How Persistently Do Firms Innovate

research policy ELSEVIER

Research Policy 26 (1997) 33-48

How persistently do firms innovate? P.A. Geroski a, j. Van Reenen b,c, C.F. Walters

~

a Department of Economics, London Business School, Sussex Place, Regents Park, London, NWI 4SA, UK b Department of Economics, University College London, Gower Street, London, WC1E 6BT, UK c Institute for Fiscal Studies, 7 Ridgemount Street, London. WC1E 7AE, UK

Received 28 September 1996

Abstract

This paper examines the innovative history of a number of UK firms using two large databases, looking for evidence consistent with the view that firms that innovate typically do so persistently. The first sample contains 3304 firms which registered at least one patent in the US at any time in the period 1969-1988, while the second consists of 1624 firms which produced at least one major innovation at any time in the UK from 1945to 1982. Both data sets yield the same conclusion, namely that very few innovative firms are persistently innovative. © 1997 Elsevier Science B.V. All rights reserved.

I. Introduction

Most studies of the determinants of corporate innovative activity focus on the question of how many technologically important innovations are produced by a particular firm over a certain time interval. Since the simple fact is that many finns do not innovate (in this sense) at all, studies of this type often effectively end up concentrating on the question: what makes a firm innovative? However, if firms that actually do innovate fail to do so persistently, it becomes interesting and important to focus on a second question, namely: what keeps a firm innovative over time? In this paper, we examine the innovative record of a large number of UK firms over relatively long periods of time using two particular measures of 'innovative activity'. The first is patenting activity by UK firms in the US over the

20-year period 1969-1988, while the second is the production of major innovations by UK firms over the 38-year period 1945-1982. Both sets of data tell the same story, namely that only a very small number of firms produce patents or major innovations on a regular basis. We start in Section 2 by setting out the measurement issues which arise when one tries to examine patterns of innovation over time for particular firms. Then, taking the length of time over which firms regularly innovate as the basic unit of analysis, we concentrate on examining the hypothesis that the production of innovations is subject to 'dynamic economies of scale'; that is, that the more innovations a firm produces, the more likely it is to continue to innovate. In Section 3, we analyse the data on innovation and patenting spells, and show that it is hard to reconcile what we observe with the hy-

0048-7333/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. Pll S0048-7333(96)00903- 1

34

P.A. Geroski et a l . / Research Policy 26 (1997) 33-48

pothesis that 'dynamic economies of scale' are an important driver of innovation processes (at least for the types of innovations that we consider here). We conclude in Section 4 with some speculative observations on what these results might mean for models of technological competition, theories about firms' 'dynamic capabilities' and endogenous growth theory.

2. Modelling persistent innovative activity Examining how regularly innovations occur raises a number of interesting issues of experimental design and interpretation. In this section, we explore three of the more important of these, namely: measurement issues (i.e. the definition of 'innovation' and problems associated with the frequency of observation), hypotheses about the determinants of persistent innovative activity, and the statistical modelling of innovation spells. 2.1. The measurement of innovation

There are many possible ways to measure an 'innovation'. At one end of the spectrum are measures like R & D spend (an input measure) and counts of minor technical or organizational innovations, all of which are likely to occur on a routine basis. One is likely to observe that many firms are persistent innovators using these criteria. At the other end of the spectrum are major new product or process breakthroughs (or major innovations in organizational design) which open up new markets or fundamentally transform a firm's value chain. These are 'innovations' that almost certainly occur on a highly irregular basis, and it would be surprising if any firms persistently innovated in this sense on a year in, year out basis. Our data consist of records on the patenting behavior of 3304 UK firms over the period 1969-1988, and the production of 'major' innovations by 1332 firms over the period 1945-1982. The patents data record 'innovations' that are new and technologically important enough to be granted a patent, while the 'major innovations' data record technically innovative and commercially successful new products

a n d / o r processes introduced by particular finns. 1 As measures of 'innovation', these data are limited in their focus on the generation a n d / o r use of new technology. This limitation aside, however, there is much to be said for them. They record events that can have a significant effect on a firm's market position, and are, therefore, likely to be important determinants of its long run competitiveness. 2 Further, 'innovations' defined in this way are neither routine nor earth shattering, and are, therefore, possibly as likely to occur persistently as not. They have also been extensively used as performance indicators by scholars interested in the question 'what makes a firm innovative?', and that makes it much easier to compare work on persistence with previous studies of what makes firms innovative. One further measurement issue is worth noting. Our data are recorded annually, and this means that an 'innovation spell' will be measured as the number of successive years in which a firm produces a patent (or a major innovation). This may exaggerate the episodic nature of innovative activity. What seems like a desultory pattern of innovation which produces a patent every three to five years (say) may actually be a rather rapid exploitation of a difficult and obtuse new technology. More generally, if firms typically undertake single innovation projects that last substantially longer than a year, then a continuous stream of innovative activity may produce a very irregular pattern of innovations. However, many firms undertake a portfolio of such projects and many undertake projects of only modest length. They should, therefore, produce a more continuous stream of innovations. Further, multiple spells of innovation that follow one another closely in time can be aggregated into a single spell (our conclusions are robust

See Patel and Pavitt (1995) for an overview discussion of the measurement of technological activity, Griliches (1990) on patents in particular, Townsend et al. (1981) and Geroski (1994) on the 'major innovations' data used here, and (by contrast) Acs and Audretsch (1990) for work on data that include many minor innovations. 2 For work linking these measures of innovation to corporate performance, see Geroski et al. (1993, 1995), and references cited therein.

P.A. Geroski et al. / Research Policy 26 (1997) 33-48

to this redefinition of spells). Thus, although it is possible that any conclusion about how frequently firms innovate may be an artefact of how the data are collected, it is not obviously the case that using annual data will make a regular stream of innovations produced over time look particularly episodic and irregular. 3

2.2. Hypotheses

There are many factors that may help to determine how long an innovation spell will last. These include technological opportunity, market demand, appropriability regimes, internal corporate capabilities, competitive market pressures and so on. All of these factors are exogenous to the events surrounding any particular spell, and they generate predictions that spells will either be long (if conditions are favourable) or short (if they are not). In most cases, they reflect forces that are difficult to measure, and this makes them difficult to test. The hypothesis that the production of innovations is subject to 'dynamic economies of scale' (or, more colloquially, that 'success breeds success') is of a rather different nature. If the volume of innovations produced by a firm up to date t has an effect on the probability that yet another innovation will be produced at t, then spell length depends (inter alia) on what happens just prior to a n d / o r during the spell; i.e. it is endogenously determined. This may occur if there is positive feedback between the accumulation of knowledge and the production of innovations by a firm (and, if spillovers are important, by its rivals), or if there are scale economies or learning by doing

3 This measurement problem is made worse by the fact that the annual window for enumeration of patents by the United States Patents and Trademarks Office may not reflect the periodicity of firms' decisions to patent. Two other drawbacks of the data are that we neglect spells of patenting which occur within a year, and that our measurement of spell length is not robust to random misallocations of patenting or innovation dates for low frequency innovators. The procedure of 'filling in' one-year gaps should make our results reasonably robust to the second problem, but neglecting spells of length less than a year may lead us to understate dynamic scale economies.

35

effects in the process of innovation production. 4 If such dynamic economies of scale in innovation exist, we expect (in principle) to see both short innovation spells (those that have ended before the effects of dynamic economies are felt) and some long spells (those sustained by dynamic economies) experienced by the same firm in the same set of circumstances. There are at least two ways to make inferences about dynamic scale economies from observations on the length of innovation spells. The first procedure is to look for a relationship between the number of innovations produced by a firm just prior to an innovation spell and the length of the spell that follows, expressing that relationship in terms of a 'threshold' level of pre-spell innovative activity necessary to generate a spell of length T with some probability. This measure has the great virtue of generating a natural and easy to interpret number to measure dynamic scale economies (the threshold), but it captures only those scale effects that are associated with events that occur immediately prior to the spell. A second procedure is to measure the relationship between the length of time a firm spends in a spell, and the probability that the spell will end at some time t. Since at least one innovation is produced per year during a spell, this effectively measures the relationship between cumulative within-spell innovation output and the likelihood that the spell will continue (a relationship which looks something like an innovation learning curve). 'Negative duration dependence', in which the probability that the spell will end falls the longer it goes on,

4 There are many possible sources of increasing returns in the production of innovation, including the public good nature of knowledge, any kind of benefits brought on by a more elaborate scientific division of labour and set up costs. Certainly the public good nature of knowledge means that it is likely to display increasing returns in use (see Wilson, 1975), an observation which is sometimes used to suggest that the production of innovations may display economies of scope (see Nelson, 1959, and many others). In addition, if R&D enriches a firm's 'absorptive capacity', enabling it to learn more efficiently and benefit from spillovers, then it is possible that at least some part of the relationship between R&D input and innovative output will display increasing returns (e.g. see Cohen and Levinthal, 1989, and others). For work suggesting that geography can help to create increasing returns in innovation, see Feldman (1994), Porter (1990), Krugman (1991) and others.

P.A. Geroski et al. / Research Policy 26 (1997) 33-48

36

captures dynamic effects generated within the spell, but is not so easily measured in a simple summary statistic.

2.3. The statistical methodology The statistical procedure one needs to follow to measure thresholds of initial innovation or the degree of duration dependence is fairly well known. We take the spell of time in which a firm innovates as our unit of analysis, and model the probability that the spell will end at any particular time; i.e. the hazard rate. 5 For any probability distribution function F ( t ) = P r ( T < t), there exists a corresponding density function f ( t ) = O F ( t ) / O t , and a survivor function S(t) = 1 - F(t) = P r ( T > t). Now, consider the probability h(t) of a patenting or innovation spell ending in the short period A from t given it has lasted until t: h(t) = Pr(t < t + AIT> t). The limit of this probability as A tends to zero is the hazard rate,

Pr( t < t + AIT> t) A(t) = lim a~o

A

(1)

'

and substituting for our probability distribution, density and survivor functions,

F(t + A) - F(t) A(t) = lim a-~o

AS(t)

or(t)/Ot =

S(t)

f(t) -

S(t)"

(2)

It is the determinants of A(t) that are of interest here,

5 Two arguments favour the use of this type of formulation. Firstly, there is no natural unit of time in which firms make decisions to innovate, so it is analytically convenient to model the firm's decisions in continuous time. Secondly, even if there were a natural time ordering of inventive decisions, we cannot suppose that this ordering corresponds to the annual observations in our data, or that this time ordering is synchronized across firms. These two caveats are sometimes grouped together under the pseudonym length biased sampling. Inference about the underlying stochastic inventive process based on discrete sampled data may therefore be incorrect when conventional discrete choice distributions are used (probit, logit and so forth). The functional form of these distributions is sensitive to the time interval used in their formulation, whereas continuous time models are invariant. See Kiefer (1988) Lancaster (1990) and Kalbfleisch and Prentice (1980) for useful discussions of these models.

and, in particular, how A(t) varies with the initial level of innovation (which identifies the threshold), and how it varies over time (negative duration dependence occurs when A'(t) < 0). 6 Since we are interested in the relationship between the initial level of innovative activity and the length of the subsequent innovating spell, one way forward is to use a proportional hazards model, where A ( t ) = A0(t)~b(X/3), A0(t) is the baseline hazard, X is a vector of explanatory variables and /3 a vector of parameters in some general function ~b (see Cox, 1972). There are, however, two problems with this method. First, inappropriate choice of the distribution of A0(t) can produce biased and inconsistent parametric estimates (see Heckman and Singer, 1984). This problem can, however, be avoided since /3 can be estimated without assuming a distribution for the baseline hazard by definition of the partial likelihood function. A non-parametric approach can then be used to obtain A0(t). However, correct specification of the baseline hazard brings a gain in efficiency, and enables one to say something about the direction of duration dependence which semi-parametric estimation does not. Second, proportional hazards coefficients are hard to interpret, being measured relative to this baseline hazard. Variables can be measured as deviations from their means and a regression intercept included (which admits an interpretation for the /3 relative to the mean spell), but we believe the concept of the mean spell in our skewed data to be of little use. There are two forms of reparameterisation available which would enable us to give our regression coefficients the standard classic linear regression model interpretation (that is, as affecting the mean of the dependent variable with an additive error). First, one can restrict the distribution of the additive error and allow a general transformation of the dependent variable, or second, one can restrict the transformation of the duration data and allow a general additive error distribution. This latter procedure is known as

6 These models are often used in the literature on unemployment where duration dependence (i.e. how A(t) varies as the length of a spell of unemployment increases, all other things held constant) is the main focus of interest; see Lancaster (1990) for a survey.

P.A. Geroski et al. / Research Policy 26 (1997) 33-48

the accelerated failure time model. Only the Weibull class of hazard functions is linear in both restricted and general transformations of the dependent variable. Since economic theory does not have much to say about the distribution of the baseline hazard, the Weibull distribution where A(t) = ~/c~t"-1 is a natural starting point. 7 To implement the model, the dependent variable is transformed to the natural log of the time until failure of a spell and the coefficients are estimates of the expected (log of) time until failure scaled by the duration dependence; that is, E[tIX] = e x p ( a / l ' X ) . It is worth noting that omitting relevant determinants of duration (i.e. particular X variables) biases the results towards observing negative duration dependence. Hence our data will only be informative on within-spell dynamic effects if we are using a complete model (which we cannot do) or if we observe positive duration dependence (in which case we can be sure that within-spell dynamic effects do not work to prolong spells).

3. Analysing innovative spells To explore the conditions under which innovative activity becomes persistent over time, we use two different measures of innovation: patenting and the production of major innovations. In this section, we start by examining the size of thresholds, first on patenting and then on major innovations. We then proceed to analyse the determinants of hazard rates, focusing on the degree of duration dependence.

3.1. The persistence of patenting The patents data consist of a balanced panel of 3304 UK firms, both quoted and private, observed over the period 1969 to 1988. These 3304 firms were selected from the population of over 7500 UK firms which were granted patents by the United States Patents and Trademarks Office at some time in the

7 A special case of the Weibull distribution is the exponential distribution, obtained when ot = 1 (memoryless, constant hazard), but this is a one-parameter distribution and is unlikely to accurately describe data that display both short and long spells of patenting and innovative activity. The Weibull distribution displays a hazard monotonically increasing or decreasing in duration via a. Positive duration dependence is implied by ot > 1.

37

period. The basic problem of sample design which arises in studies of persistent behaviour is to ensure that the unit under observation is the same over time. In the UK, waves of merger and divestiture make it difficult to create a satisfactory history for many businesses. Further, an examination of the raw data convinced us that a number of supposedly UK-registered firms had titles associated with countries of registration other than the UK. Thus, we decided that to qualify for entry into our sample, a firm's ownership status had to be positively known. That is, unless the finn was found to be a UK parent, subsidiary or associate in any year in which it was granted a patent, it was excluded from the data. 8 Two features of patenting activity stand out particularly clearly in the data. First, most firms never patent: a population of 7500 patenting firms is a very small fraction of the total population of UK firms operating over the period (even assuming that all of them are UK firms). Second, most firms that patent only ever patent once, and relatively few firms produce even as much as one patent per year on average. The frequency distribution of the total number of patents produced over the period 1969-1988 for our 3304 firms contains a huge spike at one patent, a much smaller spike at two patents, small and roughly equal proportions continuously between half a dozen and two hundred patents and a few sparsely distributed outliers with many hundreds of patents. The distribution of total patents per firm has a mean of 10.083, a median of two patents, and a standard deviation of 79.979. The distribution is highly skewed (32.814 centred on zero) and the tails are thick (kurtosis = 1359.25). Likewise, the distribution of the average number of patents per firm has a mean of 0.504, a median of 0.1, and a standard deviation 3.999 (the skewness and kurtosis of the two distributions are about the same). 9

8 Dun and Bradstreet's Who Owns Whom was used for this purpose. We are aware that the timing of the ownership status given in Who Owns Whom and the date of receipt of a patent may not be exactly contemporaneous, but there is little that we can do about this problem. Of the sample of 3304 finns 78% were subsidiaries, 17% were parents, 4% were associates and the rest were of mixed classification. 9 Much the same high skew and low average patenting frequency is evident in the population of 7500 firms which patented at least once over the period.

38

P.A. Geroski et al. / Research Polic~' 26 (1997) 33-48

Our interest is not in the number of patents produced by any particular firm, but in the frequency and consistency with which particular firms patent. For this reason, we focus on patenting spells, defined as the number of successive years in which a firm produces at least one patent per year. Our 3304 finns have 5178 spells between them (some firms have multiple spells). 10 Frequencies of spells of lengths between 1 and 20 years are given in Table 1, which shows rather clearly that the lengths of these spells are distributed in much the same way as the total number of patents. As it is hard to conceptualise what the distribution of these spells looks like on a per firm basis, Table 1 also presents spell frequencies of lengths l to 20 for the maximum length patenting spell per finn. The most interesting feature of the table is that although there are considerably more spells than finns, much of the difference between the number of firms and the number of spells is accounted for by spell lengths of 1 and 2 years' duration, meaning that most finns with multiple spells have two (or, occasionally, more) spells of very short length. For spell lengths between 3 and 8 years, the total number of spells is nearly equal to the number of firms having maximum duration spells of that length. H With this in mind, an inspection of

to Since we are dealing with reported spells of innovative activity over a set time period, left and right censoring may distort the observed distribution of spell lengths. The corrected mean spell length over all 5178 spells (4849 of which are not right censored) is 1.921 years, and the corrected median spell length is 1 year. For the 4574 spells that are not left censored (4267 of which are also not right censored), the mean spell length is 1.675 years and the median is 1 year. For the remaining 604 spells that are left censored (582 of which are not right censored), the mean spell length is 3.725 years and the median is 1 year. The uncorrected mean spell length over all 5178 spells is 1.799 years, with a median of 1 year. 11 There are two other features of Table 1 worth noting. Firstly, the number of all spells of 9 years or more is equal to the number of maximum length spells of the same duration. Clearly these numbers must coincide for 10 years or more (no finn could have more than one spell of 10 years' duration), but actually coincide 1 year's duration earlier. Secondly, within these coincident lengths, there exist small frequency spikes at 14 and 16 years' duration and a larger spike at 20 years. Moreover, for both measures the frequencies of lengths of 10 years and up do not fall away as quickly or smoothly as might have been expected.

our data reveals three regimes of patenting behaviour (Appendix A provides a detailed description of the data): 1. single patentors: these are firms which produce a few patents in one short spell (the vast majority patent only once in one year). This group comprises about 64% of the sample, and produced 6765 patents over the period (3.21 per firm); 2. sporadic patentors: these are firms which produce a handful of patents and do so in a small number of short spells. This group comprises about 34% of the sample, and produced 10020 patents over the period (9.58 per firm); 3. heavy patentors: these are finns which produce a large number of patents (dozens or even hundreds) and who, for the most part, patent heavily in every year for which we have data. This group comprises about 2% of the sample, and produced 16 528 patents over the period (284.97 per firm). Our interest is in relating the length of patent spells to the initial level of patenting. Table 2 shows empirical survival rates (i.e. the percentage of spells that lasts at least as long as T years) and associated standard errors for spells starting with 1, 2, 3, 4 and 5 or more patents computed using the Kaplan and Meier (1958) estimator. 12 Since only a small number of spells (less than 4%) last for more than 5 years, 5-year intervals are used beyond survival times of this length. J3 Roughly speaking, only 30% of all patenting spells are ongoing after one year. After 4 years the percentage of spells ongoing drops to around 7%, after 10 years it drops to 3% and some-

12 A total of 98.5% of all spells begin with between 1 and 5 patents: 78% with 1 patent, 14% with 2 patents, 4% with 3 patents, 2% with 4 patents, 0.5% with 5 patents. The remaining 1.5% begin with between 6 and 219 patents. 13 We also estimated these survival models for spells that were left censored. Although an inability to control for left-censoring in spells leads to a positive bias in survival rates for each start-up patent class, the effect on survival rates for all spells is modest (but increasing with the number of start-up patents). In fact, log rank and likelihood ratio tests of the homogeneity of each leftcensored and uncensored subsample by start-up patent class imply that only left-censored and uncensored spells with four patents in their first year are statistically the same.

39

P.A. Geroski et al. / Research Policy 26 (1997) 33-48

Table 1 Distribution of patenting and innovation spell lengths and maximum spell lengths by business unit Length (years)

All spells

Maximum spells

Patents

Major innovations

Patents

Major innovations

No.

%

No.

%

No.

%

No.

%

1 2 3 4 5 6 7 8 9 10 I1 12 13 14 15 16 17 18 19 20

3721 730 299 135 88 39 34 12 16 11 20 5 6 10 4 11 8 6 1 22

71.86 14.10 5.77 2.61 1.70 0.75 0.66 0.23 0.31 0.21 0.39 0.10 0.12 0.19 0.08 0.21 0.15 0.12 0.02 0.42

2632 277 68 23 6 6 2 1 0 1 1

87.24 9.18 2.25 0.76 0.20 0.20 0.07 0.03 0 0.03 0.03

2147 520 240 120 81 34 31 11 16 11 20 5 6 10 4 11 8 6 1 22

64.98 15.74 7.26 3.63 2.45 1.03 0.94 0.33 0.48 0.33 0.61 0.15 0.18 0.30 0.12 0.33 0.24 0.18 0.03 0.67

1355 182 52 19 5 6 2 1 0 1 I

83.44 11.21 3.20 1.17 0.31 0.37 0.12 0.06 (1 0.06 0.06

Total

5178

100

3017

100

3304

100

1624

100

what less than 1% o f all spells last 20 years or more. S u r v i v a l rates for spells with 1 patent in their first year are about 23%, for those with 2 patents 4 5 % , for those with 3 patents 63%, for those with 4 patents 72% and those that start with 5 or more patents enjoy a survival rate o f 89% after 1 year. Spells that start with 5 or m o r e patents h a v e an 82% chance of surviving for a third year g i v e n that they have lasted as long as 2 years, a 74% chance of s u r v i v i n g a fourth year g i v e n that they h a v e survived 3 years and an 18% chance of surviving m o r e than 15 years g i v e n that they h a v e lasted as long as 15 years. Table 2 suggests that the threshold level o f patents likely to induce a patenting spell o f 3 or m o r e years is probably around 5 patents. G i v e n an initial production of 5 o r m o r e patents, the e x p e c t e d length o f the subsequent patenting spell is 8 years. F i n n s that initially produce 4, 3 and 2 patents can e x p e c t to enjoy spells o f 3, 2 and 1 year(s) respectively. Firms with a single patent are unlikely to patent again. 14 A

f i n n that produces 4 patents in year t has only a 37% chance o f e n j o y i n g a spell of no less than 3 years, while one that produces 5 or m o r e patents has a 74% chance. Indeed, a firm that produces 5 or more patents has roughly twice the probability of e n j o y i n g a patenting spell o f any length greater than 3 years than a firm that produces only 4 patents, and, in the main, m u c h m o r e than three times the chance of e n j o y i n g a patenting spell of any length than a firm that produces 3 or f e w e r patents. This is consistent with the v i e w that s o m e f o r m o f ' d y n a m i c scale e c o n o m i e s ' m a y g o v e m the production o f patents, but this effect is only apparent after a threshold level

14 These calculations were made by observing intervals of years for given initial levels of patenting, over which the 95% confidence interval of the product limit estimator first covers 0.5. These intervals are selected from life tables where there is no aggregation of intervals above 5 years.

0.3037 0.1579 0.0971 0.0688 0.0313 0.0175 0.0089 0.0089

958.332 (0.000)

LR test c

0.4528 (0.019) 0.2492 (0.017) 0.1479 (0.014) 0.097 (0.012) 0.0429 (0.009) 0.0169 (0.006) 0.0101 (0.005) 0.0101 (0.005)

0.6315 0.3927 0.2737 0.2123 0.1061 0.0403 0.0161 0.0161

3 (0.032) (0.033) (0.03) (0.028) (0.023) (0.016) (0.011) (0.011)

0.7225 (0.048) 0.5463 (0.054) 0.3682 (0.052) 0.3078 (0.05) 0.203 (0.045) 0.1093 (0.023) 0.0298 (0.023) 0.0298 (0.023)

4 0.8899 (0.03) 0.815 (0.037) 0.7392 (0.042) 0.6633 (0.046) 0.4373 (0.049) 0.3109 (0.046) 0.18 (0.039) 0.18 (0.039)

5+ (0.0064) (0.0039) (0.0025) (0.0016) (0.0006)

9.119 (0.01)

0.1404 0.0421 0.0155 0.0066 0.0009 0.0000

All 0.1293 0.0372 0.0116 0.0048 0.0010 0.0000

1 (0.0066) (0.0039) (0.0023) (0.0015) (0.0007)

0.1457 0.0578 0.0385 0.0116 0.0000

2 (0.0238) (0.0142) (0.0118) (0.0066)

Number of innovations at the start of the spell

0.3197 (0.0544) 0.1492 (0.0421) 0.055 (0.028) 0.055 (0.028) 0.0000

3+

a Life tables are based upon groups defined according to the number of patents and innovations in the first year of each spell, with 5178 patents spells between 1969 and 1988 and 3017 innovations spells between 1947 and 1982. b Numbers in parentheses are Greenwood (1926) standard errors. c LR test is a X2(4) (patents) or X2(2) (innovations) likelihood ratio test of the null of homogeneity of groups (p-value in parentheses); see Savage (1956) for details.

(0.006) b 0.2333 (0.007) (0.005) 0.1003 (0.005) (0.004) 0.0527 (0.004) (0.004) 0.0319 (0.003) (0.003) 0.0078 (0.002) (0.002) 0.004 (0.001) (0.002) 0.0016 (0.001) (0.002) 0.0016 (0.001)

2

1-2 2-3 3-4 4-5 5-10 10-15 15-20 20-

1

Number of patents at the start of the spell

All

Spell

a

interval (years)

Table 2 Business unit spell survival rates

"~ oo

I

,.~ .~.

,....

"~"

.~

4~

P.A. Geroski et al./ Research Policy 26 (1997) 33-48

41

Table 3 Moments of key regressors by spell Patents

Innovations

Variable

Regressor

Mean(Std. Dev.)

Variable

Regressor

Mean(Std. Dev.)

Patents Start patents = 1 dummy Start patents - 2 dummy Start patents = 3 dummy Start patents = 4 dummy Start patents = 5 + dummy Parent dummy Subsidiary dummy Associate dummy Mixed ownershipdummy Growth in manufacturing output Patents spillover Observations

Omitted pat1 pat2 pat3 pat4 Omitted Omitted subsid assoc mixed growth

1.4812 (2.895) 0.7788 (0.415) 0.1391 (0.346) 0.0434 (0.204) 0.0173 (0.130) 0.0214(0.211) 0.1749(0.379) 0.7569 (0.429) 0.0465 (0.211) 0.0216 (0.145) 0.0050 (0.044)

Innovations Start innovations= 1 dummy Start innovations= 2 dummy Start innovations= 3 + dummy Independentownershipdummy Owned ownershipdummy Growth in manufacturingoutput Innovationsspillover Employment

Omitted innl inn2 OmiUed owner Omitted growth ispill emp

I. 1606 (0.489) 0.8803 (0.324) 0.0947 (0.293) 0.0250(0.156) 0.5864 (0.493) 0.4130(0.493) 0.0188 (0.045) 0.2252 (0.418) 0.0067 (0.037)

pspill 4859

2782.823(459.121)

of initial patenting which only 74 (2.24% of) patenting firms ever reach, t5 3.2. The persistent production o f major innovations The innovations data are taken from a study done by the Science Policy Research Unit (SPRU) at the University of Sussex, which identified all business units in Britain that produced a 'commercially successful and technologically important' innovation in Britain between 1945 and 1982. 16 There were a total of 1624 innovating units belonging to 1332 parent firms in the data. In the analysis which follows, we concentrate on the business unit as the main 'innovating unit' of interest, but results for the parental group as a whole ('the parent firm') are also considered as a robustness check.

15These conclusions are not inconsistent with those of Cefis (1996), who analysed the patents of 577 UK firms registered at the European Patent Office over the period 1978-1991, although she puts more emphasis on the first patent as the right threshold than we have. See also Malerba and Orsenigo (1995) for a somewhat different analysis. 16The SPRU database runs to 1983, but this year was dropped due to the fact that the survey was conducted mid-year and there was a large drop in the number of recorded innovations as a consequence.

Observations

2957

The distribution of innovations shows much similarity to the distribution of patents. Most units produced only one innovation, and most innovation spells only last for one period (see Appendix B for more details). There are on average only a total of 2.66 innovations per business unit (and a median of one). The distribution is highly skewed (5.59 centred on zero). Table 1 gives the frequency distribution of innovation spells for all spells and for the longest spell for business units. The 1624 units have 3017 spells between them (the 1332 parent firms have 2449 spells). There are very few units or firms with spells of more than two periods (5.14% and 5.19% respectively). Table 2 presents the life table for the innovating unit's spells. The spells are divided into three groups depending on the number of innovations in the initial period (accounting for 8%, 16% and 76% of all innovations produced). Group 1 had only one innovation at the start of a spell, group 2 had two innovations and group 3 three or more. What is clear from these tables is that spells last longer the greater is the initial burst of innovative activity. Only 19% of units that began a spell with only a single innovation had an expected spell of greater than a single period (and 70% of these ended after two periods). By contrast, of the units that produced three or more innovations at the start of the spell, 58% lasted for two years or more. Recall that only 71 spells (under 5%) passed this initial thresh-

P.A. Geroski et al. / Research Policy 26 (1997) 33-48

42

Table 4 Weibull regressions of patent spells ~ (i)

pat1 pat2 pat3 pat4 assoc subsid mixed growth pspill Pseudo R 2 Model x 2 ( k - 1) d 1/a Jaggia X2(3) ~ Log likelihood

(ii) -2.0089 -- 1.5227 -- 1.0838 --0.7494

(0.083) b (0.087) (0.097) (0.117)

(iii) -- 1.3943 -- 0.9626 --0.6731 --0.3112 -- 0.1443 - 0.1567 - 0.0807 0.4418

0.1697 1680.359 (0.000) 0.719 (0.006) 0.000 (l.0) - 5302.248

(0.134) (0.137) (0.145) (0.164) (0.054) (0.028) (0.075) (0.238)

0.0842 756.743 (0.000) 0.669 (0.006) 0.000 (1.0) - 4653.981

-- 1.392 (0.134) -- 0.9693 (0.136) --0.6779 (0.144) --0.3259 (0.163) -- 0.1546 (0.054) - 0.1643 (0.028) - 0.0825 (0.075) 0.4969 (0.236) 0.0899 (0.022) ' 0.0893 773.568 (0.000) 0.665 (0.006) 0.000 (1.0) - 4654.569

" Dependent variable is the log of time until failure; method of estimation is m a x i m u m likelihood; all regressions contain an intercept; estimated on 4859 spells between 1970 and 1988. b Standard errors given in parentheses beside estimated coefficients. Coefficient standard errors are conditional on l / o r , the standard error of which is conditional on estimated coefficients. c Coefficient and standard error on pspill have been scaled up by 1000. d x 2 ( k _ 1) is a W a l d test of the joint significance of coefficients on variables where k is the number of regressors ( p - v a l u e in parentheses). e Jaggia X 2(3) is a conditional Weibull moment specification test of the generalised residuals ( p-values in parentheses). The null hypothesis is that the residuals have the expected theoretical moments. See Jaggia (1991) for details.

Table 5 Weibull regressions of innovation spells a (iv)

inn1 inn2 owner growth emp emp 2 emp 3 emp 4 ispill c Pseudo R2 Model x 2 ( k - 1) d 1/or Jaggia X2(3) e Log likelihood

(v) - 0.3890 (0.060) b -- 0.2466 (0.005)

0.0115 71.966 (0.000) 0.500 (0.005) 0.000 (1.0) -2037.450

(vi) -- 0.3589 -- 0.2212 0.1607 - 0.2086

(0.059) (0.066) (0.019) (0.214)

0.0284 137.55 (0.000) 0.493 (0.005) 0.000 (1.0) - 1997.200

(vii) -- 0.3377 -- 0.2250 0.1663 - 0.1738 1.1627

(0.059) (0.066) (0.019) (0.212) (0.283)

0.0514 (0.022) 0.0346 167.875 (0.000) 0.490 (0.005) 0.000 (1.0) - 1983.003

-- 0.3084 (0.059) -- 0.1906 (0.066) 0.1603 (0.019) - 0.2011 (0.211 ) 8.550 (1.626) - 68.292 (16.616) 179.520 (50.778) - 139.670 (43.51) 0.0570 (0.022) 0.0390 188.125 (0.000) 0.488 (0.005) 0.000 (1.0) - 1970.955

a Dependent variable is the log of time until failure; method of estimation is m a x i m u m likelihood; all regressions contain an intercept; estimated on 2957 spells between 1947 and 1982. b As note b to Table 4. ispill = 1 (spillover) if there are more than 11 innovations in the unit's 2-digit (SIC) industry. d As note d to Table 4. e As note e to Table 4.

P.A. Geroski et al. / Research Policy 26 (1997) 33-48

old. As with patents, the hurdle rate to enjoy dynamic economies appears to be very high indeed. 3.3. The determinants of hazard rates To analyse the issue of duration dependence and check that the informal analysis shown in Tables 1 and 2 is not seriously misleading, we turn to estimates of the Weibull model. The major limitation that we face is that of obtaining information on potentially important determinants of spell length other than the initial level of patenting or innovation. Our two databases contain relatively little information other than the measures of innovative output production which we are using, and it is very difficult to link them to other databases that have useful information on individual firms without greatly reducing our sample sizes. However, we have been able to introduce several control variables which enable us to undertake at least a limited assessment of the results. These are: ownership structure, macroeconomic growth, spillovers and, in the case of the innovation data set, firm size. Definitions and moments of these variables are shown in Table 3, Weibull regressions of patent spells are shown in Table 4 and Weibull regressions of innovation spells are shown in Table 5. Regression (i) in Table 4 shows very clearly that firms that commence a spell with only a single patent in year t are very much less likely to patent in t + I than firms that commence a spell with 5 or more patents (which is the omitted dummy). Further, the degree of relative disadvantage declines smoothly as the initial level of patenting rises. Regressions (ii) and (iii) show that these conclusions are qualitatively robust to the inclusion of information on ownership structure, macroeconomic growth and spillovers. However, the raw data do overstate the degree of association between the initial level of patenting and the length of subsequent spells, not least because spell lengths are enhanced by spiliovers, last longer in booms and are observed to be more persistent in corporate parents than in subsidiaries. All of this said. it is also evident that many spells seem to be long (or short) simply by chance. The basic story is similar when we examine spells of major innovation production. As regression (iv) in Table 5 shows, firms that begin spells with fewer

43

innovations have, on average, significantly shorter innovation spells. This result is robust across all of the experiments which we conducted. Regression (v) includes a measure of whether the unit was definitely independent of any parent and the growth of aggregate demand in the economy. Being independent has a strongly positive effect on spell length, whereas the demand variable is insignificant. Regression (vi) includes a measure of the size of the unit (the number of employees at the start of the spell) and a proxy for spillovers (a dummy equal to one if there were more than eleven innovations used in the firm's principal two-digit industry) ~7. There is evidence that larger units have longer spells and there are some spillover effects. Finally, regression (vii) introduces a polynomial of fourth order in firm size. As with Pavitt et al. (1987), who analysed the influence of size on innovation intensity, we find evidence of a highly nonlinear relationship. However, despite the fact that the higher order terms are significant at conventional levels, the earlier results are all robust to this more flexible functional form. One common feature of the regressions shown in Tables 4 and 5 (and, indeed, of virtually all of the regressions we ran) is that the data are strongly inconsistent with the hypothesis of negative duration dependence. Recall that in the Weibull model, Aft) = yat,~- 1, so A'(t) < 0 if a < 1, or 1/o~ > 1. For the patents data 1 / a -~ 0.5, while for major innovations l / a - - - 0 . 7 , implying in both cases that c~ clearly exceeds unity. Coupled with the existence of (rather high) threshold effects, this suggests the following interpretation of the data: while dynamic economies may lead to longer, more persistent spells of innovation by .firms, they do so only when the threshold of initial or pre-spell innovative activi~ is high enough to temporarily overcome strong withinspell forces which appear to retard the production of innovation. Put more simply, 'success only follows

~7 Including a simple count of the number of industry innovations used was also positive, but less well determined. The effect is driven by the very highly innovative industries only. Experiments were also tried with including the number of innovations produced in the unit's region and the number of innovations produced in the unit's industry. These variables had no obvious effect on spell length.

44

P.A. Geroski et aL / Research Policy 26 (1997) 33-48

really major success, and then for only a limited period of time'. Finally, four incidental observations about these results are worth making. First, the fact that demand growth has a negative but not significant effect on the length of innovating spell contrasts somewhat with studies of the incidence of innovation which often show signs of a positive effect of demand on innovation (see, for example, Geroski and Waiters, 1995, and references cited therein), as well as with the positive effect of demand growth on patenting. The best explanation of this that we have uncovered derives from work which suggests that increases in cash flow (which varies in a strongly procyclical fashion) induces firms to bring forward innovations (Geroski et al., 1995), leading to a bunching of innovation production that, ceteris paribus, reduces innovating spell length. 18 Second, spillovers appear to have a positive (if rather modest) effect on spell length, something that does not seem to be a feature of innovation incidence models using these data (see Geroski et al., 1995) or of models of the determinants of corporate profits, growth or industry productivity growth (see Geroski, 1994). The obvious conclusion is that spillovers stimulate innovativeness largely because they affect the number of follow-up innovations that a firm produces given that it has already produced an innovation at time t, rather than because they affect the number produced at t. This is consistent with the view that innovations produced at t increase a firm's absorptive capacity, enabling it to benefit from spillovers and innovate longer than would otherwise have been the case. Third, it seems clear from Table 5 that independent innovating units (marginally) outperform subsidiaries as persistent innovations, presumably because stronger investment incentives outweigh any failure to exploit economies of scope. 19 Fourth and finally, persistent innovation is not strongly linked to firm size, although there does seem to be a positive relation between the length of

is One of our referees suggested that faster growth in demand may increase product turnover and, therefore, shorten product life cycles. This reduces the profitability of any individual innovation and may reduce the length of innovation spells. 19For work on the relationship between diversification and innovation, see Nelson (1959), Scott (1993) and others.

innovation spells and firm size. To explore whether the same relationship holds in the case of patenting spells, we focus on a smaller sample of 250 firms for which we have information on firm size. 20 Weibull regressions for this sample produced results similar to those shown in regression (vi) in Table 5; i.e. with small, positive coefficients on pre-spell firm size (measured by turnover). These estimates were robust to the inclusion of a wide range of other variables (such as capital intensity and export intensity), and of about the same order of magnitude in patent spell regressions as in innovation spell regressions. These size effects are, however, small. The average size of firms having patenting spells of 1. . . . . 7 years is £128m, £254m, £173m, £147m, £321m, and £171m; for innovation spells of length 1. . . . . 7 years average size is: £379m, £486m, £825m, £809m, £235m, and £639m. The simple fact is that pre-spell patenting or innovation activity has a much more powerful effect on spell length than firm size.

4. Conclusions Many economists interested in innovative activity have argued that the evolution of technology is, at least in part, endogenous. There are two senses in which this might be true. The first is the rather broad sense of endogenous which corresponds to the notion that 'technology responds to market forces', an observation which has often led people to examine the relative strength of 'supply push' and 'demand pull' models of innovation. Most scholars would be reluctant to dispute the assertion that technology responds to market forces in the sense that demand can stimulate innovative activity, although there is very little agreement on how large an effect demand has. 21 A second sense in which the evolution of technol-

20This is essentially the sample used in Geroski et al. (1995) (or, rather, those firms in that sample who innovated or patented between 1972 and 1982). On average, these firms produced 40 patents and 5 innovations; as a sample, this group of firms produced fewer one-year spells than the full sample discussed earlier. 21 See Geroski and Waiters (1995) for work on the effect that demand changes over the cycle have on patents and major innovations; for a recent survey of other empirical work on the determinants of innovation, see Cohen (1995).

P.A. Geroski et al. /Research Policy 26 (1997) 33-48

45

ogy might be endogenous is captured in the notion of 'dynamic economies of scale', namely the possibility that increases in the volume of innovations produced by a finn at any one time increase the likelihood that it will continue innovating subsequent to that time. The kinds of arguments that support this view are often summarized by a phrase such as 'success breeds success', and they command fairly widespread, if rather imprecise, support in the profession. Widely held or not, the simple fact is that they are a little hard to reconcile with the data which we have analysed here. Most firms that produce a patent or a major innovation do so only once, and the very few firms that achieve a spell of patent or innovation production of any length (say three to five successive years) generally do so only when they have passed a relatively high initial threshold of five or more patents and three or more major innovations. Further, spells during which firms produce patents or major innovations never display any sign of negative duration dependence. Even when firms cross the initial thresholds identified above, the events which occur during the subsequent innovation spell are powerful enough to sharply limit its duration. In short, it is very hard to find any evidence at all that innovative activity can be self-sustaining over anything other than very short periods of time, at least for the kinds of innovative activity that we have focused on here. There are at least two areas of theoretical work which these results cast some interesting light on. The first is the literature on patent races, which has explored the conditions under which monopoly market structures will persist, Most of the dynamics in these models are driven by two effects: the 'replacement effect', which makes firms reluctant to innovate in period t for fear that they will cannibalize rents generated from innovations which they introduced prior to t, and the 'pre-emption effect', which generates an incentive for a firm that innovated in period t to innovate again in t + 1 to realize gains from exploiting both innovations jointly. 22 The replacement effect arises when successive innovations

are substitutes, while the pre-emption effect arises when they are complements. Our data show very little sign that innovators in period t also innovate again in t + 1 (or subsequently), and, in this limited sense, suggest that the replacement effect is the stronger determinant of industry dynamics (an observation consistent with countless case studies). This implies that monopoly market structures are unlikely to persist for long periods of time (an observation that is also generally consistent with many case studies). The second body of theorizing that our results cast some light on is the process of growth and development, as discussed in recent macroeconomic theories of endogenous growth and in theories of the 'dynamic capabilities of firms'. 23 Both of these bodies of literature focus on sources of increasing returns which might sustain growth (particularly in the face of diminishing returns created by conventional factor scarcity). This means concentrating on knowledge accumulation and the underlying ability of firms/economies to absorb and then productively use knowledge. Since knowledge often is a public good, each increment of knowledge gained can facilitate the acquisition of the next increment. Our observations sit uncomfortably alongside this kind of theorizing. Although some firms do innovate persistently, only a very few do and they do not enjoy very long innovation spells. This might mean that very few firms have genuine 'dynamic capabilities', or that such capabilities lead to only very' short-lived advantages. Further, although it is hard to believe that the accumulation of knowledge does not display some sort of increasing returns in the production of subsequent knowledge, it seems to be the case that such processes of knowledge generation can yield sharply diminishing returns when knowledge is embodied in new goods or in patents. Given this, it is hard to believe that knowledge accumulation leads to the kinds of permanent increases in growth rates posited by endogenous theories of growth, or sustained competitive advantage by firms.

22The terms are based on Tirole (1988, pp. 392-393). The 'replacement effect' was identified in the classic paper by Arrow (1963), while the 'pre-emption effect' was discussed by Gilbert and Newberry (1982) (amongst others). See Beath et al. (1995) for a recent survey of models of technological competition.

2, On endogenous growth, see the recent surveys by Grossman and Helpman (1991) or Barro and Sala-i-Martin (1995). Theories of 'dynamic capabilities' focus on how firms accumulate technological capabilities which might underlie sustained competitiveness; see Teece and Pisano (1994), and references cited therein.

46

P.A. Geroski et aL / Research Policy 26 (1997) 33-48

Finally, these results carry one further implication, and that is that public policy to support innovation and patenting is likely to be rather expensive. It is clear that any kind of support for a particular activity will yield much larger benefits if increasing returns generate a more than proportionate rise in output relative to the increase in input generated by the support. Other knock-on effects such as spillovers which give rise to positive feedback will, of course, magnify the benefits of any given level of support. Making public policy more effective is at least in part a matter of targeting it at activities that display such 'dynamic economies of scale'. Popular discussions of industrial policy usually single out innovative activity as a prime example of a potentially productive public policy target. Our results suggest that the threshold levels of innovative activity triggering 'dynamic economies of scale' are rather high, and therefore, that it is easy to exaggerate the potential gains that will be realized from this type of support.

Acknowledgements We are indebted to the Gatsby Foundation and the ESRC for financial support, and to Hugh Wills, Ron Smith, Giovanni Urga, Dennis Mueller, Keith Pavitt, Jos6 Mata, Katy Graddy and three referees for helpful comments. The usual disclaimer applies.

Appendix A. How often do firms patent? There were 1649 firms with a single spell of I year, 9.3% of which are left censored and 5.2% right censored (spell length adjusting for this right-censoring is 1.055 years for all 1649 firms). Mean total patents for those left censored is 1.261 (median 1 patent) and 1.169 (median 1 patent) for those not. Mean patents for the 1410 firms neither left nor fight censored is 1.103. Of these 1649 firms, 1505 patent just once in their 1-year spell, although 8.7% are left censored and 5.2% fight censored. There were 498 firms with multiple spells of 1 year's length. These firms have 1162 spells in total, with between 2 and 6 each (mean number of spells is 2.519, standard deviation 1.324 spells). Of these

spells, 7.6% are left censored and 3.7% right censored (spell length adjusting for right-censoring is 1.038 years for all 1162 spells). Mean patents per spell are 1.235 for the 1074 spells that are not left censored, and 1.273 patents for the 88 spells that are. There are 663 gaps between these 1162 spells, which are 4.089 years long on average (standard deviation 2.797 years), ranging from a minimum of 2 years to a maximum of 17. Of these 498 firms, 410 are uncensored, as are 1031 of their 1162 spells. Mean patents per spell for these spells are 1.181 (standard deviation 0.484 patents) and the 621 gaps between these spells have mean length of 3.981 years (standard deviation 2.598 years, minimum 2 years, maximum 17 years). Of these 498 multiple 1-year patentors, 342 had just 1 patent in each of their 1-year spells. There are 770 of these spells, 6.5% of which are left censored and 3.9% of which are right censored (the spell length was 1.041 years for all 770 spells). The 342 firms have on average 2.397 spells (standard deviation 0.716 spells), with between 2 and 5 spells each. The 427 gaps between these spells have mean length of 4.368 years (standard deviation 2.961 years, minimum 2 years, maximum 17 years). Of these 342 firms, 292 are uncensored, as are their 690 spells. These firms share from 2 to 5 spells between them (mean 2.412 spells, standard deviation 0.726 spells), with gaps of between 2 and 17 years between spells (mean 4.234 years, standard deviation 2.742 years). The remaining 646 firms had multiple spells that are not all of 1 year but are less than fifteen years. There are 1850 of such spells, between 2 and 7 per firm (mean 3.285 spells, standard deviation 1.28 spells), 11.8% of which are left censored and 5.8% right censored. Mean length for the 1632 spells that are not left censored is 2.15 years (median 2 years), with 3.959 patents per spell (median 2 patents). For the other 218 spells that are left censored, mean length is 3.188 years (median 2 years) with 11.936 patents per spell (median 3 patents). The 1204 gaps between these spells are between 2 and 16 years long (mean 3.272 years, standard deviation 2.035 years). Of these firms, 428 are neither left nor right censored, nor are 1524 of their spells. These firms also have between 2 and 7 spells (mean 3.299 spells, standard deviation 1.282 spells), which are on average 1.961 years long (standard deviation 1.529 years,

P.A. Geroski et al. / Research Policy 26 (1997) 33-48

minimum 1 year, maximum 13 years) with 3.393 patents per spell (standard deviation 6.211 patents, minimum 1 patent, maximum 159 patents). The 1096 gaps between these uncensored spells have mean length of 3.222 years (standard deviation 1.946 years), ranging from 2 to 15 years. There were 459 firms with a single spell of between 2 and 14 years' duration, 22.2% of which are left censored and 13.2% right censored. Mean spell length is 3.858 years (median 2 years) with 9.983 patents, for the 357 firms not left censored and 4.363 years (median 3 years) with 19.304 patents, for the 102 left censored firms. Mean spell length for the 296 uncensored firms is 2.882 years with 5.534 patents. There were 58 firms that patented persistently with at least 1 spell of 15 years or more; 6 of these firms had two spells. Of course, these six firms have the six spells in the tail of the length distribution for two spells (ie. 15 to 17 years). Unsurprisingly, 82.7% of these 52 firms are left censored and 59.6% of them right censored. Of the 58 spells they share between them, 74.1% are left censored and 53.4% right censored. Mean spell length of the 15 spells not left censored is 26.667 years (median 17 years) with 222.167 patents (median 196 patents). The remaining 43 left censored spells have mean duration of 37.476 years with 723.571 patents. Of the 6 firms with multiple spells, 50% of their 12 spells are left censored and 25% right censored (all of the firms are left censored and half right censored). Mean spell length of the 6 left-uncensored spells is 2.667 years, with 4.333 patents, and 16.167 years (with 139.167 patents) for the 6 left-censored spells. The mean length of the gap between these two spells is 2.5 years (standard deviation 0.837 years). Of these 6 firms, 3 (and their 6 spells) are neither left nor right censored. The mean spell length of these 6 spells is 8.833 years but with a large standard deviation of 8.589 years (this is because the range of lengths is 1 to 17 years, as the preceding analysis would lead us to expect). The mean number of patents in these 6 spells is 75.667 (standard deviation 94.225 patents). The 3 gaps between these 6 spells are all 2 years long. Of the 58 persistent patentors, 22 produced at least 1 patent in all 20 years. Clearly all these firms and their single spells are both left and right cen-

47

sored, which means that adjusted mean and median lengths and patents cannot be computed since there are no uncensored spells as a basis for comparison. Nonetheless, unadjusted mean patents are 541.727 (standard deviation 788.079 patents) ranging from a minimum of 63 patents to a maximum of 3643.

Appendix B. How often do firms produce major innovations? There were 942 units that only produced one innovation (58%), 240 (15%) produced 2 and 121 (7.5%) a total of 3 over the whole period. The highest total number of innovations was 53. There were 1624 units that produced at least 1 innovation. Only one of these is right censored and none are left censored. Thus censoring does not appear to be a serious problem in the innovations data due to the long time series and the relatively short innovation spells. Of these units, 16.6% had 2 spells and 8.5% 3 spells. The maximum number of spells was 11 (only 1 firm managed this). There were 1027 units out of the 1624 that only produced a spell of a single year and 597 units with multiple spells. Of these 597, 376 multiple spellers had a length of only a single year. And 277 of these 376 only had 1 innovation in their spell. Of the 320 multiple spell units the number of spells ranged between 2 (29%) and 11 (just 1 unit). The 1027 units with a single spell had a spell Length ranging between 1 and 10 years.

References Acs, Z. and D. Audretsch, 1990, Innovation and small firms (MIT Press, Cambridge, MA). Arrow, K., 1963, Economic welfare and the allocation of resources for innovations, in: R. Nelson, ed., The rate and direction of inventive activity (Princeton University Press. Princeton). Barro, R. and X. Sala-i-Martim 1995. Economic growth (McGraw-Hill, New York). Beath, J., Y. Katsoulacos, and D. Ulph, 1995, Game-theoretic approaches to the modelling of technological change, in: P. Stoneman, ed., Handbook of the economics of innovation and technological change (Basil Blackwell, Oxford). Cefis. E.. 1996. Is there any persistence in innovative activities'?. Mimeo. (European University Institute, Florence).

48

P.A. Geroski et aL /Research Policy 26 (1997) 33-48

Cohen, W., 1995, Empirical studies of innovative activity, in: P. Stoneman, ed., Handbook of the economics of innovation and technical change (Basil Blackwell, Oxford). Cohen, W. and D. Levinthal, 1989, Innovation and learning: The two faces of R&D, Economic Journal 99, 569-596. Cox, D.R., 1972, Regression models and life tables, Journal of the Royal Statistical Society B 34, 187-202. Feldman, M., 1994, The geography of innovation (Kluwer Academic, Boston, MA). Geroski, P., 1994, Market structure, corporate performance and innovative activity (Oxford University Press, Oxford). Geroski, P. and C. Waiters, 1995, Innovative activity over the business cycle, Economic Journal 105, 916-928. Geroski, P., S. Machin, and J. Van Reenen, 1993, The profitability of innovating firms, Rand Journal of Economics 24, 198211. Geroski, P., J. Van Reenen, and C. Walters, 1995, Innovations, patents and cash flow, Mimeo. (London Business School). Gilbert, R. and D. Newberry, 1982, Pre-emptive patenting and the persistence of monopoly, American Economic Review 72, 514-526. Greenwood, M., 1926, The natural duration of cancer, Reports on Public Health and Medical Subjects 33, 1-26. Griliches, Z., 1990, Patent statistics as economic indicators, Journal of Economic Literature 28, 1661-1707. Grossman, G. and E. Helpman, 1991, Innovation and growth in the global economy (MIT Press, Cambridge, MA). Heckman, J.J. and B.L. Singer, 1984, Econometric duration analysis, Journal of Econometrics 24, 63-132. Jaggia, S., 1991, Tests of moment restrictions in parametric duration models, Economics Letters 37, 35-38. Kalbfleisch, J.D. and R.L. Prentice, 1980, The statistical analysis of failure time data (John Wiley, New York). Kaplan, E.L. and P. Meier, 1958, Nonparametric estimation from incomplete observations, Journal of the American Statistical Association 53, 457-481.

Kiefer, N.M., 1988, Economic duration data and hazard functions, Journal of Economic Literature 26, 646-679. Krugman, P., 1991, Geography and trade (MIT Press, Boston, MA). Lancaster, T., 1990, The econometric analysis of transition data (Cambridge University Press, Cambridge). Malerba, F. and L. Orsenigo, 1995, Schumpeterian patterns of innovation, Cambridge Journal of Economics 19, 47-65, Nelson, R., 1959, The simple economics of basic scientific research, Journal of Political Economy 67, 297-306. Patel, P. and K. Pavitt, 1995, Patterns of technological activity: Their measurement and interpretation, in: P. Stoneman, ed., Handbook of the economics of innovation and technical change (Basil Blackwell, Oxford). Pavitt, K., M. Robson, and J. Townsend, 1987, The size distribution of innovating firms, Journal of Industrial Economics 35, 297-316. Porter, M., 1990, The competitive advantage of nations (Macmillan, London). Savage, I.R., 1956, Contributions to the theory of rank order statistics: The two sample case, Annals of Mathematical Statistics 27, 590-615. Scott, J., 1993, Purposive diversification and economic performance (Cambridge University Press, Cambridge). Teece, D. and G. Pisano, 1994, The dynamic capabilities of firms: An introduction, Industrial and Corporate Change 3, 537-556. Tirole, J., 1988, The theory of industrial organization (MIT Press, Cambridge, MA). Townsend, J., F. Henwood, G. Thomas, K. Pavitt, and S. Wyatt, 1981, Innovations in Britain since 1945, Occasional Paper 16 (SPRU, University of Sussex). Wilson, R., 1975, Informational economies of scale, Bell Journal of Economics 6, 184-195.