Absorptive capacity investment in new product innovation

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1 Absorptive capacity investment in new product innovation Rosemary Humberstone March 20, 2012 Abstract This paper asks how much firms will choose to invest in in-house research and accessing external research when competing in a patent race for a new product. When the amount of publicly available research or the spillover rate increases, firms invest more in absorptive capacity and less in in-house research. Compared to the social optimum, firms always over-invest in absorptive capacity and may over- or under-invest in in-house research When an incumbent is already operating in the market and there is a market for a superior replacement product, the incumbent will never invest more in both in-house research and absorptive capacity relative to an entrant when the two firms compete in a patent race. Keywords: Innovation, Absorptive Capacity, Patent Races I am grateful to Nisvan Erkal and Jeff Borland for valuable comments and suggestions. This paper is based on a chapter of my dissertation and so I am also grateful for the comments provided by two external examiners. All errors are my own. Department of Economics, Level 5 Arts West, The University of Melbourne, Victoria 3010, Australia. Phone: ( Fax: ( rhumberstone@gmail.com 1

2 1 Introduction This paper explores to what extent firms invest to access external knowledge and invest in in-house research in order to be the first firm to succeed in a patent race. Although knowledge is often regarded as a pure public good, Cohen and Levinthal (1989 and Stiglitz (1999 have challenged this idea, arguing that firms must invest to absorb knowledge that is external to the firm, such as that produced by other firms or public agencies. 1 They argue that while knowledge may be public, firms must invest to access and understand outside knowledge. This can be achieved by forming connections with each other and public agencies to access outside information, and by investing in basic research to better understand a broader base of external knowledge. Cockburn and Henderson (1998 have termed this type of investment absorptive capacity. Distinguishing between absorptive capacity and in-house research is important for two reasons. First, the two types of investment are different in the way that they are conducted and the effect they have. Second, separating the two investments means that the effect of an increase in publicly available research or the spillover rate can be better understood. Investing in absorptive capacity may assist a firm in finding a solution to a problem or better direct their in-house research, but it may also reduce a firm s inhouse research if they substitute external knowledge for in-house research. This raises a number of questions. First, does an increase in publicly funded research or spillovers between firms lead to an increase or decrease in either type of research investment? Second, do innovators over- or under-invest in in-house research and absorptive capacity relative to the social planner and third, how do incumbents and potential rivals differ in their research strategies? To address these questions, a standard patent race model is modified so firms simultaneously choose how much to invest in absorptive capacity and in in-house research. The winner of the race is the firm that first innovates a product. As in Loury (1979 and Lee and Wilde (1980, the winner receives a patent to produce a new product of known 1 Nelson (1959 and Arrow (1962 first advocated the idea that knowledge was a public good and subject to the free rider problem. Rosenberg (1990 alleges this leads to under-investment in research. Property rights in the form of patents can solve this free-rider problem to some extent, but not all knowledge is patentable to the extent that competitors can be fully excluded from utilizing it. 2

3 value, while the loser receives nothing. The usual assumption in the patent race literature is that firms invest in in-house research to improve their ability to innovate. 2 This is supported in Griliches (1980 who argues that firms can directly improve their ability to innovate by investing in in-house research. However, this paper departs from the standard literature on patent races by adopting Cohen and Levinthal (1989 s finding that each firm can also invest in absorptive capacity. This latter investment strengthens the firm s ability to integrate knowledge developed external to the firm into their own knowledge base. The value derived from investing in absorptive capacity includes publicly available research and a portion of the rival firm research (determined by the spillover rate that the firm can capture. 3 One important contribution of this paper is that it isolates the effect of changes in publicly funded research and spillovers on each of absorptive capacity and in-house research, rather than treating them in the same way. In equilibrium, an increase in inhouse research or absorptive capacity raises a firm s probability of success. An increase in absorptive capacity causes the rival firm to reduce their investment in both in-house research and absorptive capacity because their probability of success declines. In contrast, an increase in in-house research causes the rival firm to increase their investment in absorptive capacity (because there is more external research to capture and to reduce their investment in in-house research. The results also show that an increase in either the spillover rate or the amount of publicly available research leads to an increase in a firm s investment in absorptive capacity and a decrease in in-house research. Absorptive capacity investment increases because it becomes more beneficial, while in-house research declines because the firm and its rival are both more likely to innovate successfully, making in-house research less beneficial. 4 This is driven by the assumption that in-house 2 See Loury (1979, Lee and Wilde (1980, Dasgupta and Stiglitz (1980, Katz and Ordover (1990, Choi (1991, Chang (1995, Green and Scotchmer (1995, Scotchmer (1996, Denicolo (2000, Martin (2002 Platikanova (2005 and Erkal (2005 for standard patent race models. 3 Publicly available research also includes research done by firms outside of the market (for example, buyers and suppliers. They differ from the rival firm as they are not competing in the patent race but they may be doing research that is beneficial to firms in the patent race. 4 In an extension to the non-tournament model in D Aspremont and Jacquemin (1988, Kamien and Zang (2000 remove the first effect by assuming that before investing in research, firms can choose a research strategy that determines how far away their research is from the mainstream approach. When firms behave noncooperatively, there will be no spillovers while if they do cooperate. 3

4 research and absorptive capacity are substitutes. 5 These findings suggest that making universities more open, investing in more public research, or developing better shared infrastructure between firms may lead to lower levels of in-house research. In addition, it also implies that if connections between firms intensify (fewer downstream or upstream firms, more transition of employees between firms or more industry events, then firms will decrease their investment in in-house research and invest more in absorptive capacity. Unlike in Loury (1979, firms may either be over- or under-investing in inhouse research relative to the social optimum, but they are always shown to over-invest in absorptive capacity. Over-investment in absorptive capacity relative to the social optimum occurs because firms do not take into account the negative impact that their investment has on the rival firm. In particular, investing in absorptive capacity raises a firm s own probability of winning the patent race, and consequently has a negative impact on their rival. The social planner considers this negative impact and cares only about the overall success of the project and not about who is successful. There may be over investment in in-house research for a similar reason, but there may also be under-investment in inhouse research if firms attempt to restrict spillovers accruing to their rival. Hence, the actual effect is determined by the relative strength of the opposing forces. When the model is extended to allow for an incumbent and potential entrant, the entrant is shown to invest more than the incumbent in at least one of in-house research and absorptive capacity. That is, the incumbent will never invest more in both in-house research and absorptive capacity because a successful incumbent has less to gain than a successful entrant. This explains why established firms may differ in their research behavior from new entrants. In the special case where there are no inter-firm spillovers but publicly available research still exists, the entrant invests more in both in-house research and absorptive capacity provided the new innovation is sufficiently valuable. Here, the only benefit of investing in absorptive capacity is to access publicly available research 5 In some circumstances, it may be more realistic to model in-house research and absorptive capacity as complements if investments in absorptive capacity make investments in in-house research more effective. The implications of this assumption are discussed in more detail later in the paper. 4

5 which is the same for both firms. 6 When there are spillovers and the entrant invests more in in-house research, the incumbent may invest more in absorptive capacity than the entrant to capture the entrant s spillovers. 7 A number of other papers have modelled absorptive capacity. Frascatore (2006 models in-house research and absorptive capacity as two distinctly separate investments in a non-stochastic cost reducing innovation, and assumes that the only form of external information is generated by the rival firm. He shows that the difference between firm expenditure and the socially optimal level depends on the magnitude of the costs faced by the firms. In addition, Frascatore (2006 shows that when decisions are made jointly, firms invest too little into absorptive capacity. In contrast, Campisi et al. (2001, Martin (2002, Kamien and Zang (2000 and Grünfeld (2003 differ from this paper by assuming that firms invest in in-house research and that this has both a direct effect and an indirect effect on the firm s total knowledge or research intensity. Campisi et al. (2001 show that changes in the spillover rate do not substantially alter a firm s research investment in a non-stochastic innovation setting. 8 This result arises because the impact of a higher spillover rate on accessing rival firm research and preventing outgoing spillovers cannot be separated. Martin (2002 models a patent race between two firms for a cost reducing technology and shows that when the exogenous spillover rate between firms increases, firms reduce their research investment. Kamien and Zang (2000 and Grünfeld (2003 both extend D Aspremont and Jacquemin (1988 by assuming that the firm s investment in research lowers the marginal cost of production directly and also by influencing the spillover that can be captured from the rival firm. Grünfeld (2003 shows that investing in absorptive capacity leads to an increase in in-house research if the market is small or the absorptive capacity effect is weak, while Kamien and Zang (2000 focus on the impact of cooperation on research strategies given the possibility of spillovers. 6 As the entrant has more desire to be successful than the incumbent, they will invest more in absorptive capacity and in-house research than the incumbent. 7 This also relies on the assumption that the new invention does not violate the incumbent s existing patent. Otherwise, the successful innovator would have to pay a license fee to the incumbent. 8 Campisi et al. (2001 extends D Aspremont and Jacquemin (1988 where firms invest in a non-stochastic, cost reducing technology that is subject to spillovers, then they compete in Cournot competition. In this original model, spillovers between the firms are exogenous. Each firm is allowed to access externally available research if and only if the firm conducts in-house research. 5

6 This paper proceeds as follows. Section 2 provides a discussion of how firms invest in absorptive capacity by providing case studies to highlight the importance of absorptive capacity investment for successful innovation. Section 3 outlines the model. Section 4 derives the private non-cooperative equilibrium. Section 5 characterizes the socially optimal investments and contrasts these with the equilibrium results. Finally, Section 6 presents a variation of the model where an incumbent and an entrant compete in a patent race. Concluding comments and implications for empirical research are made in Section 7. All proofs are in Appendix A. 2 Investing in absorptive capacity There are two key ways that absorptive capacity can help firms be successful. First, it enables firms to understand externally produced research as public research is not a free input for firms. Rosenberg (1990 asserts that while most basic research is completed in universities, in order to plug in and utilize this knowledge, a firm must invest in basic research so that they can monitor and evaluate outside research. Cockburn and Henderson (1998 reinforce this point and argue that firms must invest in basic research if they wish to utilize general scientific knowledge. This notion is supported by their interviews of academic research scientists, senior pharmaceutical company scientists, and research managers from pharmaceutical firms, demonstrating the importance of investing in basic research to take advantage of publicly generated research. Gambardella (1995 offers further support for this idea by asserting that basic research helps a firm remain aware of recent scientific developments and improves a firm s ability to utilize new scientific findings into the commercialization process. 9 Merck s discovery of the anti-cholesterol drug, Mevacor, illustrates how investing in absorptive capacity by doing basic research assists a firm in understanding externally produced research. Gambardella (1995 explains that scientists from the University of Texas identified how cholesterol was produced in the body between 1972 and While this information was publicly available following the discovery at the uni- 9 Note that Rosenberg (1990, Cockburn and Henderson (1998 and Gambardella (1995 all support the notion of in-house research and absorptive capacity being substitutes. 6

7 versity, Merck was able to better utilize the findings as their basic research helped them understand the results. Merck was then able to market Mevacor in In contrast, Bristol-Myers were unable to capitalize on the new scientific knowledge. In the early 1980 s, Bristol-Myers did not have strong scientific expertise because they had not invested enough in absorptive capacity to be able to understand the findings. 10 This was despite the fact that Bristol-Myers already had an anti-cholesterol drug (Questar on the market. Second, investing in absorptive capacity may provide a firm with access to external knowledge by allowing them to connect into a knowledge network. Firms can invest in absorptive capacity by establishing networks and connections to other industry scientists and public sector institutions. Cockburn and Henderson (1998 argue that a firm s ability to access public sector research may be important in determining the firm s research productivity. Their interviews with academic researchers, pharmaceutical scientists and research managers emphasized the importance of hiring the right people, rewarding scientists for their public scientific standing and encouraging interaction with the public sector as crucial to assisting firms in accessing external knowledge. Accessing external knowledge can also be assisted by location choice as demonstrated by the study of industry clusters in Porter and Stern (2001 as well as national infrastructure that allows for collaboration. Porter and Stern (2001 argue that firms must be actively involved in industry associations and invest in relationships with universities in order to benefit from clusters. This idea is also explored in a study of Silicon Valley and Route 128 by Saxenian (1998, and by Agrawal and Cockburn (2003 in their analysis of the medical imaging, neural networks and signal processing industries. MacCormack and Herman (2005 detail the development and aims of Intel Research. Intel provided grants to universities and required that each grant was associated with an Intel sponsor to enable fast knowledge transfer from the university to Intel. In addition, Intel Research established Lablets close to universities where Intel employees, academics and graduate students could work collaboratively. Academics who joined 10 Gambardella (1995 explains that in the mid to late 1980 s, Bristol-Myers did increase their investment in absorptive capacity by consolidating their research centres into one research laboratory located by Yale, thereby increasing their access to publicly available research. 7

8 the lablet were chosen not just for their skills and expertise, but also because they provided a gateway into that department and had extensive collaborative networks. In this sense, the lablets were an investment in absorptive capacity rather than in-house research as they aimed at accessing, understanding and incorporating university produced research into Intel s knowledge base. Similarly, Procter and Gamble (P&G established a new innovation strategy called Connect and Develop to access external knowledge. 11 Rather than develop a technology in house to print images, P&G used their extensive global networks to find a solution that could be adapted to their requirements. An Italian bakery was found that had developed a way of printing images onto cakes and cookies. This method was then adapted in-house to be used to create Pringle Prints. This led to the product being produced in half the time and with less risk and cost to P&G. 3 The model The research environment considered in this paper is adapted from Loury (1979 where n firms compete for a reward given to the first successful firm. 12 This model is extended here to allow firms to invest in absorptive capacity as well as in-house research as they compete in a patent race. As in the standard patent race models, there is assumed to be no knowledge accumulation, so a firm s probability of success is solely determined by current investments in innovation. 13 For simplicity, there are two firms competing in the race and the value of the innovation, V, is exogenous and known by both firms. The loser receives nothing. 14 Firms compete to be the first firm to successfully innovate the new product. As in Loury (1979 and Lee and Wilde (1980, each firm i chooses how much to invest in in- 11 Huston and Sakkab (2006 explain that P&G developed external networks to take advantage of outside sources of new ideas and projects. 12 See Reinganum (1989 for a survey of the literature on patent races and Platikanova (2005 for an excellent overview and explanation of modeling patent races and Poisson innovation processes. 13 Reinganum (1981 and Doraszelski (2003 both model a patent race with knowledge accumulation where past success increases the probability of being successful in the future. Laincz and Rodrigues (2009 construct a model where the spillover rate between firms is determined by the stock of knowledge. 14 To model a cost reduction innovation, the model can be adjusted so that until either firm is successful, both firms earn V, but then upon one firm being successful, the winner earns W > V and the loser earns L < W. In this case, all the results of the paper are qualitatively the same. 8

9 house research x i R +, costing the firm C(x i where C(x i > 0 for all x i > 0, C(x i > 0 x i and 2 C(x i > 0. Each firm i also chooses a level of absorptive capacity a x 2 i [0, 1], i costing the firm D(a i where D(a i > 0 for all a i > 0, D(a i > 0 and 2 D(a i > a i a 2 i Thus, it is more costly to acquire higher levels of external knowledge than lower levels. There are no interaction effects between the cost functions because undertaking in-house research uses different resources from developing absorptive capacity. In particular, scientists who conduct in-house research are not the same scientists who are responsible for developing networks with external organizations (such as universities and other firms. Absorptive capacity allows a firm to access publicly available research, P, which is conducted by universities and public research institutes, and some of their rival s inhouse research. Inter-firm spillovers are denoted by θ and characterize the proportion of rival firm in-house research that is available for the firm to access. If firms use very different research strategies or patents are very strong and used extensively in the industry, there may be no inter-firm spillovers (θ = 0. Alternatively, a firm can access all of their rival s in-house research if spillovers are complete (θ = 1. High values of θ are consistent with high rates of publication or general openness of the industry. In line with Martin (2002, θ reflects the nature of the industry and is exogenous to the model. Cockburn and Henderson (1996 argue that the pharmaceutical industry is characterized by high rates of publication. Firms simultaneously choose their level of absorptive capacity, and a level of inhouse research, x i, but are unable to observe their rival s choice. In the existing literature on patent races, the expected time to successful innovation usually depends solely on the firms investment in in-house research, x i, and is exponentially distributed according to a Poisson innovation process with hazard rate h(x i. This implies that there is no learning or benefit from external research. This paper follows Cohen and Levinthal (1989 and defines firm i s hazard rate, h i (x i, as the sum of their own in-house research plus any external research that they obtain. That is, in-house research and absorptive capacity are 15 Cost functions are assumed to be separable so that the firm s investment in in-house research does not impact on the cost of investing in absorptive capacity. The case where absorptive capacity and in-house research are modeled as flow costs is considered in Appendix B. 9

10 assumed to be substitutes. 16 This is consistent with the case studies presented in Section 2 where firms invest in absorptive capacity to access and utilize external research. Firm i s hazard rate is based on their total research intensity and is denoted 17 h(x i ; x j = x i + a i (θx j + P. (1 A firm s hazard rate is a function of their in-house research, x i, as well as the amount of external research acquired (θx j + P. In particular, (1 means that even if firms have the same research strategy (θ = 1, a firm is unable to learn anything from its rival if it has not invested in absorptive capacity (a i = 0. Using this, the probability density function for firm i being the first firm to succeed at time t is given by h(x i ; x j e (h(x i,a i ;x j +h(x j,a j ;x i t where j is the rival firm and h(x j, a j ; x i represents the rival firm s research intensity. Hence for a common, known interest rate, r, the expected benefit to firm i of conducting in-house research and investing in absorptive capacity is π i (x i ; x j, a j = = 0 e rt e (h(x i,a i ;x j +h(x j,a j ;x i t h(x i ; x j Vdt V(x i + a i (θx j + P r + x i (1 + a j θ + x j (1 + a i θ + P(a i + a j. (2 The payoff function for firm i is given by Π i (x i ; x j, a j = V(x i + a i (θx j + P r + x i (1 + a j θ + x j (1 + a i θ + P(a i + a j D(a i C(x i. (3 4 Equilibrium analysis In this section, equilibrium behavior is analyzed, where each firm, i, decides how much to invest in in-house research, x i, and absorptive capacity a i. To do this, each firm max- 16 If it is necessary to invest in absorptive capacity to access general publicly available knowledge before inhouse research is possible, then absorptive capacity plays the role of an entry fee. In this case, absorptive capacity does not have a substitutionary or complementary effect on in-house research. Furthermore, if inhouse research and absorptive capacity are complements, then the hazard rate could be given as h(x i ; x j = x i (1 + a i (θx j + P. 17 The non-tournament models developed in Campisi et al. (2001, Martin (2002, Grünfeld (2003 define a firm s total research intensity in a similar way by either assuming that a i = g(x i (in the case of Campisi et al. (2001, or that a i = 1, P = 0 (in the case of Grünfeld (

11 imizes their payoff function as given in (3. This gives the following two first order conditions for firm i (for a i and x i respectively, 18 V(r + x i θa j + a j P + x j (P + θx j (r + x i (1 + a j θ + x j (1 + a i θ + P(a i + a j 2 D (a i = 0 (4 and V(r + x j (1 θ 2 a i a j + Pa j (1 θa i (r + x i (1 + a j θ + x j (1 + a i θ + P(a i + a j 2 C (x i = 0, (5 and similarly for firm j. From (4 and (5, a change in a rival s investment in absorptive capacity, x j, and inhouse research, a j, is shown to affect an innovator s investment as follows. Proposition 4.1 Absorptive capacity and in-house research investments are strategic substitutes. Intuitively, when firm j increases their investment in absorptive capacity, j s probability of success increases because h j (x j, a j increases. This reduces the expected time until success, which in turn reduces firm i s incentive to invest in absorptive capacity. Similarly, an increase in x j increases the probability of success for the rival and to a lesser extent, the firm (through absorptive capacity investments and spillovers. This reduces the benefit to the firm of investing in in-house research, leading to a reduction in firm i s in-house research investment. Since firms are assumed to be identical, the symmetric Nash Equilibrium is given by x = x i = x j and a = a i = a j. From (4 and (5, the level of absorptive capacity chosen by each firm satisfies 19 V(r + x (1 + θa + a P(P + θx (r + 2x (1 + a θ + 2a P 2 D (a = 0, (6 18 It is straightforward to check the second order conditions to ensure that each of the first order conditions maximizes profit. 19 Analogous results can be found for the case where in-house research and absorptive capacity are complements. 11

12 and the level of in-house research completed by each firm satisfies V(r + x (1 (θa 2 + a P(1 θa (r + 2x (1 + θa + 2a P 2 C (x = 0. (7 4.1 Comparative statics on equilibrium investments Interfirm spillovers play an important role in a firm s research strategy. Exogenous informational spillovers between firms arise from a variety of sources. Employees may release details of research findings at industry conferences, through publications or patent applications, while buyers and suppliers may also disclose knowledge about a firm s direction and approach to other competing firms. Thus, inter-firm spillovers are likely to increase if there is a greater degree of interaction between employees, there are fewer buyers or suppliers or if the intellectual property law changes so that more information is required to be released in patent applications. When spillovers increase, both absorptive capacity and in-house research are affected. Proposition 4.2 When the spillover rate increases, a firm will increase its investment in absorptive capacity and decrease its investment in in-house research. This is similar to the result found in Martin (2002. Intuitively, an increase in θ means that there are higher spillovers in not only the rival s in-house research, but the firm s own in-house research. This leads to an increase in the probability of success for both the firm and the rival. As a result, the firm will reduce its investment in in-house research. Furthermore, reducing in-house research restricts the increase in spillovers from accruing to the rival firm. 20 Proposition 4.2 suggests that when firms are more similar or patent laws are relaxed (that is, θ increases, then firms will spend more resources to take advantage of spillovers and will restrict spillovers to their rival by reducing their investment in in-house research. Holding all else constant, this result implies that pharmaceutical companies 20 In the case of in-house research and absorptive capacity being complements, an increase in θ may lead to an increase in in-house research. Here, an increase in θ makes absorptive capacity and in-house research more beneficial. However, in-house research may decrease as firms attempt to restrict spillovers. The overall net effect depends on the preceise formulation of the hazard function and the level of in-house research and absorptive capacity. 12

13 (with a higher θ as suggested by Cockburn and Henderson (1996 will invest more into absorptive capacity and less in in-house research than, say firms in the semiconductor industry. This may be observed through the number of connections that pharmaceutical companies have with other firms and institutes or the amount that they spend on basic research. Firms are also able to access publicly generated and available research, P, through their investment in absorptive capacity. P can increase in two ways. First, more money may be invested in public research or public research institutes, or alternatively, university research may become more open and publicly available. Common ways this occurs is through an increase in publications or an increase in communication and interaction with industry. While this does not increase the amount of research performed in universities, it does increase the amount of research that is available to firms. Proposition 4.3 When the amount of publicly available research increases, a firm will increase its investment in absorptive capacity and decrease its investment in in-house research. The intuition for Proposition 4.3 is similar to Proposition 4.2. An increase in P raises the probability of success because it raises the amount of knowledge available to the firm. Firms will invest more to take advantage of this. 21 Proposition 4.3 suggests that while an increase in publicly funded research may increase the overall amount that firms invest in research, it redirects firms from investing in in-house research to investing in acquiring external research. Thus, it supports the notion that firms do less in-house specific research when the amount of publicly available research increases Social optimum Loury (1979 shows that firms invest more in in-house research than is socially optimal 21 For the case of complements, absorptive capcity will increase and in-house research may also increase as it becomes more efficient and effective when more outside information is available. 22 See Cohen et al. (2002, David and Hall (2000, David et al. (2000, Howe and McFetridge (1976, Leyden and Link (1991, Lichtenberg (1987 for theoretical and empirical analysis that has asked whether an increase in public R&D funding and private R&D funding are complements or substitutes. 13

14 because they do not factor in the negative externality they impose on other firms. Loury (1979 is a special case of this model where there are no spillovers and no publicly available research (θ = 0 and P = 0. Subsequently, firms do not invest in absorptive capacity (so a i = 0, and instead only invest in in-house research. This section asks whether firms continue to over-invest in in-house research when they can also benefit from outside knowledge, both from other firms and from public institutes. The socially optimal level of investment is found by choosing x i,x j and a j to maximize joint profits 23 Π i (x i ; x j, a j + Π j (x j, a j ; x i. (8 The optimal values of x i, x j and a j are found from the first order conditions of (8. Since C(x i and D(a i are convex and the firms are identical, it is socially optimal for each firm to invest the same amount into in-house research (x i = x j and absorptive capacity(a i = a j. The symmetric equilibrium is defined as x S = x i = x j and a S = a i = a j Comparison of social optimum to the symmetric equilibrium The socially optimal values of both in-house research and absorptive capacity can be compared to the equilibrium levels found in Section 4 to see whether firms over- or under- invest relative to the social optimum. Both the firm and the social planner choose in-house research such that the marginal benefit is equal to the marginal cost. Proposition 5.1 When firms can benefit from external knowledge by investing in absorptive capacity, there will be over-investment in in-house research iff π i a j a j x i + π i x j x j x i < 0. (9 Otherwise there will be under-investment in in-house research. 23 If the social planner were also concerned about consumer issues, the overall level of R&D investment would be higher because consumers would benefit from the product being developed sooner without any additional cost. 24 See appendix for details. 14

15 Two opposing effects are present. First, as in Loury (1979, firms may over-invest in in-house research because they do not factor in the negative externality they exert on their rival. As a result, they invest more than they should in in-house research. From a social perspective, the social planner is indifferent between which firm is successful, and only cares about the time of success. Hence, the social planner s optimal investment is lower. Second, firms may under-invest in in-house research when external knowledge is available. Intuitively, firms may reduce their in-house research investment to restrict spillovers to their rival, thereby lowering the probability of success of their rival. This is particularly likely if the optimal absorptive capacity investments are high, resulting in the rival firm benefiting more from a firm s in-house research investment. The net effect depends on the relative magnitude of each of these effects. The equilibrium level of absorptive capacity can also be compared to the socially optimal level to show the following. Proposition 5.2 Firms always over-invest in absorptive capacity relative to the socially optimal level. Over-investment in absorptive capacity occurs because the firm does not take into account the negative impact that their investment in absorptive capacity has on their rival. In particular, a firm fails to take into account that increasing their investment in absorptive capacity leads to a decline in the probability of success for the rival firm. 5.2 Comparative statics on social optimum Comparative static results on the socially optimal levels of in-house research and absorptive capacity show how changes in the spillover rate and the amount of publicly available research impact each type of investment. Proposition 5.3 An increase in the spillover rate leads to 1. an increase in in-house research if x S is small, and 2. an increase in absorptive capacity if a S is small. 15

16 As in the equilibrium case considered earlier, an increase in the spillover rate increases the probability of success for both firms, indicating a decline in the level of inhouse research. However, a second opposing effect also exists in the socially optimal case. An increase in the spillover rate means that a firm s rival will benefit more from an increase in in-house research. This suggests that an increase in θ should lead to an increase in x S. Even though an increase in θ raises the probability of success, the second effect dominates for low values of x S because in spite of the probability of success increasing, it is still low when x S is low. In contrast, when x S is high and θ increases, the probability of success is already high and so x S decreases (the first effect dominates. The intuition is similar for absorptive capacity. An increase in θ raises the probability of success for both firms, so firms should invest less in absorptive capacity. However, an increase in θ also raises the marginal benefit of absorptive capacity. Proposition 5.3 states that when a S is low and the spillover rate increases, this latter effect dominates and the socially optimal level of absorptive capacity increases. When a S is high and θ increases, the first effect dominates. In this case, the socially optimal level of absorptive capacity declines because the probability of success is already high when a S is high, so there is little reason for a S to increase further. An increase in the amount of publicly available research also has an effect on the socially optimal levels of in-house research and absorptive capacity. Proposition 5.4 An increase in the amount of publicly funded research leads to 1. a decrease in the socially optimal level of in-house research, and 2. an increase in the socially optimal level of absorptive capacity when a S is low. The intuition for why x S decreases when P increases is the same as for why x (the equilibrium case decreases. An increase in P always leads to an increase in the probability of success for the firm and its rival, so firms have an incentive to reduce their investment in absorptive capacity. However, an increase in P has two competing effects on the socially optimal level of absorptive capacity. First, an increase in P leads to an increase in the probability of success for both firms, suggesting that firms will decrease their investment in absorptive capacity. However, a higher value of P increases the marginal benefit 16

17 of investing in absorptive capacity, provided neither firm has been successful. When a S is low, the probability of success is low and so the second effect dominates, leading to an increase in a S. In contrast, when a S is high, the probability of success is high. An increase in P, and hence an increase in the marginal benefit of absorptive capacity is less beneficial, so the first effect dominates and a S declining when P increases. 6 Incumbents and entrants Often an incumbent firm will already have a patent and consequently be operating as a monopolist when they are competing in a patent race with a competitor. 25 For example, in the case of Merck and Bristol-Myers, Bristol-Myers was originally an incumbent, but Merck successfully created a new product because of its investment in absorptive capacity. This raises a number of questions. First, how do incumbents and rivals differ in their research strategies, and second, what roles does the nature of the industry (P and θ play on the differences between incumbents and entrants? The model presented in Section 3 can be adjusted to allow for an incumbent (I and an entrant (E to compete to innovate a new product that supersedes the original project but does not infringe on it. 26 The old patent is worth V I > 0 to the incumbent between time t and t + dt if neither the incumbent nor the entrant has been successful up to time t. The new innovation is worth V > V I to the successful firm between time t and t + dt. The instantaneous payoffs to each player, given the current state of the world, are given in Table 1. To formulate the payoff functions for each player, note that at time t, the probability that neither firm has been successful is e (h I (x I,a I +h E (x E,a E t where h I (x I, a I = x I + a I (x E + P is the incumbent s hazard rate and h E (x E, a E = x E + a E (x I + P is the entrant s hazard 25 Cassiman et al. (2002 model a similar situation with a leading firm and a fringe of followers who produce a lower quality good. The leading firm decides how much to invest in in-house research (termed applied research in their paper, absorptive capacity (basic research and protection to minimize outward spillovers to the followers. The followers are unable to invest in research and so only benefit from spillovers from the leader. 26 For example, an MP3 player may replace a cassette walkman as they perform the same function of allowing consumers to listen to music on a portable device, but they rely on different technologies. 17

18 State Incumbent (I Entrant (E Neither successful V I 0 Incumbent successful V 0 Entrant successful 0 V Table 1: Instantaneous payoffs for incumbent and entrant rate. 27 From this, the entrant s payoff is Π E (x E, a E ; x I, a I = 0 e rt e (h I (x I,a I +h E (x E,a E t h E (x E, a E Vdt = V(x E + a E (θx I + P B IE C(x E D(a E (10 where B IE = r + x E (1 + a I θ + x I (1 + a E θ + P(a E + a I, and the incumbent s payoff is Π I (x I, a I ; x E, a E = 0 e rt e (h I (x I,a I +h E (x E,a E t ( h I (x I, a I V + V I dt = V(x I + a I (θx E + P + V I B IE C(x I D(a I. (11 Note that if the two firms choose the same investment levels (x E = x I and a E = a I, the incumbent s payoff is higher because the incumbent earns V I if there is no innovation. The optimal investments for the incumbent and entrant can be compared to show that the entrant never invests less than the incumbent in both in-house and absorptive capacity. Proposition 6.1 The entrant invests more than the incumbent 1. in in-house research and absorptive capacity if x E x I < V I V ( 1 + θae 1 θ 2 a E a I (a E a I P 1 θ 2 a E a I (12 27 The incumbent does not have any stored knowledge or cost advantage in conducting research. If they had a stock of knowledge that positively affected h I (x I, a I, their incentive to acquire information would be reduced (unless the new knowledge was complementary to their existing stock. In this paper, stored knowledge does not give firms an advantage because firms are trying to be the first to come up with something new. If they had already been successful, then the race would be over. If the incumbent had a cost advantage, their incentive to invest would increase. This is likely to be the case if the potential competitor is new to the field, for example, a new player in the pharmaceutical industry, but is unlikely to be the case if the firm is already in the industry and is similar in size and capability. 18

19 and a E a I < V I V ( 1 P + θx I (x E x I (P + θ(r + x E + x I, (13 (P + θx E (P + θx I or 2. in in-house research but not absorptive capacity if (12 holds but (13 does not hold, or 3. in absorptive capacity but not in-house research if (13 holds but (12 does not hold. The intuition is as follows. While a successful incumbent gains the same payoff V as a successful entrant, the incumbent gives up receiving V I once either firm is successful. Subsequently, there are greater incentives for the entrant to invest in being successful. 28 In the context of investing in in-house research and absorptive capacity, the entrant does not necessarily invest more in both in-house research and absorptive capacity. Rather, they will invest more in at least one of these two types of research investment. There are two ways this can occur. Since the benefit of absorptive capacity is increasing in the rival s in-house research, the incumbent may invest more in absorptive capacity than an entrant. This occurs if the entrant invests more in in-house research than the incumbent does, thus making the benefit of absorptive capacity to an incumbent higher. Alternatively, the incumbent could invest more in in-house research than the entrant. In this case, the incumbent will invest less in absorptive capacity because the total amount of external knowledge that he/she desires is less than the entrant (P + θx E < P + θx I. It is straightforward to see that although the incumbent may invest more in in-house research than the entrant, it cannot be much more since h I (x I, a I < h E (x E, a E, x I > x E and a I < a E must hold, which implies that x I x E < P(a E a I + θ(a E x I a I x E. (14 This finding could be empirically tested to determine when industries are more likely to foster innovative new entrants (x E > x I, or entrants that are trying to build off external research (a E > a I by comparing an incumbent firm s investment in research, basic re- 28 Gilbert and Newbery (1982 and Reinganum (1983 have explored this issue in their work on persistent monopolies. Vickers (1985 has also considered this idea when there are several incumbent firms. His model shows that joint R&D between the incumbent firms may deter entry when the innovation is small. 19

20 search and interaction with universities, with an entrant s investment in these areas. It is expected (based on (14 that the incumbent will invest more in in-house research than the entrant (x I > x E if there is a lot of publicly available research (P is high, the entrant invests more in absorptive capacity than the incumbent (a E > a I and the spillover rate is sufficiently high (θ is high. In the special case when there are no inter-firm spillovers (θ = 0, the entrant will invest more than the incumbent in both in-house research and absorptive capacity provided the value of the invention is sufficiently large. Proposition 6.2 When there are no inter-firm spillovers, the entrant invests more in both inhouse research and absorptive capacity than the incumbent provided V I V > x E x I + P(a E a I (15 for the equilibrium values of x E, x I, a E and a I. As there are no inter-firm spillovers, the benefit of investing in absorptive capacity is the same for both firms and is independent of the amount of in-house research completed by the rival. 7 Conclusion This paper explored whether firms invest in in-house research or invest to access external knowledge and spillovers from a competitor. In the context of a patent race model, firms can invest in both in-house research and absorptive capacity in an effort to be the first firm to successfully innovate a new product. As the amount of publicly available knowledge or firm spillovers increases, firms invest more in absorptive capacity and less in in-house research. Intuitively, absorptive capacity becomes more beneficial when there is more public knowledge or when firm spillovers are higher. At the same time, firms invest less in in-house research. Compared to the social planner, innovators may over- or under- invest in in-house research, but always over-invest in absorptive capacity. This is because firms do not factor in the negative effect their investment has on their rival. 20

21 When the model is extended to an asymmetric case of an incumbent and entrant, an entrant has more incentive to innovate successfully because they have more to gain from being successful. However, when public knowledge and firm spillovers are present, it is not necessarily the case that the entrant will invest more in both in-house research and absorptive capacity. In particular, if the entrant invests substantially in in-house research, the incumbent has more to gain by investing in absorptive capacity. Thus, it is possible that an entrant will invest more in new, innovative in-house research, while an incumbent will invest in developing connections to public research institutes and into basic research. The impact of external research and knowledge on a firm s decision about how to invest in research can also have important consequences on the way a firm structures its internal research. Firms can choose for their researchers to work in small or large teams where teams are responsible for deciding their own level of in-house research and absorptive capacity investments and are rewarded if they are the first team to successfully innovate. A firm may choose the level of interaction and engagement between the teams (thereby choosing the spillover rate by choosing where the research laboratory teams are located, for example, whether they are in the same city or in different countries. This may also affect how diverse a firm s research is. If research teams are further apart, a team s in-house research is likely to differ more than if the teams were closer together. Moreover, the results from this paper could influence whether firms choose to be part of a joint research venture and if they do, how much interaction the joint research team has with the firm s other researchers. Cassiman and Veugelers (2002 explore the effects of knowledge flow (both into and out of a firm on R&D analysis. They show a significant relationship between external information flows and a firm s decision to cooperate in R&D. Another extension that is not pursued here is the analysis of a firm s optimal protection of their in-house research. That is, the firms may be able to invest to prevent spillovers accruing to their rival by restricting employees from interacting with rival firm employees or preventing employees from working for a competitor for a period of time if they leave the firm. Both of these would raise the wage the firm pays the employee. 21

22 A further application of the model is to a country context. Countries are able to invest in in-house research or can invest to acquire other knowledge created in other nations (through human capital investments such as education and good diplomatic relationships. A country s decision may be influenced, in part, by the spillover level between the two countries. Countries with similar climates, economies and tastes are likely to have higher spillover parameters and so would benefit more from investing in absorptive capacity. 29 As already mentioned, this paper suggests several avenues for empirical research. First, the level of in-house research and absorptive capacity for firms in different industries can be used to calculate the spillover rate for each industry. This information can lead to a better understanding of firm decisions, and help policy makers direct public funding for public research and collaboration. 30 Second, the investment of incumbents and entrants can be compared to determine whether particular industries are more likely to foster innovative new entrants or entrants that build off existing research. Policy makers could use this information to better determine the geographical location and direction of public research institutes, as well as to develop policies to assist new firms enter existing markets. A Proofs and derivations Proof of Proposition 4.1 The first order conditions from (4 and (5 are defined as F(a i = V(r + x i θa j + a j P + x j (P + θx j (r + x i (1 + a j θ + x j (1 + a i θ + P(a i + a j 2 D (a i (16 and G(x i = V(r + x j (1 θ 2 a i a j + Pa j (1 θa i (r + x i (1 + a j θ + x j (1 + a i θ + P(a i + a j 2 C (x i (17 29 See Easterlin (1981 for a cross country discussion on spillovers. 30 In their empirical study, Audretsch and Feldman (1996 show that firms tend to cluster their innovative activity to obtain knowledge spillovers. In addition, firms are found to locate close to sources of knowledge such as university research facilities. 22