Innovation And Persistence Effects: Theory And Experimental Evidence

Transcription

1 Innovation And Persistence Effects: Theory And Experimental Evidence Christos A. Ioannou Miltiadis Makris Carmine Ornaghi University of Southampton This draft: April 1, 2018 Abstract Persistence effects in R&D can take the form of (i) learning-by-doing (i.e. knowledge transmission from the firm s own past innovative efforts), and (ii) dynamic externalities (i.e. knowledge transmission from the rivals past innovative efforts). The present study proposes a theoretical model that investigates the interaction of persistence effects with product substitutability on innovative efforts in a duopoly setup. Innovative effort reflects firms activities towards cost-reduction and/or quality-enhancement, while taking as exogenously given product substitutability (i.e. the degree of horizontal product differentiation). The testable predictions of our model are taken to the lab. In unlevelled industries, we find that, regardless of the absence or presence of persistence effects, innovative effort for the laggard decreases with substitutability. However, in levelled industries, in the absence of persistence effects, effort increases with substitutability, whereas, in the presence of persistence effects, innovative effort is non-monotone with substitutability. JEL: C12, C72, C91, L13 Keywords: Duopoly, product differentiation, laboratory experiments We would like to thank Michele Boldrin, Holger Herz, David Levine, Manolis Petrakis, Nikolaos Tsakas and Daniel Zizzo for their insightful comments, which significantly improved the paper. The research was supported by research funds from the Strategic Research Development Fund of the University of Southampton and the British Academy (under grant number SG to Christos A. Ioannou). The usual disclaimer applies. Mailing Address: Department of Economics, University of Southampton, Southampton, SO17 1BJ, United Kingdom. c.ioannou@soton.ac.uk Mailing Address: Department of Economics, University of Southampton, Southampton, SO17 1BJ, United Kingdom. m.makris@soton.ac.uk Mailing Address: Department of Economics, University of Southampton, Southampton, SO17 1BJ, United Kingdom. c.ornaghi@soton.ac.uk

2 1 Introduction Persistence effects in R&D can take the form of (i) learning-by-doing (i.e. knowledge transmission from the firm s own past innovative efforts) and (ii) dynamic externalities (i.e. knowledge transmission from the rivals past innovative efforts). 1 While empirical evidence has amassed on the importance of learning-by-doing (see e.g. Lundberg (1961), Lucas (1988), Benkard (2000), Thornton and Thompson (2001), Thompson (2012), Levitt, List, and Syverson (2013)) and dynamic externalities (see e.g. Griliches (1979), Griliches (1992), Ornaghi (2009)), theoretical models of R&D have starkly neglected their relevance. The present study proposes a theoretical model that investigates the interaction of learning-by-doing and dynamic externalities with product substitutability on innovative efforts in a duopoly setup. Innovative effort reflects firms activities towards cost-reduction and/or quality-enhancement, while taking as exogenously given product substitutability (i.e. the degree of horizontal product differentiation). 2 As a motivation for this modelling choice consider the case of the two most popular aircrafts around: Boeing 737 and Airbus A320. The two planes cannot be considered perfect substitutes due to the use of different operating systems. Cabin crews spend considerable amount of time in training to get used to these operating systems, which makes it very costly for a carrier to switch from one aircraft to the other. Given such horizontal differentiation, the two firms spend a significant amount of resources to reduce costs and improve the quality of the aircrafts (e.g. wireless controls, larger cargo areas, more comfortable seating arrangements, increased fuel efficiency etc). The proposed model retains the defining feature of the step-by-step innovation model of Aghion, Harris, and Vickers (1997), where a laggard must draw level before surpassing the leader. It also allows for a holistic approach to study the impact of a firm s stock of knowledge on its R&D decision in levelled and unlevelled duopolies. Specifically, in our model, a firm s accumulated stock of knowledge (referred to as technology capacity level hereafter) may, not only, influence its own effectiveness in increasing its research capacity, but, also, spill over to its rival. We capture this by postulating that the higher the industry s technology capacity levels, the higher the cost-efficiency of firms in terms of R&D investment. Given the profile of the industry s technology capacity levels, our duopolists decide on their R&D investment, and, subsequently, decide on their production levels. In doing so, they 1 Typically, dynamic externalities are multidirectional. A notable exception is the study of Amir and Wooders (2000), where dynamic externalities flow from the firm with the higher R&D activity to its rival (but never vice-versa). A unidirectional spillover structure is appropriate whenever there is a natural order to the innovations that can be achieved. 2 In the IO literature, our setup corresponds to a model where firms R&D affects products vertical differentiation given some fixed level of horizontal differentiation. In the Macro literature, our setup is related to models of quality ladders (see, for instance, Grossman and Helpman (1991)). 1

3 take their rival s current decisions as given while anticipating the best responses at future interactions. Each firm s R&D investment will stochastically influence its new technology capacity level. The relative technology capacity levels will, in turn, affect the share of the economic rents that the two firms will capture. Therefore, the current technology capacity levels will affect both the industry s innovative efforts (directly) and the appropriation of the duopoly s economic rents (indirectly). As we will see this will be crucial for our results. In our model, in a levelled industry, increased product substitutability reduces the duopoly s economic rents and consequently increases the incremental benefit from innovating and becoming a leader. In an unlevelled industry, increased substitutability reduces the incremental benefit for the laggard from innovating and catching up with the leader. Thus, in the absence of persistence effects, the model predicts increased innovative effort with product substitutability in a levelled industry, and decreased innovative effort with substitutability for the laggard in an unlevelled industry. Though the decrease in innovative effort with substitutability is still predicted for the laggard in the presence of persistence effects in an unlevelled industry, the model predicts non-monotone investment with substitutability in a levelled industry. The non-monotonicity of investment with product substitutability in a levelled industry is, perhaps, a surprising result, which sheds new insights into the interplay of persistence effects with substitutability. In contrast to what one might have thought by hastily extrapolating the implications of lower costs on a firm s research capacity, the firm may, all other things equal, actually choose not to increase its R&D investment. The intuition is the following. Firms decide on their R&D investment by locating the point where the marginal cost equals their expected marginal benefit from higher investment. The expected marginal benefit captures the higher economic rents from avoiding being the laggard in the event where the opponent has been successful in innovating, as well as higher economic rents from becoming the leader in the event where the opponent has failed to innovate. The former gain is decreasing in substitutability, whereas the latter gain is increasing in substitutability. As a result, the expected marginal benefit from higher investment is increasing with substitutability if the opponent s R&D investment (and hence the likelihood that the opponent will innovate) is sufficiently low, while it is decreasing with substitutability if the opponent s R&D investment is sufficiently high. Importantly, the threshold that determines whether the likelihood that the opponent will innovate is sufficiently high (low) and hence whether R&D investment is decreasing (increasing) with substitutability is itself dependent on the level of substitutability because the latter affects both the gains from avoiding being a laggard and from becoming a leader. It follows that fixing the level of persistence effects (and hence the investment of the opponent) at a high enough level, the impact of changes 2

4 in substitutability on own R&D investment may be non-monotone. As an example, consider the case where the aforementioned probability threshold is increasing with the level of substitutability over some range of degrees of substitutability (we will show later that this can occur under some parametarization of the model). In this case, for low degrees of substitutability (in the range in question), the opponent s likelihood of innovating is higher than the aforementioned threshold, whereas for high degrees of substitutability (in the range in question) the opponent s likelihood of innovating is lower than the said threshold. As a result over this range of degrees of substitutability, own R&D investment expressed as a function of substitutability has a U-shape. The testable predictions of our model are taken to the lab. The advantage of controlled laboratory experiments is that they mitigate measurement errors of field studies. Furthermore, our experimental framework does not suffer from the simultaneity bias because we exogenously select different degrees of substitutability. Therefore, we circumvent the endogeneity problem that empirical studies of the relationship between substitutability and innovative effort often face. Subjects are randomly matched in pairs to form duopolies, and are asked to decide on the level of investment to be undertaken in each of three scenarios that differ in the starting relative standing of the two firms on a fictional point score; specifically when (a) both firms have the same number of points (i.e. they are in a levelled industry), (b) the other firm is one point ahead from their firm (i.e. as a laggard), and (c) their own firm is one point ahead from the other firm (i.e. as a leader). The investment choice as a percentage reflects the probability of a successful innovation, so that an investment choice of α signifies an α/100 probability of success. A successful innovation leads to an increase in the fictional point score of the firm by one point. Therefore, successful innovation may, potentially, improve the relative standing of the firm, if the other firm s investment was unsuccessful. Investments are costly. The cost depends not only on the investment level chosen, but also on the persistence effects of the firm, where, ceteris paribus, the higher the persistence effects the lower the cost of the firm s investment. Rents are then distributed to the two subjects according to their final relative standing. On one hand, if subjects end up to be levelled, the rents of the two firms are equal, but are decreasing in the degree of product substitutability. On the other hand, if one subject is ahead of the other, then, the leader always receives a higher rent than the laggard, with the difference in rents be increasing in the degree of substitutability. The lab results are largely in line with the proposed model s predictions. The layout of this paper adheres to the following plan. In Section 2, we review additional related literature. In Section 3, we describe the novel theoretical model, and in Section 4, we present the experimental design and formulate the testable predictions based on our 3

5 parameter choices. In Section 5, we provide the main experimental results. Finally, in Section 6, we offer concluding remarks and directions for future research. 2 Literature Review There are three different strands of the literature to which this study relates to. The first is the vast work on learning-by-doing in economics and organisational learning in management (see e.g. Arrow (1962), Argote (1999), Schilling, Vidal, Ployhart, and Marangoni (2003)). In its original and purest form, learning-by-doing refers to the productivity increases that are realized as a by-product of the production process (Arrow (1962)). In his seminal paper, Wright (1936) found that labor costs of producing air-frames fell by 20% with every doubling of cumulative output. 3 Differently from the original view, in this study, we refer to learningby-doing as learning that arises from specific investments in R&D. Our idea is that individuals accumulate extensive knowledge from past efforts and thus improve their performance on subsequent learning tasks. In this respect, the learning process we model is what Ellis (1965) defines as learning to learn. Our setup is supported by the findings of Hatch and Mowery (1998). Specifically, the authors note that, in the semiconductor industry, in contrast to most previous studies of learning by doing, the learning curve is shown here to be the product of deliberate activities intended to improve yields and reduce costs, rather than the incidental by-product of production volume (p. 1461). A second strand of the literature that this study relates closely to is that on the incentives to invest in the presence of externalities. The paper by D Aspremont and Jacquemin (1988) is amongst the first theoretical studies to analyze firms incentives to innovate in a duopoly with externalities. The authors assume that firms production costs decrease with the amount of research that the two firms undertake. Differently from us, their model assumes that past research efforts do not have any effect on the firm s cost-efficiency; instead, production costs in some period only depend on the amount of research that the two firms undertake in that period. The assumption that technology improvements, in the form of cost-reducing process innovation and/or quality-enhancement product innovation, depend only on current investments is maintained in most of the theoretical studies in the R&D literature (see e.g. Spence (1984), D Aspremont and Jacquemin (1990), Kamien, Muller, and Zang (1992), Amir (2000), Amir, Evstigneev, and Wooders (2003), Cellini and Lambertini (2009) and 3 Several other studies also have found uncontroversial evidence of learning-by-doing in production for different industries (see e.g. Bahk and Gort (1993), Irwin and Klenow (1994), Hatch and Mowery (1998)). 4

6 Schmutzler (2013)). However, such modelling assumption is refuted by factual evidence, which suggests that firms become more productive as a result of the cumulative stock of knowledge. 4 Furthermore, this modelling assumption is also at odds with the approach used in the empirical literature since the seminal paper by Griliches (1979), where firm-specific knowledge and competitors knowledge is measured by the accumulated stock of research investments using the perpetual inventory method (see Griliches (1992) for a survey based, mainly, on industry-level data, and Ornaghi (2009) for more recent evidence using firm data). Our results are also pertinent to the strand of the literature studying the relationship between competitive pressure and innovative effort. The impact of competitive pressure on innovative effort has culminated in a voluminous theoretical and empirical literature, where the results often appear contradictory (see also Gilbert (2006) for a survey on this literature). Specifically, the studies of Vives (2008) and Schmutzler (2013), among others, have shown that theoretical models can support a positive, negative or non-monotone relationship between competitive pressure and innovative effort depending on, amongst other things, how competitive pressure is modelled (e.g. increasing substitutability between products, market structure), the extent of efficiency differences among rivals, and the existence and magnitude of externalities. Though some aspects and ideas in the aforementioned studies do find common ground with our model, what we propose here is different in that we model investment with a stochastic outcome, and incorporate into the modelling framework learning-by-doing and dynamic externalities. We also draw similarities to the models by Sacco and Schmutzler (2011) and Aghion, Bechtold, Cassar, and Herz (2018). The former model though differs from ours in two substantial ways. First, the authors assume that the probability of successful R&D investment is independent of the investment level. Second, economic rents depend on the level of R&D investment conditional on successful innovation having taken place. In contrast, we assume that the success probability is increasing in the level of investment, while rents depend on the relative technology capacity levels of firms, but not on the actual levels of investment that are behind these capacity levels. In this respect, the model proposed in this study (without persistence effects) is closer to the theoretical framework by Aghion, Bechtold, Cassar, and Herz (2018). However, to re-emphasize, our model departs from (and thus contribute to) the existing literature in that it incorporates learning-by-doing and dynamic externalities, with the aim of investigating the interaction of persistence effects with product substitutability on innovative effort. 4 In fact, this process is described in the management literature as learning-to-learn (see Cohen and Levinthal (1990)). 5

7 3 The Model In what follows, we present and analyze a reduced-form model that describes the firms expected payoffs for any given profile of R&D investment. The reduced-form model captures the essential ingredients that are needed to derive our predictions; it thus conveys the main message of our study in the most transparent way. We note that this model is static only in appearance. In the Appendix, we provide a microfoundation for this reduced-form model, which is based on a two-stage strategic interaction between the two firms. In the first stage, firms engage in R&D with the aim of reducing the production cost and/or enhancing the quality of their product. In the second stage, firms choose their production. We need to emphasize here that our main results are robust to any extension of the second-stage output market as long as the duopolists economic rents and product substitutability satisfy assumptions (1) - (3) below. Finally, any such two-stage interaction can also be thought of as a snapshot of a fully dynamic Markov model, where the Markov state is the profile of the industry s research capacity levels. What we have here as economic rents, would be in that dynamic model, the appropriately defined value functions of the two firms in levelled or unlevelled industries. Our analysis of the reduced-form model here, can thus be thought of as corresponding to the investigation of the firms investment decisions in any given period and for any given Markov state that is consistent with the underlying assumptions on how technology capacity levels evolved. There are two firms i = 1, 2 and two stages. The firms behave non-cooperatively. The market environment and available (potential) technologies are such that the duopoly can be levelled or unlevelled. In a levelled industry, each firm earns the same rents. Denote the second-stage rents in such a duopoly by π s (where s is a mnemonic for symmetric). In an unlevelled industry (henceforth, duopoly and industry are used interchangeably), one firm obtains higher rents than the other. We refer to the firm with the high rents as the leader, and to the firm with the low rents as the laggard. We also denote second-stage high rents in such an industry by π h, and the corresponding low rents by π l. We postulate that π h > π s > π l, (1) where π h π l is finite. We also parametrize second-stage rents by a variable θ, which captures the degree of horizontal product differentiation in the industry: the higher the θ, the easier for consumers to substitute the products. Therefore, one can also think of θ as the inverse measure of switching costs in the industry. We also assume that [π h π s ] θ > 0 (2) 6

8 and [π s π l ] θ < 0; (3) that is, the higher the θ, the higher the gain from being the leader, and the lower the loss from being the laggard compared to the situation where firms operate in a levelled industry and earn π s. The first assumption introduces a stronger incentive, all other things equal, on the part of firms to become the leader as the level of the product s substitutability increases. The second assumption introduces a weaker incentive, all other things equal, on the part of firms to avoid being the laggard as the level of the product s substitutability increases. In the first stage, firms engage in R&D with the aim of becoming more efficient than their opponent in terms of reducing the production cost and/or enhancing the quality of their product in the second stage. In this model, efficiency is represented by discrete technology capacity levels, and innovations come in the form of one-level increases in the technology capacity level. Technology capacities determine whether the industry is unlevelled or levelled. In the former case, technology capacities are not the same and the firm with the higher (lower) technology capacity is the leader (laggard). In the latter case, technology capacities are the same and no firm has an advantage in terms of attained rents. Firms can differ by, atmost, one technology capacity level: an obsolete technology becomes freely and immediately available to the laggard firm. Therefore, if the current leader successfully innovates while the laggard does not, the technology that was giving the advantage in the first stage to the leader becomes immediately and, at no cost, available to the laggard. Let k i be the technology capacity level of firm i in the first stage. Technology capacity levels are assumed to be finite: k i < k for some k > 0. R&D investment is described in terms of the implied probability of success in innovating (i.e. going up one level in technology capacity) p i [0, 1]. We refer to this probability as research capacity. The novelty of our model is that the industry s technology capacity levels in the first stage (which are predetermined here capturing past interactions in the industry) have an impact also on the cost of R&D investment. In more detail, we postulate that because of learning-by-doing and dynamic externalities, the cost of research capacity p i is given by C(p i, K i ) = c(p i) K i, (4) where c(p i ) is an increasing and convex function with c(0) = 0, and lim pi 1 c (p i ) =, while K i 1 captures the impact of the first-stage technology capacities in the industry on the cost-efficiency of firm i in terms of R&D investment. Thus, K i summarizes any learning-by-doing and dynamic externalities in R&D investment. Let c := c (0). 7

9 Hereafter, we define K i as the persistence effects of firm i, and we set K i = 1 + ψ[k i + φk i ], (5) where the parameter ψ 0 captures the strength of learning-by-doing and dynamic externalities (ψ = 0 represents the case where there are no persistence effects), and the parameter φ 0 measures the impact of dynamic externalities relative to learning-by-doing (the higher the φ, the higher the relative impact of dynamic externalities). We also assume that φ 1 to capture that, all other things equal, it is not easier to generate knowledge from the rivals innovative efforts than it is from the firm s own innovative efforts. 5 We finally assume that min p i c (p i ) > [1 + ψ(1 + φ)k][(π s π l ) (π h π s )]; (6) that is, the persistence effects are not very high and/or the gain in rents from not being the laggard relative to the gain from being the leader (with both gains be calculated with reference to the situation where firms are identical) is not very high. Condition (6) is a regularity condition, which ensures that there is a symmetric equilibrium with positive investment in the levelled industry (see Subsection 3.1.2). We now turn to the study of the firm s R&D investment problem. 3.1 The R&D Investment Problem In this subsection, we discuss the Nash equilibrium (simply referred to as equilibrium hereafter) investment choices of the firms. At equilibrium, the investment problem of a firm is to maximize its expected payoff with respect to its research capacity, taking as given the research capacity of its rival. Optimal choices are denoted with an asterisk. The investment decision depends on whether a firm is the leader or the laggard or in a levelled industry in the first stage. Given our assumptions so far, we have that p i < 1 for any i = 1, 2. We first characterize the equilibria when the industry is unlevelled, and, subsequently, the symmetric equilibrium when the industry is levelled. 6 5 Irwin and Klenow (1994) using quarterly, firm-level data on semiconductors, find that firms learn three times more from an additional unit of their own cumulative production than from an additional unit of another firm s cumulative production. 6 In the levelled industry, there are also asymmetric equilibria when 1 c 1 (K(π h π s )) π h π s c K π h π s+π l π s > 0. However, for the set of parameters used in our experiments, the symmetric equilibrium is the unique equilibrium, and so here, to simplify our discussion, we abstain from discussing asymmetric equilibria. 8

10 3.1.1 The First-Stage Unlevelled Industry To fix ideas, suppose that firm i = 2 is the laggard and that firm i = 1 is the leader in the first stage. The investment problem of the laggard is to maximize with respect to p 2 : (1 p 2 )(π l ) + p 2 [p 1π l + (1 p 1)π s ] C(p 2, K 2 ) = π l + p 2 (1 p 1)(π s π l ) c(p 2) K 2. Based on the aforementioned assumptions, this problem is well-defined. To understand this problem note that increasing marginally the research capacity of firm i = 2 leads to a higher cost by c (p 2 )/K 2 units, and to an increase in expected rents by (1 p 1)(π s π l ) units. The latter increase is the gain from being in a levelled industry in the second stage, which occurs when firm i = 2 innovates and the rival does not succeed in innovating. Taking the first-order condition with respect to p 2, we have at an interior solution (i.e. when p 2 > 0) that K 2 (1 p 1)(π s π l ) = c (p 2). (7) The optimal research capacity of the laggard p 2 is increasing in its relative marginal benefit K 2 (1 p 1)(π s π l ). Clearly, if K 2 (1 p 1)(π s π l ) c then p 2 = 0. The problem of the leader, in turn, is to maximize with respect to p 1 : (1 p 1 )[p 2π s + (1 p 2)π h ] + p 1 π h C(p 1, K 1 ) = π h (1 p 1 )p 2(π h π s ) c(p 1) K 1. This problem is well-defined as well. As with the laggard s problem, increasing marginally the research capacity of firm i = 1 leads to a higher cost by c (p 1 )/K 1 units now, and to an increase in expected rents by p 2(π h π s ) units. The latter increase is the gain from avoiding being in a levelled industry in the second stage, which will occur when firm i = 1 fails to innovate and the rival succeeds in innovating. Taking the first-order condition with respect to p 1, we have at an interior solution (i.e. when p 1 > 0) that K 1 p 2(π h π s ) = c (p 1). (8) The optimal research capacity of the leader p 1 is increasing in its relative marginal benefit K 1 p 2(π h π s ). If K 1 p 2(π h π s ) c, we then have that p 1 = 0. Observe that if c K 2 (π s π l ), (9) 9

11 then, at equilibrium, there is no R&D investment by either the laggard or the leader. In this case, the laggard s marginal cost from investment at any strictly positive level of investment is higher than the highest possible marginal benefit from investment, making zero investment optimal. This, in turn, implies that zero investment is optimal for the leader as well (i.e. p 1 = p 2 = 0). In order to ensure a strictly positive research capacity for the laggard, we rewrite the first-order condition of the laggard (after dropping the asterisks) as p 1 = 1 c (p 2 ) K 2 (π s π l ). (10) Viewing this as a function of p 1, we see that it is decreasing and concave in p 2. Moreover, it goes to minus infinity as p 2 approaches 1. In addition, when p 2 = c 1 (K 2 (π s π l )), we have that p 1 = 0. Clearly, then, if c < K 2 (π s π l ), (11) the highest research capacity for the laggard is equal to c 1 (K 2 (π s π l )). consequence, if, also, c 1 (K 2 (π s π l )) As a direct c K 1 (π h π s ), (12) then, the leader s marginal cost from investment at any strictly positive level of investment is higher than the highest possible marginal benefit from investment, making zero investment optimal. Thus, in this case, we have that p 1 = 0 and from (10): p 2 = c 1 (K 2 (π s π l )) > 0. Turning to the case where both firms invest, we rewrite the first-order condition of the leader (after dropping the asterisks) as p 2 = c (p 1 ) K 1 (π h π s ). (13) Viewing this as a function for p 2, we observe that it is increasing and convex in p 1. Moreover, it goes to infinity as p 1 approaches 1. A diagrammatic inspection of (10) and (13) is enough to convince the reader that these two curves have a unique intersection at strictly positive values of p 1 and p 2 (together defining the equilibrium profile of research capacities) when c < K 2 (π s π l ) (ensuring a strictly positive intercept of the function for p 1 in (10) and thereby that c 1 (K 2 (π s 10

12 π l )) > 0), and c 1 (K 2 (π s π l )) > c K 1 (π h π s ) (14) (ensuring that the intercept of the function for p 2 in (13) is lower than the intercept of the function for p 1 in (10)). This completes the characterization of equilibria when the industry is unlevelled in the first stage. We have identified three cases: (a) where neither the leader nor the laggard invests, (b) where the laggard but not the leader invests, and (c) where both the leader and the laggard invest. We restrict attention to the (more interesting) case where there is strictly positive investment from the laggard in the equilibrium. To start with, we observe that if p 1 = 0, then innovative effort for the laggard decreases with substitutability: in this case p 2 = c 1 (K 2 (π s π l )), where, by assumption, c 1 (K 2 (π s π l )) is decreasing in θ. Turning to the case where both firms invest, to find the effect of θ on the equilibrium research capacities, we need to use the Implicit Function Theorem. So, dropping the asterisks for notational simplicity, and using (7) and (8), we have that [ c (p 1 ) K 1 (π h π s ) K 2 (π s π l ) c (p 2 ) ] [ p 1 / θ p 2 / θ ] = [ K 1 p 2 [π h π s] θ K 2 (1 p 1 ) [πs π l] θ Therefore, the effect of θ on laggard s innovative effort is determined by the sign of ]. p 2 / θ = c (p 1 )K 2 (1 p 1 ) [πs π l] [π K θ 2 (π s π l )K 1 p h π s] 2 θ. c (p 1 )c (p 2 ) + K 1 (π h π s )K 2 (π s π l ) Note that the denominator is positive by the convexity of the cost function and assumption (1). In addition, the numerator is negative by the convexity of the cost function and assumptions (2) and (3). Therefore, innovative effort for the laggard decreases with substitutability in this case as well. 7 These findings are formalized in our first theoretical prediction below. Theoretical Prediction in an unlevelled industry. Innovative effort for the laggard decreases with substitutability 7 One can easily see from the above that the effect of higher θ on the leader s investment (i.e. p 1 / θ) cannot be signed without further assumptions. 11

13 3.1.2 The First-Stage Levelled Industry We turn our focus to the investment of firms in a levelled industry in the first stage. Here, K 1 = K 2 := K. The problem of any firm i is to maximize with respect to p i : (1 p i ) [ ] [ ] p iπ l + (1 p i)π s + pi p i π s + (1 p i)π h C(pi, K) = p iπ l + (1 p i)π s + p i [ p i (π s π l ) + (1 p i)(π h π s ) ] c(p i) K. This problem is also well-behaved. Under this problem, increasing marginally the research capacity leads to a higher cost by c (p i )/K units, and to an increase in expected rents by p i(π s π l ) + (1 p i)(π h π s ) units. The latter increase is the gain from being the leader in the second stage, compared to a situation where either firm i fails to innovate and the rival succeeds in innovating, or when both firm i and its rival fail to innovate. Taking the first-order condition with respect to p i, we have at an interior solution (i.e. when p i > 0 for all i) that K [ p i(π s π l ) + (1 p i)(π h π s ) ] = c (p i ). (15) Note that the optimal research capacity p i is increasing in the relative marginal benefit K [ p i(π s π l ) + (1 p i)(π h π s ) ]. We restrict attention to (symmetric) equilibria with strictly positive investment by both firms. This is ensured by condition π h π s > c. (16) Let p = p i = p i denote the symmetric equilibrium research capacity. We can then rewite (15) as K [p (π s π l ) + (1 p )(π h π s )] = c (p ). (17) Assumption (6) and π h > π s imply directly that there is a unique solution p > 0 to the above condition. This solution is increasing in persistence effects K. Therefore, equilibrium R&D investment is increasing in persistence effects. We now turn to the analysis of the effect of θ on innovative effort. Note from the above equilibrium condition (after dropping the asterisks) that 12

14 { } p K p [πs π l] + (1 p) [π h π s] θ = θ θ, (18) K [2π s π h π l ] c (p) and observe that (6) implies that the denominator is negative. Therefore, innovative effort increases with θ if the numerator is positive. The numerator, however, cannot be signed without further assumptions on the fundamentals of the environment we study, due to our assumptions that [πs π l] < 0 < [π h π s]. To this end, note that these assumpptions imply θ θ that if, in equilibrium, p is high enough, then, we have that p < 0, whereas if p is low θ enough, we have that p > 0. The relevant threshold level of equilibrium research capacity θ is defined by that is, p [π s π l ] θ p + (1 p) [π h π s ] θ [π h π s] θ [π h π s] [πs π l] θ θ = 0; (0, 1). (19) Note that this threshold level depends on the degree of θ through the impact of the latter on the profile of rents π h, π s, π l. In particular, the effect of θ on p depends on the relative concavity of π h π s and π s π l with respect to θ, something for which our model is agnostic. Moreover, we note that p does not depend on persistence effects. Importantly, observe that persistence effects do, however, have an impact on R&D investment because K will ultimately influence the equilibrium value of p and thereby whether, for the given p, p < p or not. Recall from (17) that p is increasing in K. We thus have two cases. If persistence effects are low enough, then p < p and innovative effort increases with θ, whereas if persistence effects are high enough, then p > p and higher substitutability leads to lower R&D investment in the symmetric equilibrium of a levelled industry. The equilibrium condition (17) implies directly that the threshold level of persistence effects that defines these two cases, K, is given by K c ( p) p(π s π l ) + (1 p)(π h π s ). (20) Note that this threshold level does not depend on persistence effects. However, it does depend on the degree of substitutability θ. It follows that persistence effects together with substitutability interact to determine the impact of the latter on optimal investment in the levelled industry: both influence the optimal investment p, while the extent of substitutability determines the threshold values p and K. The equilibrium for the case where π h π s > π s π l 13

15 is described in detail in Figure 1. Therefore, our second theoretical prediction is formalized as follows. Theoretical Prediction In a levelled industry, innovative effort increases with substitutability only if K < K, otherwise it does not when persistence effects are high enough so that K > K. Figure 1: Equilibrium Research Capacity Notes: Recall (17) after dropping the asterisk: K [p(π s π l ) + (1 p)(π h π s )] = c (p). The upward convex line is the right-hand side. The solid blue line corresponds to the left-hand side for some initial θ, whereas the dotted line corresponds to the left-hand side for some higher θ. Their intersection with c (p) gives the equilibrium research capacity under these two alternative θs. The orange line corresponds to the lefthand side when K = K; its intersection with c (p) provides p for the given initial θ. The left-hand side is decreasing in p if π h π s > π s π l. Furthermore, for any given θ, the left-hand side increases (and so the line that represents it shifts upwards) when the persistence effects K increase. The threshold level of research capacity p defines thus two cases. If persistence effects are high enough (i.e. K > K) then p > p. This case is depicted at the left panel. If persistence effects are low enough (i.e. K < K) then p < p. This case is shown at the right panel. The left-hand side is increasing in θ when p < p, whereas it is decreasing in θ when p > p. Thus, when shifting from the initial θ to the higher one, we must have that the dotted line is below the solid blue line for p > p and above the solid blue line for p < p. Therefore, at both panels, an increase in θ, for given persistence effects K, results in a clockwise movement around the pivotal point of the line representing the left-hand side of (17). As a result, at the left panel, we observe a decrease in the equilibrium research capacity, and at the right panel, we observe an increase in the equilibrium capacity. Before we leave this section, we note that we cannot say more about the monotonicity properties of p with respect to the degree of substitutability θ, unless we impose more assumptions on the dependence of the industry s rents profile on θ. One possible scenario, for instance, could be that the rents profile is such that p is increasing in θ. In this case, 14

16 we can think of an increase in the degree of substitutability as an increase in p. In such an environment, the left panel of Figure 1 would depict a situation where substitutability is low, whereas the right panel would depict a situation where substitutability is high. For fixed K 1, after recalling that p (0, 1) (under condition (16)) and that p (0, 1), it follows immediately that the relationship between R&D investment and θ is U-shaped (locally). 8 However, if p is decreasing in θ, then analogous reasoning implies that the relationship between R&D investment and substitutability is inverted U-shaped. 9 4 Experimental Design In the experimental design, we focused on two dimensions. The first dimension is the degree of substitutability. We allowed for four levels of substitutability measured by θ, where the higher the θ the easier for consumers to substitute the products. The second dimension is the presence or absence of persistence effects. We thus applied a 4 2 experimental design to examine the impact of substitutability and persistence effects on firms investments. 4.1 Treatments In the game play, subjects were recruited to play the role of firms. Initially, subjects were randomly matched in pairs to form duopolies. After reading the game instructions, subjects had to complete a quiz to ensure their understanding of the game. Subjects were then asked to decide on the level of investment to be undertaken under three scenarios that differed in the relative standing of the two firms on a fictional point score. The game was single shot; that is, the three decisions were the only decisions subjects were asked to make in the game 8 To see this, simply, start from the substitutability behind the left panel of Figure 1 and increase θ for any given K. By doing so, the red line shifts upwards and the solid black line pivots clockwise. At some level of substitutability, the environment will be represented by the right panel of Figure 1 and so on. Therefore, by continuity, for low θ or p, we have that p < p, while for high θ or p, we have that p > p. In the former case, investment is decreasing in θ, and in the latter case, it is increasing in θ. 9 Of course, in principle, p may not be monotonically related to θ, in which case the relationship between R&D investment and substitutability becomes more complicated to describe. However, our discussion in the main text is still useful to understand this relationship locally. 15

17 play. 10 Specifically, subjects were asked to choose an investment level α {0, 2,..., 80} 11 in each of the following three scenarios: (a) assuming that both firms had the same number of points in the point score, (b) assuming that the other firm was one point ahead in the point score from their firm, and (c) assuming that their firm was one point ahead in the point score from the other firm. The order the subjects were presented with the three scenarios was randomized to eliminate any order effects. Moreover, no feedback on the game play was provided until subjects had responded to all three scenarios. This information was common knowledge. The probability of success or research capacity, as defined in the previous section, was given by p = α/100. Furthermore, for each investment level α, there was an associated cost. We deployed the cost function p i c(p i ) = c, (21) 1 p i where c = The investment levels and the corresponding probabilities of success and costs were displayed in an easy-to-read table. The table was identical in all three scenarios. In fact, the only change in the table across treatments was the cost schedule to reflect the presence or absence of persistence effects. Specifically, in the four treatments without persistence effects K was set to 1, whereas in the four treatments with persistence effects K was set to 5. Therefore, the cost schedule in the treatments without persistence effects was five-fold the one in the treatments with persistence effects (recall (4)). 12 To determine subjects payoffs in the game, one scenario was selected at random for each pair. In addition, a separate draw of an integer from 1 to 100 for each subject took place to determine whether the investment of that subject in the selected scenario was successful or not. Recall that a subject s investment choice reflects the probability of success; if the subject s investment in the selected scenario was below the computer-drawn integer then 10 We reiterate that the single-shot game play can be thought of as a snapshot of a fully dynamic Markov model, where the Markov state is the profile of the industry s research capacity levels and economic rents are the appropriately defined value functions of the two firms in levelled or unlevelled industries. Thus, our single-shot setup can be thought of as corresponding to the investigation of firms incentives to innovate in any given period and for any given Markov state that is consistent with the underlying assumptions on how technology capacity levels evolved. 11 We chose to place an upper bound to the probability of success to maintain realism. 12 The numerical value of K was not included in the experimental instructions. Similarly, we did not provide any information on ψ, φ, c as well as the numerical values of the point scores of the two firms. Based on our theoretical framework, the only relevant factors for subjects decisions were the starting relative standing of the two firms on the fictional point score, the cost schedule and the respective payoffs for all possible final standings. We thus chose not to provide any redundant information to the subjects to simplify their cognitive environment as such information could potentially compromise the clarity of the instructions and lead to confounding effects. 16

18 that subject s investment was considered unsuccessful, otherwise it was considered successful. This information was common knowledge. A subject s successful investment would increase the point score of that subject by one point, and lead to, potentially, an improvement in the relative standing if the other subject s investment was unsuccessful. In each duopoly, the final payoffs of the two subjects were determined based on the selected scenario, their investment choices and corresponding costs, the outcomes of their investments and the final relative standing. In the experimental sessions, we used the following payoff function π h C(p i, K i ) u i = π s C(p i, K i ) π l C(p i, K i ) if i was the leader in the final relative standing, if i and j were levelled in the final relative standing, if i was the laggard in the final relative standing, (22) where, recall, π h is the economic rent of the leader, π s denotes the economic rents of the two firms in a levelled industry, and π l is the economic rent of the laggard. The numerical values of the economic rents for each level of substitutability θ are shown in Table 1. To safeguard against potential losses, subjects were endowed with 3 in lieu of a show-up fee. Table 1: Economic Rents θ π h π s π l Notes: θ is the level of substitutability, π h is the economic rent of the leader, π s denotes the economic rents of the two firms in a levelled industry, and π l is the economic rent of the laggard. The experimental sessions were conducted in the Social Sciences Experimental Laboratory (SSEL) of the University of Southampton in May and October of We conducted two sessions per treatment, where each session had 16 subjects and 8 duopolies. The 256 subjects were recruited from the undergraduate and graduate population of the University of Southampton using ORSEE (Greiner (2015)). Participants were allowed to participate in only one session. Each session lasted around 40 minutes. Average payoffs per participant were Subjects were paid in cash privately at the end of the session. The experiments were programmed and conducted with the use of the experimental software z-tree (Fischbacher (2007)). The detailed instructions are reported in the Appendix. 17

19 4.2 Testable Predictions We formulate next our testable predictions based on the proposed theoretical model and the parameter choices in the experiments. First, we hypothesize on the equilibrium research capacity of the laggards in an unlevelled duopoly in the absence and presence of persistence effects. Second, we hypothesize on the equilibrium research capacity of firms in a levelled industry, again, in the absence and presence of persistence effects. Figure 2: Equilibrium Research Capacity of Laggard in the Absence of Persistence Effects Notes: We provide the equilibrium research capacity of the laggard for K = 1; that is, when there are no persistence effects. Clearly, as θ increases, the equilibrium research capacity goes down. The leader should invest 0. To map equilibrium research capacity to the subjects choices in the actual experiments, simply, multiply the values on the vertical axis by 100. The vertical dotted lines indicate the four levels of substitutability chosen in the experiments. We look at the unlevelled industry first. In the absence of persistence effects (i.e. K = 1), the model, based on our parameter choices, predicts that the leader should invest 0. However, the laggard should invest a strictly positive value. In Figure 2, we plot a laggard s equilibrium research capacity against θ for K = 1. Clearly, as θ increases, the equilibrium research 18

20 Figure 3: Equilibrium Research Capacity of Laggard and Leader in the Presence of Persistence Effects Leader Laggard Notes: We provide the equilibrium research capacity of the laggard and the leader for K = 5; that is, when there are persistence effects. In the case of the laggard, we see that research capacity goes down with θ. In the case of the leader, the equilibrium research capacity is rather flat as θ increases. To map equilibrium research capacity to the subjects choices in the actual experiments, simply, multiply the values on the vertical axis by 100. The vertical dotted lines indicate the four levels of substitutability chosen in the experiments. capacity goes down. On the other hand, in the presence of persistence effects (i.e. K = 5), the model predicts that both the leader and the laggard should invest a strictly positive value. Specifically, in Figure 3, we display the equilibrium research capacity against θ of a leader and a laggard for K = 5. In the case of the leader, the equilibrium research capacity is rather flat as θ increases, whereas, in the case of the laggard, the equilibrium research capacity goes down with θ. The two plots highlight that regardless of the absence or presence of persistence effects, innovative effort decreases for the laggard in an unlevelled duopoly. Our first prediction is formalized as follows. Prediction 1 Research capacity by a laggard in an unlevelled duopoly should decrease with substitutability regardless of any persistence effects. 19

21 Figure 4: Dependence of p on θ Notes: We provide the relation between p and θ. The most intense level of substitutability chosen in the experiments is θ = 0.6. The vertical dotted lines indicate the four levels of substitutability chosen in the experiments. Up to θ = 0.66, p is increasing in θ. Next, we look at the levelled duopoly. Recall that, as pointed out in the last paragraph of Subsection 3.1.2, we cannot say more about the monotonicity properties of p with respect to the degree of substitutability θ, unless we impose more assumptions on the dependence of the industry s rents profile on θ. Based on the industry s rents profile chosen in the experiments, the dependence of p on θ is shown in Figure 4. The relation is non-monotone. However, for the θs chosen in the experiments, p is increasing in θ. As we have argued in the last paragraph of Subsection 3.1.2, for this range of θs, the relationship between research capacity and substitutability is U-shaped. In fact, in our experiments, in the absence of persistence effects, equilibrium research capacity should increase with θ, whereas, in the presence of persistence effects, the relation between equilibrium research capacity and substitutability should be U-shaped. This is shown in Figure 5. Based on these conclusions, we formulate the following two predictions. 20

22 Figure 5: Equilibrium Research Capacity in a Levelled Duopoly Notes: We display the equilibrium research capacity in a levelled industry. On the left, we display the equilibrium research capacity for K = 1 (i.e. no persistence effects). On the right, we display the equilibrium research capacity for K = 5 (i.e. with persistence effects). In the absence of persistence effects, the equilibrium research capacity is increasing in θ. In the presence of persistence effects, the equilibrium research capacity is U-shaped; notice that the differences in research capacity across the various levels of θ are very small. To map equilibrium research capacity to the subjects choices in the actual experiments, simply, multiply the values on the vertical axis by 100. The vertical dotted lines indicate the four levels of substitutability chosen in the experiments. Prediction 2 Research capacity by levelled firms increases with substitutability in the absence of persistence effects. Prediction 3 Based on the parameters chosen, the relation between research capacity by levelled firms and substitutability should be U-shaped. 21

23 5 Results This section is divided into three subsections. Subsection 5.1 discusses the research capacity choices of subjects in the different scenarios (i.e. as laggards or leaders or levelled duopolies). Subsection 5.2 tests the formulated predictions about the decisions of laggards and levelled competitors in the absence and presence of persistence effects. Each prediction is matched with the corresponding result; that is, result i is a report on the test of prediction i. These results are the main focus of our study. Finally, in Subsection 5.3, we present the results of the leaders in unlevelled duopolies. 5.1 Preliminary Analysis Descriptive Statistics Figures 6 and 7 show the average research capacity of laggards, leaders and levelled duopolies for the four levels of substitutability investigated in the absence and presence of persistence effects, respectively. In the absence of persistence effects, the average research capacity of laggards goes down from at θ = 0.20 to 22.5 at θ = 0.50, but increases slightly to at θ = In the presence of persistence effects, the average research capacity of laggards goes down monotonically with substitutability. In levelled industries, the average research capacity increases with substitutability in the absence of persistence effects, while, in the presence of persistence effects, average research capacity decreases and then increases slightly at θ = Finally, average research capacity of leaders, in the absence of persistence effects, goes up and then goes down with substitutability, whereas, in the presence of persistence effects, average research capacity of leaders increases monotonically with substitutability Tests of Difference on Research Capacity Clearly, in the presence of persistence effects, the cost of research capacity decreases, hence firms, when controlling for the scenario (i.e. laggard or levelled or leader) and the degree of substitutability, should increase their research capacity. To test whether research capacity choices in the presence of persistence effects are higher, we regress research capacity of laggards, levelled firms, and leaders on a dummy variable taking the value of 1 when K = 5 (i.e. in the presence of persistence effects) and on the level of substitutability θ. Table 2 reports the estimated coefficients on the persistence dummy in each of the three scenarios. In the first row, we regress research capacity on the persistence dummy and on the level of 22

24 Figure 6: No Persistence Effects Leader 40 Levelled 30 Laggard θ = 0.1 θ = 0.2 θ = 0.5 θ = 0.6 Notes: We provide the average research capacity of laggards, leaders and levelled duopolies for the four levels of substitutability investigated in the absence of persistence effects. substitutability θ in all experimental sessions (i.e. we have 256 observations) and for each of the three scenarios. In the next four rows, we regress research capacity on the persistence dummy when fixing the level of substitutability θ (i.e. we have 64 observations) in each of the three scenarios. Results in Table 2 show that research capacity choices by laggards and leaders are higher in the presence of persistence effects (with the exception of the coefficient for the laggard at θ = 0.6). The findings for levelled firms are not as clear. Research capacity choices in the presence of persistence effects are significantly higher for levelled firms at θ = 0.1, but are not significantly different for higher levels of substitutability when compared to research capacity choices in the absence of persistence effects. Overall, results in Table 2, confirm the theoretical prediction that subjects tend to invest more in the presence of persistence effects. 5.2 Analysis of Laggards and Levelled Firms The purpose of our empirical framework is to investigate the impact of substitutability on the research capacity decisions of firms in the absence and in the presence of persistence effects. To test the predictions of the proposed model, we use the following linear form 23

25 Figure 7: Persistence Effects Leader 40 Levelled 30 Laggard θ = 0.1 θ = 0.2 θ = 0.5 θ = 0.6 Notes: We provide the average research capacity of laggards, leaders and levelled duopolies for the four levels of substitutability investigated in the presence of persistence effects. α i = β θ + γ Xi + εi, (23) where the investment α of firm i depends on the degree of substitutability θ in the industry, the vector of control variables Xi, which consists of the characteristics of player i (i.e. age, gender, race, university degree),13 and the error term εi, which captures individual unobservable factors affecting the level of investment that are assumed to be uncorrelated with the degree of substitutability θ. We used two different measures of substitutability in (23). In the first specification, we included θ as a discrete variable taking increasing values from 0.1 to 0.6. In the second specification, we created three dummy variables for each of the values θ = 0.2, 0.5, 0.6 with θ = 0.1 set as the base group. The second specification allowed us to assess how investments change in response to marginal increases of θ. However, this comes at a cost of reduced precision as three different parameters need to be estimated. The β parameters in (23) were estimated using the OLS regression. Results are displayed in Table 3. In Panel A, we regress investment of laggards on substitutability. In Panel B, we 13 50% of the participants were self-reported as White, 40% were self-reported as Asian, and 10% were self-reported as Other in the racial background question. Specifications include dummy variables for each of the three racial groups. In addition, given that the largest major was economics (around 23% of the sample), we felt compelled to include a dummy taking the value of 1 for economics students and 0 otherwise. Finally, for the gender, we assigned a value of 1 to the participants who were self-reported as Female and 0 otherwise in vector X. 24