means, wiping out the unobservable heterogeneity across firms. Importantly, log(E + (1 + (D -1) • R)) can be negative, implying that Eq.( 14) cannot be estimated. To deal with this issue, all knowledge variables are standardised in such a way that E, D, R ∈ [2; 3].

[Table 7 about here.]

Table 7 reports the results for the whole sample and for the high-technology sectors. It also distinguishes between the two measures of knowledge relatedness based on the W AR and W AR computations. Although the parameter estimates for knowledge relatedness are at the borderline of significance (Columns 17 and 19), the results remain globally consistent with the previous remarks. First, the elasticity of deflated sales with respect to physical capital, although overestimated, remains quite stable across the specifications. The parameter for returns to scale is consistently negative for the sample as a whole, whereas firms active in high technology sectors operate in constant returns to scale.

A c c e p t e d M a n u s c r i p t

The estimates depicting the elasticity of output with respect to firm knowledge are globally satisfactory. In columns ( 17) and ( 19), parameter δ is largely significant and positive, suggesting that firm total knowledge is tightly linked with firm output per employee. The weights E and R imply that knowledge capital is the prime intangible capital, more so than knowledge relatedness. They also suggest that the effect of knowledge diversity on firm productivity may not be a simple residual (columns 17 and 19). Computing D = E -R shows that the role of knowledge diversity becomes quite large (0.218 in column 17 and 0.210 in column 19) for the whole sample of firms.

The comparison of columns ( 17) with ( 18) and ( 19) with ( 20) suggests that in high-technology sectors, the role of knowledge relatedness is essential in boosting firm productivity. This is further compatible with the last estimates relating to the newness of physical capital (N C/C). Its large and significant effect in high-technology sectors suggests that much of firm productivity gains go through investments embodied in high-technology equipment. The supposedly higher technological turbulence in sectors such as chemicals (including the highly turbulent pharmaceutical industry), instruments, and electronics challenges large corporations in their ability to assimilate and exploit new technical knowledge by integrating it into their own production function.

Globally, the non-linear specifications produce estimates that compare well with previous estimations. There is an issue regarding the role of knowledge relatedness, but the associated parameter estimate remains at the borderline of significance. Its value is consistent with previous estimations: knowledge capital and knowledge relatedness are active components of firm productivity, especially in high-technology sector.

28

A c c e p t e d M a n u s c r i p t

Conclusion

This paper has developed a model linking firm knowledge with productivity. This model generalises the traditional econometric specification where only intangible capital is assumed to play a significant role. Instead, our model captures three characteristics of firm knowledge (knowledge capital, diversity and relatedness) that are then tested on a sample of 156 of the world's largest corporations. The major finding is that unlike knowledge diversity, knowledge capital and relatedness are important sources of productivity at the firm level. The traditional econometric specification has repeatedly underestimated by about 15% the overall short-run contribution of intangible assets to firm performance. This underestimation becomes fiercer in high technology sectors.

Importantly, knowledge capital cannot exhaust the contribution of intangibles to firm productivity. The intrinsically heterogeneous nature of knowledge implies that the way scientific and technical knowledge is combined impacts on firm productivity. The econometric results show that more integrated, better-articulated knowledge bases reach higher levels of productivity, beyond and above the prime role of knowledge capital. The theoretical justification lies at the heart of economic theory: the cost of coordinating coherent knowledge bases is simply lower than that of coordinating unrelated pieces of knowledge.

Several issues relate to the heterogeneous nature of the sample across time, industries and regions. Although there are important differences, these apply to the knowledge base as a whole more than they question the economic relevance of knowledge relatedness. Globally, the role of knowledge relatedness becomes stronger in knowledge-intensive sectors such as chemicals, drugs, electronics and instruments. In other sectors, its contribution remains positive and significant,

29

A c c e p t e d M a n u s c r i p t but significantly lower, even after controlling for plausible mismeasurements in the knowledge variables and possible mispecifications in the econometric model.

The persistent non-significance of knowledge diversity contradicts the view that technological diversification is a major characteristic of modern productive activities: firms differ more on the basis of their product portfolio than they do in terms of their technological competencies. The reason for this is that for a given product line, the share of scientific and technical knowledge in productive activities has increased dramatically with the rise of the knowledge economy. However, firms must develop technical competencies other than those they directly exploit in their very productive activities in order to cope with technological turbulence.

Thus, one should keep in mind that firms seek several goals at once, some contradicting others. Unquestionably in the short run firms need to generate revenues.

In the long run, they must anticipate as accurately as possible the potential technological opportunities that may impact directly on their productive operations.

In other words, firms must invest in several research avenues, few of which may prove highly profitable.

This tension between profitability and survival has long been identified [START_REF] March | Exploration and exploitation in organisational learning[END_REF]. I suspect that the characteristics of firm knowledge must reflect these di- 2

The USPTO advertise only patent grants, not patent applications. This should not be a problem for computing all knowledge variables, since it acts as a quality filter on the firm's patent portfolio. Note that I use the year of application, not the year in which the firm was awarded the patent.

3 The number of patents held by the world's largest manufacturing firms reached 500,000 prior to consolidation, but increased to 800,000 after controlling for consolidation. This illustrates the need for such an exercise as well as it indicates the difficulty of the task. I am very thankful to

Parimal Patel for providing the information.

4 This was completed using all IPC codes as displayed on the Internet Web Site of the European Patent Office. I am indebted to Bart Verspagen and Paola Criscuolo for their much appreciated help during the automated process.

5 The aggregation of technology classes into larger categories is a necessary but delicate exercise, because it influences negatively the variance of knowledge diversity and relatedness across firms. Prior literature [START_REF] Jaffe | Technological opportunity and spillovers of R&D: Evidence from firms' patents, profits and market values[END_REF][START_REF] Hall | The NBER patent citation data file: Lessons, insights and methodological tools[END_REF], suggests that a thirty-dimensional technological space may be an appropriate aggregation. But since this paper deal with the largest manufacturing firms, using such a level of aggregation is likely to reflect product more than knowledge diversification while decreasing too severely the variance of knowledge diversity and relatedness across firms.

A Measures of Technological Relatedness

Technological relatedness has been investigated in several publications [START_REF] Sherer | Using linked patent and R&D data to measure interindustry technology flows[END_REF][START_REF] Jaffe | Technological opportunity and spillovers of R&D: Evidence from firms' patents, profits and market values[END_REF][START_REF] Breschi | Knowledge-relatedness in firm technological diversification[END_REF]

= N -1, so that σ 2 kl ≈ fkl • ( N -f k N ) • ( N -f l N ).
Considering the number N of patent grants for each year, it is a reasonable approximation. This may go some way against the intuition that knowledge and technologies form a hierarchical tree [START_REF] Popper | Objective Knowledge: An Evolutionary Approach[END_REF]) but it offers the advantage of simplicity when dealing with multi-technology firms.

In a non-parametric setting, one makes no assumption about the form of the distribution of technological co-occurrences across patents applications. A straightforward way to measure relatedness is then to compare the observed probability of any patent to combine technologies k and l with the expected probability, under the assumption that the event "patent with technology k" is independent from the event "patent with technology l". Let s kl , s k and s l denote the shares of number of patent applications with respectively both technologies k and l, technology k, technology l in the total number of patents applications N :

S kl = f kl N ; S k = f k N ; S l = f l N
. By definition, s k •s l is the share of patents with technologies k and l under the assumption that both technologies are independent, so that s k • s l represents the expected share ŝkl with random technological co-occurrences. Using information theory [START_REF] Theil | Statistical Decomposition Analysis[END_REF], one can then define the non-parametric technological relatedness τ N P kl as follows: technologies k and l are rather well related. If s kl ÷ ŝkl < 1 , then τ N P kl < 0:

the technologies k and l are rather poorly related. Again, relatedness is a real number that can be either positive or negative and is symmetric, so that relatedness between k and l is strictly equal to relatedness between l and k. two-by-two technological combinations, whereas in a 120-dimensional technological space, the total number of potential co-occurrences is K × (K -1) × 1 2 = 7140. This gap suggests the presence of some determinism, possibly objective and scientific [START_REF] Popper | The Logic of Scientific Discovery[END_REF], or sociological [START_REF] Kuhn | The Structure of Scientific Revolution[END_REF], since the explored technological combinations are substantially less numerous than all their potential co-use. On average, the mean number of patents f kl in which two technologies are used together is 44. Value f kl ranges between 1 and 6,650, implying a considerable variance in technological co-occurrences. In fact, the distribution of f kl is positively skewed, implying notable departure from normality.

Turning to the relatedness measures, the most immediate observation is that the mean value of both τ P kl and τ N P kl is negative and significantly below 0. This suggests that most technological combinations are unexpected as compared to what should be expected under the random co-occurrence hypothesis. This reflects, on the one side, behaviours of technological exploration, and on the other side choices of local (idiosyncratic) technological combination negatively captured by A c c e p t e d M a n u s c r i p t the metrics developed here. Both computations yield the same number of positive relatedness; 25% of relatedness measures are positive, derived from the same observations. In terms of distributional spread, the parametric approach produces a larger dispersion, with higher variance, lower minimal and higher maximal values.

Last, the distribution of the non-parametric measure is closer to normality than the parametric counterpart, the latter having positive skewness and heavier tails.

However in both cases, the Kolmogorov-Smirnov test of normality rejects the null hypothesis that the variables are distributed Normal. Which of these two measures should one choose? The most immediate advantage of the non-parametric approach lies in the interesting distributional properties of the computed τ N P kl . Its distribution is very close, albeit not equal, to normality. In this paper however, I opt for the parametric approach for two reasons. First, unlike the non parametric setting, the parametric approach has already received considerable attention in the literature. Hence this choice offers more consistency with previous works (Teece et al. 1994, Breschi et al. 2003, Nesta and kl and τ N P kl reach 0.70 and 0.86 respectively. This large correlation implies that our choice will affect the computations of R only marginally. In fact, Subsection 5.3 explores the robustness of the results by computing knowledge relatedness R at the firm level using the non-parametric measure τ N P kl . It confirms that this choice does not affect the direction and significance of the contribution of knowledge relatedness to the firm productive efficiency.

44

A c c e p t e d M a n u s c r i p t

  of a vector P of D productive activities, P = [p 1 , ..., p d , ...p D ]. Each activity p d draws primarily on its associated scientific and technical expertise e d , so that the firm's total expertise is vector E = [e 1 , ..., e d , ...e D ]. However, activity p d may also benefit from the expertise developed in other activities l (l = d), depending on the level of relatedness τ between technical expertise e d and e l . It follows that the knowledge base k used by the d th activity is k d ≡ e d + D l =d e l • τ ld .(2)Eq.(2) means that the knowledge base k available to activity d is knowledge expertise e d and all other knowledge expertise e d (l = d), weighted by their associated relatedness τ ld . Generalising Eq.(2) to all productive activities within the firm yields the aggregate knowledge base K: let us hold τ ld constant across activities d's and l's, so that 5 A c c e p t e d M a n u s c r i p t τ ld = R across all productive activities within the firm. Since d e d is the firm's knowledge stock E, Eq.(3) simplifies to

  t-τ . Now let d kit = 1 if the firm has developed competencies in technology k, (P kit > 0), 0 otherwise. Knowledge diversity D is simply the number of technology classes in which the firm develops scientific competencies over the past five years D = k d kit .

  3 . Third, the USPTO dataset provides only one U.S. patent technology class per patent grant, hampering the computation of technological relatedness. An appealing opportunity is to use citations across patents to link technologies with one another, but as emphasised by[START_REF] Jaffe | Evidence from patent citations on the impact of NASA and other federal labs on commercial innovation[END_REF], citations remain a rather noisy event, for they encompass various legal matters regarding the validation of the technological novelty. Instead, information on the technological content of patents was completed by collecting all international technology classes (IPC) assigned to every US patent documents 4 . The six-digit technology classes prove too numerous, and I choose to use them at the three-digit level, analogous to a technological space of 120 technologies 5 . Because more than one technology may be listed within one single patent document, it is then possible to calculate the frequency with which two technologies are listed together 6 . This new patent dataset further enhances the computation, at the firm level, of the variables measuring knowledge capital (E), knowledge diversity (D) and knowledge relatedness (R) between 1968 and 1999.

  productivity, and β, ϕ and θ k are the parameters of interest and can be estimated by ordinary least squares. Additional data on the net value of property plant and equipment (N C), R&D investments(R), main industry group (two-digit IPC) and secondary industry groups are also used to control for the age of capital by calculating the ratio of net over gross capital (N C/C), R&D intensity(R/Q), industry specific effects and product diversification, respectively. Financial data originally expressed in national currency have been converted in US dollars using the exchange rates provided by the Organisation for Economic Co-operation and Development (OECD). All financial data were then deflated into 1996 US dollars using the Implicit Price Deflator provided by the U.S. Department of Commerce, Bureau of Economic Analysis.14A c c e p t e d M a n u s c r i p t

18A

  c c e p t e d M a n u s c r i p t remains difficult to assess. Given that little is known about investments by firms to improve knowledge relatedness, these results inform us exclusively on the significance and direction of the relationship between the firm's productive efficiency and knowledge relatedness. To gain insights on its relative weight, one way to go forward is to compute the standardised coefficients of variables using the Least Square Dummy Variable (LSDV) specification. The exercise shows that the standardised coefficients for knowledge capital θ sd e and knowledge relatedness θ sd r reach respectively 0.245 and 0.045. Hence the contribution of intangible assets is due primarily to its knowledge stock. However knowledge relatedness is of importance.Computing the ratioθ sd r θ sd e +θ sd r , I find that 16% of the short-run contribution of intangible assets to productive efficiency has been ignored by the usual specification that implicitly assumes R = 0. The coherence of the firm's technological diversification does have an impact on productive efficiency, and ignoring its contribution leads to a substantial underestimation of the overall contribution of intangible assets to firm performance. Altogether, the various specifications show that: (i) large corporations face steep decreasing returns to scale; (ii) the stock of knowledge is a prime determinant of firm productivity; (iii) knowledge relatedness plays a significant role, contributing positively to firm productivity; (iv) positive changes in the previously mentioned variables entail positive changes in firm productivity; and (v) knowledge diversification remains insignificant, suggesting that the breadth of firm knowledge is not linked to productivity. The rationale for the important role of knowledge relatedness to firm productive efficiency lies in the fact that the cost of coordinating coherent knowledge bases is simply lower than that of coordinating unrelated pieces of knowledge. Such economies arise when diversifying in related 19 A c c e p t e d M a n u s c r i p t technologies increases the potential for scope economies and lowers the sunk costs of investing in and mastering additional technologies. Sub-sections 5.2, 5.3 and 5.4 address three issues that may potentially affect the results: the characteristics of the sample, alternative measures for intangible assets, and alternative econometric specifications overcoming the simplifications that K = E • D • R.

  21

A

  c c e p t e d M a n u s c r i p t suitable for high technology sectors, where frontier technologies are more likely to be embodied in patent documents than in low technology sectors. More generally, the two explanations provided meet when one mentions that in low technology sectors, productivity growth may be imported from other sectors (i.e embodied from technical change developed in other sectors). In high-technology sectors, productivity growth would be more the results of within sector technical change.

A

  c c e p t e d M a n u s c r i p t measure of technological relatedness τ N P kl based on information theory. Regarding the latter choice, one can start by representing firm knowledge as forming a graph G = (K, R), where K is the set of vertices (i.e. firm technological competencies), and R is the set of edges (i.e. technological relatedness), that links technologies together. In fact, Eq.(8) assumes firm competencies to form a fully connected graph; in a corporation with k technological competencies, all k × (k -1) ÷ 2 pairs of technologies are included in the computation of W AR. Quite likely however, not all technologies within the firm are related to all other ones: only subsets of technologies relate to other subsets of technologies. To account for this, I follow Teece et al.

  e p t e d M a n u s c r i p t remains virtually unchanged at 15%, implying that the choice of the relatedness measure has virtually no effect on the amount of information brought by the iden-tity K ∼ = E • D • R. In column (15), knowledge relatedness based on W AR P is positive and significant at the 5% level, while the θ sd r θ sd e +θ sd r ratio drops to 12%. In column (16), knowledge relatedness based on both τ N P kl and W AR becomes nonsignificant, raising the issue regarding the very measure of knowledge relatedness.

1

  verging goals, and future work shall investigate more systematically the behaviour of the knowledge variables with respect to alternative measures of firm economic performance. This research was financed by the writing fellowship scheme of the Science and Technology Policy Research (SPRU) of the University of Sussex. I would also like to thank Parimal Patel for his stimulating comments during the research and for providing the data on firm consolidation. I thank Bart Verspagen for his remarks and for providing the software collecting information on patent documents. I am thankful to Flora Bellone, Gustavo Crespi, Paola Criscuolo, Jean-Luc Gaffard, Franco Malerba and Pier Paolo Saviotti for helpful comments on prior version of this paper. All remaining errors are my sole responsibility.35A c c e p t e d M a n u s c r i p tNotes For a thorough discussion and empirical analysis on the various foundations for technological relatedness, see[START_REF] Breschi | Knowledge-relatedness in firm technological diversification[END_REF]

  40

  Eq.(A-6) is straightforward. If s kl ÷ ŝkl > 1 , then τ N P kl > 0:

  Saviotti

A

  c c e p t e d M a n u s c r i p t 2005). Second, the major advantage of τ P kl over τ N P kl is that it can be interpreted as a Student statistics, so that one can evaluate the statistical significance of the observed relationship between any two technologies. The rule of thumb here is that when |τ P kl | > 1.96, one can reject the null hypothesis that the observed use of any two technologies equals their random co-use. In other words, technological relatedness is significant when |τ P kl | > 1.96. By way of conclusion, let us consider the strength of the relationship between both measures of technological relatedness. It appears that the Pearson's correlation coefficient and the Spearman's rank correlation coefficient between τ P

  display the descriptive statistics for the set of variables and provide general information on the various industry groups of the sample (Standard Industry Classification -SIC two digit). The sample is composed of firms from 11 industry groups. These are rather heterogeneous, as they differ significantly in terms of their aggregate productivity levels, research inten-

sity, and knowledge characteristics (

Table II). The largest sectors in the sample are Chemicals and Allied Products, including Drugs (SIC 28, 29 corporations); Transportation Equipment (SIC 37, 27 corporations); Electronic and Other Electric Equipment (SIC 36, 17 corporations); and Industrial Machinery and Equipment (SIC 35, 16 corporations). These sectors are generally highly intensive in R&D activities (see table

Table 2

 2

	. High-technology sectors comprise 53 large corporations from
	Chemicals (29 firms), Electronics (17 firms) and Instruments (7 firms), with an ag-
	gregate (R/Q) ratio above 6 percent. Medium-technology sectors comprise 50 large
	20

r ratio reaches 21%, implying that in high-technology sectors, the impact of diversifying in related technology on labour productivity becomes considerably fiercer.

  . Similar to Teece et al., I rely on the so-called survivor principle that less efficient pairs of technologies are called to disappear ultimately and assume that the frequency with which two technology classes are jointly assigned to the same patent documents may be thought of as the strength of their technological relationship, or relatedness. The analytical framework is similar to Breschi et al. and departs from the square symmetrical matrix obtained as follows. Let the technological universe consist of a total of N patent applications. Let p nk = 1 if patent n is assigned to technology k, k = {1, . . . , K}, 0 otherwise. The total number of patents assigned to technology k is thus f k = n p nk . Now let p nl = 1 if patent n is assigned to technology l, 0 otherwise. Again, the total number of patents assigned to technology l is f l = n p nl . Since two technologies may co-occur within the same patent document, then f k ∩ f l = , and thus the number f kl of observed joint occurrences of technologies k and l is f kl = n p nk p nl . Applying the latter to allpossible pairs, we then produce the square matrix Ω(K × K) whose generic cell is the observed number of joint occurrences f kl . This count of joint occurrences is used to construct our measure of relatedness, relating it to some measure of expected frequency fkl under the hypothesis of random joint occurrence.There is no authoritative measure of fkl , and I shall consider below a parametric and non-parametric setting. In a parametric setting, one can consider the number f kl of patents assigned to both technologies k and l as a hypergeometric random variable. The probability of drawing f patents with both technologies k and l follows the hypergeometric density function (Population N , special members f k , and l is strictly equal to relatedness τ P lk between l and k. This is the case if one assumes that N

	itive indication of the relatedness between any two pairs of technologies. Note that
	relatedness measure τ P kl has no lower or upper bounds: τ P kl ∈] -∞; +∞[. Second,
	relatedness τ P kl is similar to a t-student, so that if τ P kl ∈] -1.96; +1.96[ , one can
	safely accept the null hypothesis H 0 of no relatedness between technologies k and l.
	Third, τ P kl is a symmetric measure of technological relatedness so that relatedness A c c e p t e d M a n u s c r i p t τ P kl between k

Table A -

 A 1 provides the descriptive statistics of the computed values for f kl , τ P kl and τ N P kl , between 1968 and 2000. The total number of observed technological co-occurrences is above 138,000. It equates with a yearly mean number of 4,195

Table A -

 A 1. Descriptive Statistics for f kl , τ P kl and τ N P

			kl
		f kl	τ P kl	τ N P kl
	Number of Observations	138,464.00 138,464.00 138,464.00
	Mean	43.83	-1.70 a	-1.02 a
	Number of positive τ kl	-	35,876.00	35,876.00
	Standard deviation	162.46	10.04	1.57
	Minimum	1.00	-62.50	-7.22
	Maximum	6,050.00	155.40	4.52
	Skewness	12.91	3.37	-0.05
	Kurtosis	259.82	30.52	2.98
	KS b Test: H0 : F (Θ) ∼ ℵ(µ, σ 2 )	0.00	0.00	0.00

a Mean value significantly below 0 at 5% level b KS: Kolmogorov-Smirnov test of normality

Table 1 :

 1 Descriptive Statistics. Pooled Sample

	43

Table 2 :

 2 Sectoral Decomposition of the Main Variables. 1986[START_REF] Henderson | Scale, scope and spillovers: the determinants of research productivity in drug discovery[END_REF] Test computed from the analysis of variance, where H 0 is all sector means are equal. All F-Test statistics significant at one percent level except for ∆(Q/L). Square represents the proportion of variance of all variables explained by the sector.

	Sectors	N	Q	L (Q/L) ∆(Q/L) (R/Q)	E	D	D	R
	CHEM a	29	13.0	55.9	232.6	4.83	6.47 1,705.5	46.2	-3.2	32.2
	COM b	7	23.3 185.0	126.4	6.33	4.02 1,282.0	38.0	-8.2	67.4
	ELEC c	17	22.7 129.9	174.7	5.99	6.67 3,162.1	60.1	-0.1	0.6
	FOOD d	6	21.7 135.1	160.8	6.12	1.42	359.9	29.2	-10.1	19.1
	INST e	7	12.1	75.6	160.4	2.63	6.38 2,672.7	64.2	7.6	-5.7
	IND. MACH f	16	21.6	98.2	219.6	5.24	5.05 3,134.2	54.9	-5.1	-5.0
	METAL g	11	13.0	34.9	372.6	5.75	1.67	501.9	46.4	6.1	-2.8
	OIL h	5	41.4	50.2	824.7	5.79	2.60 1,776.2	44.4	-5.5	16.2
	OTHER i	22	14.7	61.1	241.7	4.24	2.90	513.5	40.5	0.0	6.0
	PETROL j	9	29.9	63.4	471.1	4.16	1.17 1,686.2	58.6	9.4	-5.9
	TRANSP k	27	35.4 141.2	251.4	6.78	4.50 1,434.4	51.2	3.9	17.5
	Mean (Total)	(156)	21.7	91.4	237.4	5.31	4.59 1,697.2	49.3	0.0	12.5
	F-Test l	31.98 36.08	5.55	0.29	58.48	44.80 29.53 22.92	8.22
	R-Square m	0.167 0.184	0.034	0.002	0.303	0.219 0.156 0.126 0.049
	N : Number of firms
	Q: Deflated sales (In Billions of 1996 US Dollars)
	L: Number of employees (In thousands)
	(Q/L): Deflated sales per employee (Thousand of 1996 US Dollars)
	∆(Q/L): Annual growth rate of labour productivity
	(R/Q): R&D intensity
	E: Knowledge capital
	D: Knowledge diversity
	D : Unexpected knowledge diversity
	R: Knowledge relatedness

a CHEM: Chemicals and allied products (Including drugs) b COM: Communications c ELEC: Electronic and other electric equipment d FOOD: Food and kindred e INST: Instruments and related products f IND. MACH: Industrial machinery and equipment g METAL:Primary metal industries h OIL: Oil and gas extraction i OTHER: Other industries j PETROL: Petroleum and coal products k TRANSP: Transportation equipment l Fm R-

Table 3 :

 3 Correlation Matrix. 1986-1996. Pooled Sample. N = 1,608 Natural logarithm of deflated sales per employee (c -l): Natural logarithm of gross capital per employee l: Natural logarithm of labour e: Natural logarithm of knowledge capital d: Natural logarithm of knowledge diversity d : Natural logarithm of unexpected knowledge diversity r: Natural logarithm of knowledge relatedness (N C/C): Age of Capital

		(q -l) (c -l)	l	e	d	d	r	(N C/C)
	(q -l)	1.000	0.852	-0.551 -0.065 -0.049 -0.032	0.021	-0.079
	(c -l)		1.000	-0.452 -0.017	0.027	0.037	0.016	-0.196
	l			1.000	0.487	0.432	0.194	-0.042	0.009
	e				1.000	0.806	0.282	-0.173	-0.195
	d					1.000	0.701	-0.420	-0.337
	d						1.000	-0.372	-0.263
	r							1.000	0.223
	(N C/C)							1.000
	(q -l):

For a thorough discussion and empirical analysis on the various foundations for technological relatedness, seeBreschi et al.

The USPTO advertise only patent grants, not patent applications. This should not be a problem for computing all knowledge variables since it acts as a quality filter on the firm's patent portfolio. Note that I use the year of application, not the year in which the firm was awarded the patent.

The number of patents held by the world's largest manufacturing firms reached 500,000 prior to consolidation, but increased to 800,000 after controlling for consolidation. This illustrates the need for such an exercise as well as indicating the difficulty of the task. I am very thankful to Parimal Patel for providing the information.

This was completed using all IPC codes as displayed on the Internet Web Site of the European Patent Office. I am indebted to Bart Verspagen and Paola Criscuolo for their much appreciated help during the automated process.

The aggregation of technology classes into larger categories is a necessary but delicate exercise because it influences negatively the variance of knowledge diversity and relatedness across firms. Prior literature[START_REF] Jaffe | Technological opportunity and spillovers of R&D: Evidence from firms' patents, profits and market values[END_REF][START_REF] Hall | The NBER patent citation data file: Lessons, insights and methodological tools[END_REF], suggests that a thirty-dimensional technological space may be an appropriate aggregation, but since this paper deal with the largest manufacturing firms, using such a level of aggregation is likely to reflect product more than knowledge diversification while decreasing too severely the variance of knowledge diversity and relatedness across firms.

Altogether, of three million patents,

751,935 US patents have more than one technology class, which proves adequate to measure technological relatedness. 13

Conversely, a value below unity indicates an area of relative weakness. See also[START_REF] Fai | Corporate technological competence and the evolution of technological diversification[END_REF] for a detailed analysis of the world's largest corporation based on the RT A.

Altogether, of three million patents,

751,935 US patents have more than one technology class, which proves adequate to measure technological relatedness.7 The results are not reported here, but can be obtained upon request to the author.

A c c e p t e d M a n u s c r i p t 8 Conversely, a value below unity indicates an area of relative weakness. See also [START_REF] Fai | Corporate technological competence and the evolution of technological diversification[END_REF] for a detailed analysis of the world's largest corporation based on the RT A.

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A c c e p t e d M a n u s c r i p t and sample size f l ):

where f is the hypergeometric random variable. Its expected frequency is

If the actual number f kl of co-occurrences observed between two technologies k and l greatly exceeds the expected frequency fkl of random technological cooccurrence (f kl > fkl ), then the two technologies are highly related: there must be a strong, non-casual relationship between the two technology classes. Inversely, when f kl < fkl , then technologies k and l are poorly related. Hence, a preliminary parametric-based measure of relatedness r P kl is

Eq.(A-3) may further be designed to control for the variance of the sample at use. Assuming a hypergeometric distribution, the variance and relatedness measures are

Thus,

Eq.(A-5) has three attractive features. First, relatedness τ P kl is a real number that can be either positive or negative, the sign being a straightforward and intu- A c c e p t e d M a n u s c r i p t

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A c c e p t e d M a n u s c r i p t

Abstract

This paper develops a model linking firm knowledge with productivity. The model captures three characteristics of firm knowledge -capital, diversity and relatedness -that are tested on a sample of 156 of the world's largest corporations. Panel data regression models suggest that unlike knowledge diversity, knowledge capital and knowledge relatedness explain a substantial share of the variance of firm productivity. Activities based on a related set of technological knowledge are more productive than those based on unrelated knowledge because the cost of coordinating productive activities decreases as the knowledge used in these activities is being integrated efficiently. The traditional econometric specification has repeatedly underestimated by 15% the overall short-run contribution of intangible assets to firm productivity. This underestimation becomes fiercer in high technology sectors.

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