The Path of R&D Efficiency over Time

Transcription

1 The Path of R&D Efficiency over Time Pilar Beneito a,b María Engracia Rochina-Barrachina a Amparo Sanchis a Abstract In this paper we investigate the pattern of R&D efficiency in terms of the number of product innovations achieved by firms over time. Embodied in the R&D capital stock, we distinguish among physical R&D capital and human R&D capital, and allow the latter to be subject to dynamic returns along firms R&D histories. We assume that firms innovation outcomes depend on the length of the period of time they have been investing in R&D and explore whether the interruption in this temporal sequence of engagement in R&D affects the rate of achievement of innovation outcomes. For this purpose, we estimate an innovation production function using a panel dataset of Spanish manufacturing firms for the period Our results suggest that R&D activities exhibit dynamic returns that are increasing but at a decreasing rate, possibly due to exhaustion of innovation opportunities. In addition, our findings indicate that interruptions of R&D activities reduce R&D efficiency, probably due to organizational forgetting. However, spillover effects seem to exist between firms R&D spells since firms resuming R&D activities achieve innovation success rates above the innovation rates of their initial years of R&D activities. Keywords: R&D, dynamic returns, interruptions, product innovation, count data. a University of Valencia and ERI-CES b Corresponding author: Pilar Beneito, University of Valencia (Spain) and ERI-CES, Facultad de Economía, Departamento de Análisis Económico, Avda. de los Naranjos s/n, Valencia (Spain); address: pilar.beneito@uv.es 1

2 1 Introduction The returns to R&D investments and their measurement have been a major concern of innovation economics since the seminal work of Griliches (1958). A primary issue to deal with has been the way in which knowledge accumulates over time in order to construct acceptable measures of firms or industries R&D capital stocks to be introduced into production functions, or equivalent approaches such as firms market value equations (Griliches, 1991), to estimate R&D returns. Empirical research about how to construct a stock measure derived from the flows of firms R&D investments has focused the bulk of the attention on the measurement of the depreciation rates of knowledge capital, still a central problem in the measurement of the returns to R&D (Hall, 2010). Griliches and subsequent researchers used a conventional declining balance formula (the perpetual inventory method) for the construction of the knowledge capital (also called R&D capital), in a similar form to that used with ordinary investment and capital in production theory. It is somewhat surprising how a close analogy between ordinary physical capital and knowledge capital has been taken as given when applying that methodology to obtain a stock measure of R&D capital from the flow of R&D investments, when, in fact, they differ in quite fundamental aspects. 1 One of the most prominent differences is that, unlike ordinary capital investments, firms R&D expenditures involve both the purchase of capital goods in the classical sense (machinery, equipment and so on) and the purchase of R&D labour. Schankerman (1981) stressed that the inclusion of spending on labour, capital and materials within R&D flows could introduce a problem of double counting in production functions (to the extent that these inputs are already included within the values of ordinary capital, labour and 1 As argued by Boulding (1966) and Pakes and Schankerman (1984), among others, the different nature of (traditional) physical capital and knowledge capital determines the definition of the rate of decay in productivity (or depreciation) that should be considered in each case. They pointed out that the rate of decay of knowledge does not obey the laws of physical deterioration in the same way as traditional capital, and that the appropriate definition of depreciation in the case of knowledge capital has to do with the decay of the market valuation of the output of knowledge (i.e., the decline in the appropriable revenues from R&D). 2

3 materials) that could bias the estimation of R&D returns. However, this diverse nature of R&D spending also implies that there are at least two different concepts of capital accumulation embodied in the R&D capital stock, one corresponding to physical capital and another one corresponding to human capital. How the efficiency of these two components evolves over time is probably a question very difficult to address and identify empirically, but it seems sensible to assume that, whereas the rate of efficiency of R&D physical capital probably decays over time because of physical deterioration and obsolescence, the rate of efficiency of R&D workers could be even increasing over time if knowledge grows with cumulative experience. The reasons why this could be so are well grounded in the vast literature on learning-by-doing, firstly developed to explain the evolution of productivity advance over the lifetime of the firm. This line of the literature started with the pioneer empirical studies of Wright (1936) or Hirsch (1956), which gave rise to the concept of learning curves or progress ratios, and the theoretical contributions of Arrow (1962) or Rosen (1972), among others. More recently, authors like Benkard (2000, 2004) and Besanko et al. (2010) have revisited the learning-by-doing hypothesis within the production theory, emphasising that not only cumulative experience but also organizational forgetting is essential to explain the dynamics in the industry. According to these authors, the decrease in marginal costs of production arising from experience (the learning-by-doing effect) might be undone by organizational forgetting due to labour turnover, periods of inactivity or failures to institutionalize tacit knowledge. Besanko et al. (2010) argue that organizational forgetting, which has been largely ignored by the theoretical literature, may lessen the market dominance promoted by learning (Dasgupta and Stiglitz, 1988), thus equalizing differences between firms and making improvements from learning-by-doing more transitory. The aim of this paper is to investigate whether the efficiency of firms R&D investments in terms of innovation outcomes depends upon the length of time firms have been undertaking R&D activities. In addition, we also explore whether periods of interruption in R&D activities may undo accumulated learning, and thus affect firms rates of innovation outcomes. We acknowledge the twofold composition of R&D investment, embodying both physical capital and human capital, and assume that, as firms engage in R&D in a continuous 3

4 way, two effects may be at work: on the one hand, R&D physical capital may follow the classical assumptions of depreciation and its corresponding replacement with new R&D spending; on the other hand, that part of R&D investment that has to do with human capital provides the firm with a potential source of increasing efficiency of R&D investments over time. This second effect is based on the notion that with increasing time spent on R&D activities firms may become more efficient in obtaining innovations from a given level of R&D investment. This second effect is probably more relevant in shaping the evolution of firms R&D returns, and this is the main focus of this paper. We use for our purpose a representative sample of Spanish manufacturing firms for the period 1990 to The dataset is drawn from the Encuesta sobre Estrategias Empresariales (ESEE, henceforth), a survey carried out annually since 1990 by Fundación SEPI (a Spanish government agency) that provides detailed information at the firm level on a broad number of issues, including innovation activities. Our empirical approach is based on an innovation production function augmented to include the temporal sequence of R&D investments. In particular, we assume that firms obtain innovation outcomes from their R&D investment at a rate that depends on the length of the period of time they have been investing in R&D. This period of time may be uninterrupted (continuous sequences of R&D activity, which we call R&D spells, henceforth) or, on the contrary, firms may interrupt their R&D activities for a given number of years. We explore whether the interruption in the temporal sequence of engagement in R&D, that is, periods of R&D inactivity between R&D spells, affects the rate of achievement of innovation outcomes. The underlying assumption in this latter case is that acquired knowledge may depreciate during R&D interruptions, so that a given total length of time is associated with a different R&D efficiency if it is distributed in more than one spell of R&D activity, that is, if there exists intermediate periods of R&D inactivity. Notice that these assumptions imply a type of dynamic returns that are endogenous to the firm (arising from its own accumulated R&D experience), a source of improvement over time that differs from that affecting the quality of R&D capital or the qualification of R&D workers available to all firms, and taking place with the passage of time per se. To give an example, although two firms investing today 4

5 in R&D may have access to higher quality R&D capital or better-qualified R&D workers than twenty years ago, the one with a longer R&D history is likely to be able to achieve higher rates of innovation success from its current investment. In the next section we discuss with more detail these and other aspects of time assumed to affect firms R&D efficiency. Our paper is an attempt to characterise better the knowledge production function by introducing a new source of firms heterogeneity, arising from the firm s temporal sequence of R&D investments. It is not our aim in this paper to measure the private returns to R&D in a firm s production function approach, or other equivalent approaches such as the market value approach, but to measure the efficiency of R&D in terms of achieved innovations. As Pakes and Shankerman (1984) correctly emphasized, although the private rate of return of R&D investment is affected by the rate of decay of the revenues accruing to industrially produced knowledge, this rate of decay in the revenues arises from a reduction in the market valuation of innovations but not from any decay in the productivity of knowledge. This amounts to say that, depending on the approach used, the relevant dynamics to consider differ: how the market value of an innovation changes in time is the relevant question if our goal is to estimate private returns to R&D, whereas how the efficiency of R&D in achieving innovations changes over time is the relevant one if our goal is to estimate the firms production process of innovations (i.e. their innovation success rates). As stated above, our objective is to analyse this latter aspect, whereas the analysis of the evolution over time of the market valuation of a given innovation is beyond the scope of the paper. The issue addressed in this paper suggests a number of important implications both for empirical and for theoretical research in R&D economics. First, it has direct implications on the analysis of the depreciation of R&D capital. Given that the depreciation rate of an asset is closely related to its path of efficiency over time, one could claim that, if the efficiency of R&D investments is different for firms with different temporal sequences of R&D investments, then it does not exist a common depreciation rate across firms. 2 The idea that a constant depreciation rate across firms may not be a 2 Hulten and Wykoff (1996) discuss the most common types of efficiency functions found in the literature, and explain the direct relationship between the efficiency patterns of an asset and the corresponding path of economic depreciation. 5

6 reasonable assumption when constructing R&D stocks has been recently stressed by authors as Hall (2010). She states that the appropriate depreciation rate is endogenous to a firm s behaviour and, therefore, it is not reasonable to assume that it is constant over time or across firms. In turn, this has also implications for measuring the private rate of return to investment in research. In the model of Pakes and Schankerman (1984), for instance, the private return to a dollar of research depends (negatively) on the mean gestation lag, defined as the average time between the outlay of an R&D dollar and the beginning of the associated revenue stream (pp. 82). If firms accumulate experience managing R&D projects as time goes on, one should expect a reduction in these gestation lags and a corresponding rise in the private returns to R&D. A second implication of a changing R&D efficiency over time has to do with the optimum path of accumulation of R&D capital. Rosen (1972), for instance, in his theoretical model of learning by experience in production, established that the marginal cost of knowledge is its discounted future marginal product adjusted for the fact that greater knowledge reduces future learning costs. If this kind of dynamic internal economy exists also in the production of innovations, then the optimality of any additional R&D effort (i.e., additional R&D spending and time) has to be evaluated in terms of its contribution to current innovations as well as to the capacity of innovating more and better in the future. Conversely, the losses for a firm of interrupting its R&D activity for a given period of time exceed the innovations that could have been achieved during this period, and includes, also, the losses derived from a lower probability to innovate in the future. The issues addressed above directly suggest interesting policy implications. On the one hand, if learning effects exist in R&D, it could be the case that on early stages of their innovative path firms have negative profits from their R&D activity and returns start to arise in the form of positive profits later on. According to Rosen (1972) if dynamic internal economies describe the infant industries case, it is not necessarily true that protection is required to establish a competitive position in the market. The social rate of return of subsidies on new R&D firms could be below their social opportunity cost. An alternative policy could be, for example, to facilitate finance to young R&D firms on account of the future stream of profits arising from successful R&D 6

7 projects. On the other hand, if forgetting exists, the impact of economic downturns, financing constrains, or other determinants of firms exits from R&D activities may be higher than usually thought since these interruptions deteriorate firms future capabilities to succeed in innovation. As noted by Benkard (2000), at a macroeconomic level the presence of forgetting implies that recessions (that may halt or reduce R&D efforts) may lead to a reduction in productivity that lasts beyond the rebound in output. How to promote innovative firms incentives to maintain R&D activities when facing this type of setbacks is a challenge for the innovation policy. To anticipate our results, we obtain that the number of years of R&D engagement has a positive effect on expected innovation outcomes, that is, R&D investments exhibit dynamic returns due to a process of learning taking place with the passage of time. These dynamic returns are positive but decreasing over time, possibly because of exhaustion of innovation opportunities. In addition, our findings suggest that interruptions of R&D activities may reduce R&D efficiency, probably due to an organizational forgetting effect. However, we also observe spillover effects between firms R&D spells since, if the interruption of R&D activity is relatively short, firms resuming R&D activities seem to achieve innovation success rates that grow above the innovation rates of their initial years of R&D activities. Thus, our findings provide evidence in support of both learning and organisational forgetting effects in R&D engagement. The rest of the paper is organized as follows. In section 2 we present the empirical model, which accounts for our main theoretical considerations changing the standard assumptions of accumulation of firms R&D flows. Section 3 reports the data and some descriptive statistics, section 4 presents the econometric results and, finally, section 5 concludes. 2 Empirical Model Our approach is based on the concept of an innovation production function that may, in a very general form, be expressed as follows: N = f ( K, x, β ) it it it (1) 7

8 where i refers to the firm and t to the time period, N it stands for any chosen indicator of innovation outcomes, K it stands for the firm s knowledge capital in period t, and x it represents a vector of other relevant variables and controls in the equation. We assume that K it is the outcome of a knowledge production function with two R&D inputs: the first is R&D physical capital ( C K it ) arising from the accumulation of present and past R&D investments devoted to acquire capital for R&D projects, such as equipment; the second is human R&D capital H ( ) coming from the accumulation of present and past R&D investments K it devoted to hire and pay for the R&D workers. Just as output is the outcome of a production process where capital and labor are combined, the firm s knowledge capital is assumed to be the output of the combination of these two components of R&D capital: C K it = A t ( K it ) c H ( K it ) r (2) where A t is technical progress of a general type that translates into higher quality of physical R&D capital and higher qualification of R&D human capital, and which is common to all contemporary firms in a given moment of time. It reflects the idea that all those firms investing in R&D in, say, 2006, have access to a higher quality of R&D capital and R&D workers than in 1990, no matter whether or not the firm has invested in R&D in the past. Taking logs in expression (2) we obtain: log K it = log A t + c log K it C + r log K it H (3) In estimation we approximate log A t by time dummies. In what follows we focus on how physical R&D capital and human R&D capital accumulate on time. 2.1 Physical R&D capital Regarding physical R&D capital, K it C, we follow the traditional approach of the R&D capital stock model assuming a geometric decay of the efficiency of the R&D investment. In particular, we assume that the productivity of the investment decays at a constant rate, which results (after applying a Koyck transformation) in a constant depreciation rate of the R&D capital stock (see, 8

9 for instance, Hulten, 1991). This also implies that a constant percentage of the existing capital stock is displaced every year. We consider these are reasonable assumptions for that part of R&D investment subject to physical deterioration and obsolescence, i.e., that part of R&D investment that has to do with physical equipment for research. Thus, we assume that physical R&D capital follows the standard path of accumulation of ordinary capital investments, and is subject to a physical deterioration at a constant rate d. Assuming also a constant rate of growth for firms R&D expenditures, we can write the standard perpetual inventory formula as K C it = R C it 1 + (1 d) g + (1 d) 2 g (4) where c R it refers to the firm i s investment in physical R&D capital, and where g is the within-firm first-order correlation coefficient of a firm s R&D expenditures between any two periods t-1 and t. We assume a constant value of g across firms. In addition, the firm s investment in physical R&D capital in a given period t may be considered to be a share of the firm s total R&D investment during that period, so that we may specify: R it C = φ c R it (5) We further assume that the share of R&D investment devoted to physical R&D capital, φ c, depends on characteristics of the industry where the firm s product belongs to, and, at most, on other firm-specific characteristics and general technical progress. Then, we consider φ c to be captured in the econometric setting by industry dummies, firm-specific effects and time dummies. Given the assumptions above regarding the depreciation rate and the growth rate of R&D expenditures, we may consider the term in brackets in (4) to be a constant term. 3 C Therefore, log K it may be written as: c log K it = log φ c + log R it + log const. (6) 3 For econometric purposes we could relax the assumption that g and d are constant across firms provided we still assume they are constant over time. The terms in brackets in (4) could then be considered a whithin-firm constant, and, thus, absorbed by a firm-specific effect η i analysis. 9, alike we will assume later on for other elements in our

10 2.2 Human R&D capital Now we deal with the path of accumulation on time of that part of R&D capital that comes from investments on the human component of R&D activities. We argue in this paper that the path of accumulation of this component of R&D investment does not obey the laws of physical deterioration and obsolescence but, on the contrary, the efficiency of R&D researchers in converting R&D investments into useful knowledge is probably higher the longer the period of time of engagement in R&D activities. We are therefore allowing for dynamic returns due to learning through experience. Learning may exhibit increasing returns but at a decreasing rate (Lucas 1988) and also firms technological opportunities may get exhausted with the passage of time. We consider then that the length of time of engagement in R&D activities may have a positive but non-linear effect on firms R&D success rates. We further assume that R&D knowledge may be subject to depreciation or deterioration due to forgetting occurring during interruptions of the R&D activity. Building on the determinants of organizational forgetting in production, David and Brachet (2011) argue that human capital depreciation arises from three main sources, skill decay during activity, labour turnover and periods of inactivity. Skill decay refers to the deterioration of acquired skills of active workers over time. We consider that this is a source of deterioration of working capabilities that may affect production workers, for which fixed-sequence tasks based on physical and manual abilities are more relevant (Hagman and Rose, 1983), but that are unlikely to affect R&D research workers. Labour turnover causes knowledge depreciation when human capital embodied in fired workers is lost and not properly replaced by the human capital embodied in new workers. We do not consider that this is a potential relevant source of depreciation in the case of human R&D capital, since firms are usually reluctant to lay off R&D researchers, mainly because of specific human capital formation costs and the risk of leakages of R&D secrets to competitors. However, we do regard periods of R&D inactivity as a potential source of reduction in R&D efficiency, because the loss of human capital accumulated by previous R&D researchers who left the firm will probably not be completely recovered should the firm reinitialize its R&D activity. This amounts to saying that the R&D efficiency of a firm with any given number of years of uninterrupted R&D engagement is expected to be higher, ceteris 10

11 paribus, than that of a firm with the same number of years of R&D engagement but with periods of R&D inactivity (interrupted years) within its R&D path. Firms may, however, stop their R&D activity because of several reasons. One of them could be, of course, as a response to bad economic conditions that may oblige firms to cut off R&D spending. They may, however, stop R&D programmes to look for new ideas or projects once previous lines of research get exhausted. In this latter case, although forgetting may have occurred during the interruption, it could also be possible that firms start new and more fruitful R&D lines of research and, even, counting on the previously accumulated experience. We, therefore, allow firms R&D efficiency after a period of R&D inactivity to be different from the R&D efficiency before stopping R&D activities. In particular, we consider that the evolution over time of R&D efficiency may take place at a different rate after the R&D interruption. For instance, a firm that stops R&D activities is likely to lose some R&D knowledge but it may have a rapid recovery after R&D activities are reinitialized. This would imply that after a period of R&D inactivity the rate of R&D efficiency of a firm might be higher than that at the beginning of its R&D history, explaining a sort of catching-up effect on time with respect to other counterfactual cases. To sum up, we model the path of human R&D capital accumulation of firms assuming that: i) R&D efficiency grows over time; this implies that a firm i s R&D investment in a given period t adds to its knowledge R&D capital at a rate that depends on the length of its R&D history; ii) R&D efficiency grows at a positive but non-linear rate due to likely diminishing returns to learning and exhaustion of technological opportunities; iii) depreciation of knowledge only occurs (if it does) during interruptions of the R&D activity; iv) the efficiency path of R&D may be different when firms resume their R&D activities after interruptions. Thus, firms human R&D capital accumulation is given by K it H = R it H [ h it + h it 1 g + h it 2 g h it (T2 1) gt f s i + h it T2 s gt 2 s + h it T2 s 1 gt 2 s h it (T 1) s g (T 1) s ] (7) where s i denotes the number of years the firm has interrupted its R&D activities and T 2 refers to the number of years after the interruption. The 11

12 parameter f associated to the number of years of R&D interruption accounts for the depreciation of knowledge during interruptions of the R&D activity and, therefore, is expected to be negative in estimation. We assume, just as in the case of physical R&D capital, that the growth rate of R&D spending is constant across firms and over time, what implies a constant value for the correlation coefficient g. For the sake of simplicity and without loss of generality, we assume this growth rate is 1 (in fact, our data shows that this within-firm growth rate is near 0.9 for firms R&D spending). In expression (7), each h it represents the addition to the stock of knowledge from a firm i s R&D investment in period t (the hat symbol over the h s ( h ) denotes the possible different effect on knowledge accumulation of R&D investments after having interrupted R&D activities). Then, expression (7) can be rewritten as: K it H = φ H R it hit + h it 1 + h it h it (T2 1) + f s i + h it T2 s + h it T 2 s h it (T 1) s (8) The share of R&D investment devoted to human R&D capital,, depends on the same determinants explained above for the share of physical R&D capital ( φ H =1 φ C ), that is, the industry of the firm, other firm-specific characteristics and time control variables. We assume that the addition to the stock of knowledge in each period depends on the number of years the firm has been developing R&D activities according to a positive but not necessarily constant function that takes the following form: φ H h it =α n it + β n it 2 or h it = α n it + β n it 2 (9) where n it and n it are the number of years of R&D engagement of firm i up to current year t in the first or in the second spell of R&D, respectively. We can rearrange the sequence in brackets in (8) distinguishing between the period without interruption, or before interruption, of the R&D activity, and the period after the interruption. We call these sequences first spell sequence S it and second spell sequence S it, respectively, which can then be written as S it = h h =(α n + β n 2 it T2 s it (T 1) s it T 2 s it T 2 s 2 ) (α n it (T 1) s + β n it (T 1) s ) (10) 12

13 S it = h it h =( it (T2 α n 1) it + β n 2 it ) ( α n + it (T2 β 2 n 1) it (T2 ) (11) 1) Notice that for a firm which has never interrupted its R&D activity, S it is the unique relevant sequence, with s i = 0 and T = 0. Notice also that n 2 is it (T 1) s the number of years of R&D engagement in the first year of R&D performance, so that it is equal to 1 (and followed by 2, 3, 4, in the sequence). Applying to (10) the rules for the sums of powers of positive integers, we can write the first spell sequence as: S it = γ 1 n it + γ 2 n it 2 + γ 3 n it 3 = ϒ(n it ) (12) where the parameters γ are a combination of the initial parameters α and β. 4 This suggests a third-order polynomial as an approximation for the effect of the number of years doing R&D on the efficiency of the human R&D capital accumulated up to a given year. For a firm that takes up again R&D activities after a period of inactivity, the term in brackets in (8) is: ( α n it + β n 2 it ) ( α n + it (T2 β n 2 1) it (T2 )+ f s 1) i + γ 1 T 1i + γ 2 T 2 3 1i + γ 3 T 1i (13) where T 1i stands for the number of years of R&D engagement in the first spell, that is, the number of years the firm was conducting R&D activities before interrupting them. The first part of the above sequence (the sum of terms in parentheses)0 is again a combination of sums of powers of positive integers but, instead of starting at 1 as in the first spell case, it starts at (T 1i + 1). In this case, (13) could be rewritten as: γ 1 n it + γ 2 n 2 it + γ 3 n 3 it + f s i + (γ 1 γ 1 ) T 1i + (γ 2 γ 2 ) T 2 1i + (γ 3 3 γ 3 ) T 1i (14) where the parameters γ are a combination of the initial parameters α and β (just as expressed in footnote 4 for the first spell case). Given that for any firm in its second spell, T 1i is an invariant value, we consider all those terms in (14) 4 In particular, γ 1 = α. 2 + β 6, γ = α + β and γ = β 3 13

14 involving T 1i, to be a firm-specific constant that is absorbed into by the firmspecific effect η i in the econometric estimation. Thus, (14) may be written as follows: γ 1 n it + γ 2 n 2 it + γ 3 n 3 it + f s i + η i = ϒ( n it )+ f s i + η i (15) We finally consider the expression of our human R&D capital as: K H it = φ H R it p i ϒ( n it )+ f s i + η i ( ) +(1 p i ) ( ϒ(n it )) (16) where p i is an indicator variable that takes value 1 if the firm is in its second spell of R&D and 0 if otherwise. Taking logs in (16): log K H it = log φ H + log R it + log p i ϒ( n it )+ f s i + η i ( ) +(1 p i ) ( ϒ(n it )) (17) Finally, substituting (6) and (17) into (3) and rearranging terms, we can express firms total R&D capital (in log form) as follows: log K it = const. + log A t + (c log φ C + r logφ H ) +(c + r ) log R it + r log p i ϒ( n it )+ f s i + η i ( ) +(1 p i ) ( ϒ(n it )) (18) Then, for estimation purposes, we need to include in our estimation model the level of current R&D expenditure, R it, jointly with the corresponding polynomials approximating for the effect of past years of R&D in knowledge capital, the number of years of R&D interruption, plus a number of control variables such as time dummies, industry dummies and firm-specific effects. Given that we are interested on estimating the coefficients of our third-order polynomials in n it, and given that the log of a number is a monotone positive function of that number, we will abstract in estimation from the logs in the last bracket in (18) and consider the following specification for total R&D capital: log K it = (Control variables) + (c + r ) log R it +r p i ϒ( n it )+ f s i ( ) +(1 p i ) ( ϒ(n it )) + η i (19) 14

15 3 Data and descriptive statistics In our paper we use data drawn from the ESEE for the period This is an annual survey conducted by the Fundación SEPI (a Spanish government agency) that is representative of Spanish manufacturing firms classified by industrial sectors and size categories. The sampling procedure of the ESEE is the following. Firms with less than 10 employees were excluded from the survey. Firms with 10 to 200 employees were randomly sampled, holding around 5% of the population in All firms with more than 200 employees were requested to participate, obtaining a participation rate of about 70% in Important efforts have been made to minimise attrition and to annually incorporate new firms with the same sampling criteria as in the base year, so that the sample of firms remains representative of the Spanish manufacturing sector over time. The ESEE provides exhaustive information at the firm level on a number of issues, including information on innovation activities. This information includes, on the one hand, innovation sources, such as R&D expenditures and, on the other hand, a quantitative measure of innovation outcomes such as the number of product innovations introduced by firms each year. 5 The particular question related to product innovations included in the ESEE is as follows: Indicate if during year t the firm obtained product innovations (either completely new products or with so important modifications that they are perceived as different from the previous ones). If yes, indicate its number. In our original sample of firms in the ESEE, around 74 percent of firms observations in the sample correspond to small firms and, among small firms observations, 19 percent are associated to a positive R&D investment. For large firms observations these percentages are around 26 percent and 70 percent, respectively. Further, there are around 32 percent of small firms with at least one year of R&D investment during the period under analysis, reaching this percentage 80 percent for large firms. To explain our selection of sample for estimation purposes, we start presenting in Table 1 some descriptive statistics regarding firms interruptions of R&D activities. The information in this table is restricted to the subsample of firms that perform 5 See for further details. 15

16 R&D activities at least one year over the sample period (53.45 percent overall). As it can be seen in the table, most of the firms in our sample (83 percent overall, and 81 percent or 85 percent for small and large firms, respectively) do not report any interruption in their R&D activities during the analysed period, that is, they have been engaged in R&D activities in a continuous way; around 13 percent of firms report one interruption in their R&D histories, almost 3 percent report 2 interruptions and, finally, bellow 1 percent report 3 or more interruptions. Moreover, among those firms with one R&D interruption (the bulk of interruption paths in our sample), 45 percent of them stop R&D for only one year, 23 percent stop for two years, 12 percent stop for 3 years, and almost 20 percent stop for 4 years or more. Taking into account this information, and provided we need to observe a sufficiently long observation window to follow the R&D dynamics of a firm, we finally select those firms with at least eight years of R&D history and discard those cases of firms with more than one interruption in R&D. Conditioning also on firms that report information on all the variables involved in estimation, we end up with a sample of 4744 observations, corresponding to an unbalanced panel of 521 firms. [Insert Table 1 about here] Table 2 presents some descriptive statistics regarding the relationship between the number of years of R&D activity and the average number of product innovations obtained by firms in our estimation sample. As it can be seen in the table, for instance, the average number of product innovations obtained by firms with less or equal than 5 years of R&D performance is 4.30, although for firms in between 6 and 12 years is Therefore, there seems to be, in general, a positive relationship between the number of years of R&D engagement and the achievement of a higher number of product innovations (taking into account that most of the weight of the distribution of the variable number of years of R&D is located below 13 years in our sample). 6 In Table 2 6 For the interval that goes from 13 to 17 years of R&D activity, the average number of product innovations has decreased to But, given that the bulk of the distribution is below 13 years, it is difficult to judge, at this descriptive level of analysis, the statistical significance of this change. Additionally, this non-linearity could be reflecting diminishing returns to learning and/or exhaustion of technological opportunities. 16

17 we also observe that the annual average of R&D intensity (R&D expenditures over sales) has been quite stable over the years, what could reinforce the idea that besides R&D expenditures, an important factor explaining the higher number of innovations could be the number of years of R&D performance. To be able to establish conclusive results in this respect, it is necessary to take into account the econometric results in section 4, where we also control for the variable R&D expenditure in estimation. [Insert Table 2 about here] In order to analyse further the shape of the relationship between the number of years of engagement in R&D and innovation results, we have performed a fitting exercise between the two variables (presented in Figures 1 to 3) as follows. First, following Fan and Gijbels (1996) and Gutiérrez et al. (2003), we have followed a non-parametric approach through local polynomials to relate the number of product innovations with the variable years of R&D activity. This method of non-parametric regression does not impose any assumption on the functional form of the relation between these two variables, and, therefore, allows the data to determine the shape of this relationship. Secondly, we have followed a parametric approach through a quadratic regression of the number of product innovations on the variable years of R&D and its square. The data exhibits an inverted-u shape, indicating a non-linear relationship between years of R&D activity and the number of product innovations. Furthermore, as it may be observed, the quadratic specification provides a very reasonable approximation to the non-parametric shape. This inverted-u shape is reproduced independently of dividing the full sample of firms between small and large firms (see Figure 2), although large firms seem to reach a higher number of product innovations as compared to small ones. [Insert Figure 1 about here] [Insert Figure 2 about here] Taking into account where is located most of the weight of the distribution for the variable number of years of R&D performance, we may also conclude from Figures 1 and 2 that the number of years of R&D engagement seems to have a positive, but at a decreasing rate, effect on the number of product innovations obtained by firms. 17

18 Figure 3 reports how the inverted-u shape relationship between years of R&D engagement and product innovations differs between firms that conduct R&D in a continuous way (first panel) and firms that have interruptions in their R&D history (second panel). We observe that although both groups of firms show an inverted-u shape, R&D efficiency in terms of product innovations is much higher for those firms with continuous engagement in R&D activities. [Insert Figure 3 about here] To motivate further our analysis, and before presenting our estimation results in next section, we provide in Table 3 some information coming from the Spanish government statistical agency (Instituto Nacional de Estadística, INE). This is aggregated information for the Spanish manufacturing sector for years 2008 to Although the period does not coincide with our estimation sample period, the figures in Table 3 can be quite illustrative of the share of total R&D expenditures devoted to payments to R&D researchers and other R&D technicians in the manufacturing sector. This share is around 50 to 54 percent, approximately, whereas physical capital R&D expenditures hardly amount to around 19 percent (year 2008), and they even decline towards the end of the period (around 13 percent in year 2010). It seems then that the bulk of firms R&D expenditures is on human R&D investment rather than on physical R&D capital, in spite of the much more attention received by this latter component of R&D. 4 Econometric issues and estimation results 4.1 Econometric issues: estimation method and instrumental variables for R&D spending As pointed out in section 2, our approach is based on the concept of an innovation production function that may, in a very general form, be expressed as N = f ( K, x, β ) it it it, where i refers to the firm and t to the time period, N it stands for any chosen indicator of innovation outcomes (product innovations in our case), K it stands for the firm s knowledge capital in period t, and x it represents a vector of other relevant variables and controls in the equation. In 18

19 estimation, K it will be replaced by its specification given in equation (19) in section 2. The type of data acting as the dependent variable in the analysis conditions the econometric estimation method to be used: the number of product innovations in a given year is an event count (non-negative integer) for unit i during time period t, and many firms may not introduce any innovation in a given year. It is standard in the literature to assume that the Poisson distribution is a reasonable description for this type of (count) data. According to the Poisson process, research results are the outcome of an unknown number of Bernoulli trials with a small probability of success. The basic Poisson probability specification is given by Pr (N it = π it ) = f (π it ) = e λ it π λ it it π it! (20) We model the single parameter of the Poisson distribution function, λ it, as a function of our knowledge capital K it and other variables as follows: 7 λ it = K it ϕ exp(x it θ) (21) or, alternatively, taking logs: log λ it = log K it ϕ + x it θ (22) [ ] [ ] It may be easily shown that λ = E N x = var N x it it it it it so that λ it represents the arrival rate of innovations per firm per year, and also the expected number of innovation outcomes (product innovations) per firm per year. In estimation, knowledge capital K it is replaced by its expression in (19) and vector x it stands for any other control variable included in the model other than those already included in (19). Parameter ϕ has to be interpreted as the elasticity of the expected number of innovations with respect to knowledge capital. One restrictive assumption of the Poisson model is that the variance of the number of outcomes equals its mean. If this assumption does not hold, and the data exhibits overdispersion, although the estimated parameters may 7 Note that λit is a deterministic function of xit and the randomness in the model comes from the Poisson specification for Nit. 19

20 still be consistent, their standard errors will typically be under-estimated, leading to spuriously high levels of significance. The Negative Binomial model arises as a natural extension of the Poisson model that allows for overdispersion. Thus, we have estimated our model using a Negative Binomial distribution assumption and tested it against the Poisson specification. 8 As derived from our empirical model in section 2, the fixed effect term η i in estimation arises in a natural way to control for fixed characteristics of firms R&D histories, such as the number of past years of R&D when they resume previously stopped R&D activities, or other firm s characteristics determining the shares of total R&D investment that are allocated to physical R&D capital and human R&D capital, respectively. Other individual effects may also affect the estimation results, such as unobserved ability of managers and researchers within a firm conditioning the efficiency of R&D investment. Fixed effects have been accounted for in estimation following the approach by Mundlack (1978) and Chamberlain (1984), who proposed to model the distribution of the unobserved effects, η i, conditional on the within-firm time averages of the explanatory variables included in estimation. There are concerns that, as the related literature has pointed out, the variable of R&D spending may suffer from endogeneity bias in our estimation setting. One possible source for such correlation could be any omitted variable that may affect simultaneously both the level of R&D spending and the probability of launching new products into the market. Technological opportunities not properly accounted for by the industry dummies could be a case. A second source of bias could be measurement error affecting our measure of R&D. To instrument this variable we follow a two-stage IVs procedure: in a first stage, we run the regression of R&D expenditures on our set of IV variables (plus all the rest of explanatory variables in the main final equation) and, in a second stage, we include in the main regression our original R&D variable and the residual coming from the auxiliary regression of R&D on the 8 2 In general, the NB model assumes that var N it x it = λ it + α λ it. Therefore, the NB model nests the Poisson model, and it is possible to test one specification against the other by testing the significance of the estimated parameter α in estimation. 20

21 list of instruments. This procedure is particularly appealing because of two reasons. First, if the residual from the first stage is statistically significant in the second stage regression, it may be considered as evidence of endogeneity of the R&D variable. Thus, it provides a direct exogeneity test for that variable (Rivers-Vuong, 1998). Secondly, if exogeneity is rejected by our data, the inclusion of the first stage residual solves the endogeneity bias affecting the variable. We need instruments that proxy for R&D spending but do not belong directly to the product innovation equation. For the choice of instruments for the R&D expenditure variable we follow previous empirical work (see, e.g. David, 2011) and instrument R&D using exogenous determinants of competitive pressure in the market. Our list of instruments includes some of the determinants of what the theoretical literature in IO has identified as the fundamentals driving competition in the market, such as product substitutability and market size, and associated to firms incentives to perform R&D. First, we have constructed a set of variables from the information provided by the ESEE that might be considered, in principle, to be indicative of the degree of product substitutability in the market. We have added to the information coming from the ESEE external information on most favoured nation import tariffs (m.f.n import tariffs, henceforth) coming from the UNCTAD-TRAINS database for the period As proxies for product substitutability we include available information in the ESEE regarding firms price changes (in percentage) in response to price changes of competing products (national and from abroad) and import UE tariffs. Market size is proxied by a dummy variable indicating that the firm claims to be facing an expansive market. Details on the construction of these instruments are provided in Table 4. Import tariffs deserve special mention for their exogenous nature in empirical work at the firm level. Import tariffs have been often used in empirical work as an exogenous and external source of competitive pressure. The exogenous nature of these tariffs in the empirical work at the firm level is 9 UNCTAD-TRAINS (TRade Analysis and INformation System) is a comprehensive computerized information system covering tariff, para-tariff and non-tariff measures for more than 140 countries. See 21

22 based on the fact that, given that the EU has a common external tariffs schedule, where each particular member does not negotiate its own tariffs, it is very unlikely that firms in any particular EU country might significantly influence EU import tariffs (see, for example, De Loecker, 2010, David, 2011 or Bustos, 2011). During the period under analysis, , the EU has (on average) steadily reduced tariffs imposed to the penetration of third countries imports, thus increasing the number of competing products for domestic firms within European countries. We use m.f.n import tariffs on imports made by the EU countries from the rest of the world, weighted by the percentage of EU imports corresponding to each exporting country. These tariffs, available per industry and year, have been selected at the three-digit level under the ISIC-Rev. 3 classification and, then, the correspondence has been made between the ISIC-Rev. 3 classification and the three-digit NACE-74 classification of our firms industries in the ESEE. This industrial classification provides 109 manufacturing industries, which is the level of disaggregation at which tariffs enter in our econometric specification. Thus, we impute to each firm in the ESEE one particular industry-year import tariff Estimation results In Tables 5 and 6 we present our econometric results for the Negative Binomial estimation (accepted as against the Poisson estimation, according to the tests of overdispersion displayed in Tables 5 and 6). As stated above, our main interest lies on the analysis of the impact of the passage of time on the number of product innovations introduced by firms, once we control for the value of the R&D spending of the firm. In Table 5 we present a first set of 10 Users of the ESEE had access to these 109 three-digit NACE-74 industrial breakdowns in the ESEE until year After this year, and for confidentially reasons, only a two-digit industrial breakdown (20 sectors) is made available to researchers. The use of the three-digit breakdown information, which we have access to, could be limiting in other setting since it implies to rule out information on all those firms entering the ESEE after 1996 (for firms observed before 1996 we assume they do not switch of industry after 1996). However, our condition of firms being at least 8 years in the panel imposes a selection of data that makes fairly irrelevant the further condition of being in the sample as early as in