Innovation & Competition in a Memory Process

Transcription

1 Innovation & Competition in a Memory Process Juan A. Correa Universidad Andres Bello Abstract Does innovation increase or decrease with more competition when innovation follows a memory process? This paper provides a theoretical and empirical framework which analyzes the innovation and competition relationship assuming that innovation follows a memory process, i.e. the current probability of innovation success depends on previous periods innovation successes. I find innovation increases with more product market competition, even under the Schumpeterian context where inventions are not completely appropriable. Assuming the probability to innovate increases with past innovations; a follower firm has a large incentive to innovate, even in a highly competitive environment, since the knowledge obtained after innovating increases its probability to innovate again and become a leader. Therefore, firms will be neck-and-neck most of the time, where they innovate in order to escape from competition. Using the same dataset of Correa and Ornaghi (14), I also find that there is a positive empirical relationship between innovation and competition when industries follow a memory process. For the memoryless industries, I find that there is an inverted-u relationship between innovation and competition. Keywords: innovation, R&D, competition, memory process JEL Classification: D43, L11, O31 1 Introduction This paper proposes a model concerning the relationship between innovation and competition, assuming a firm s current probability to innovate increases when this firm succeeded to innovate in the past. I theoretically find that the higher the competition s level, the more innovative an industry is. Using the same dataset of Correa and Ornaghi (14), I find a positive empirical relationship between innovation and competition. I find there is a negative relationship between innovation and competition in industries where firms have dissimilar technology levels (unleveled), while this relationship is positive in I would like to thank Hector Calvo, Bruno Cassiman, Robin Mason, Carmine Ornaghi, Jean-Yves Pitarakis, Stefano Trento, Xavier Vives and all participants at the IESE and University of Southampton workshops, and the International Industrial Organization, European Association for Research in Industrial Economics, University of Bath and Warsaw International conferences, for useful suggestions. I would also like to thank Santander-Abbey for its financial support. 1

2 industries where firms have the same technology level (neck-and-neck). However, since the incentive to innovate in unleveled industries is still very high at the maximum level of competition, the industries will be most of the time neck-and-neck, where the relationship between innovation and competition is upward sloping; differing from the inverted-u relationship found in Aghion et al. (5), hereafter ABBGH. I also find that more memory increases the level of research intensity. This theoretical model is tested using the Correa and Ornaghi (14) dataset. I show that there is a positive relationship between innovation and competition for the industries which show a memory process. However, there is an inverted-u relationship between innovation and competition when an industry follows a memoryless process. Some theoretical models, such as Aghion and Howitt (199), predict that more competition tends to decrease innovation activity. In these models, the innovation incentive is characterized by the difference between the expected value of post-innovation profit and pre-innovation profit. Since a monopolist would replace her/himself whenever she/he creates a better intermediate good, the incentive to innovate would be biased toward the entrant. Whenever the profit of being a monopoly is small, as in the case when there is high level of competition, entrants have little incentive to innovate and therefore there will be very little innovation. In contrast, other theoretical models, such as Boldrin and Levine (8), show that competition leads to more innovation. Boldrin and Levine (8) model assumes that any idea is costly to transmit, thus there are no unpriced spillovers and more competition leads to more innovation. Most of the empirical studies show that more competition increases the level of innovation. Geroski (199), Nickell (1996) and Blundell et al. (1999) find an empirical positive relationship between innovation and rivalry indicators 1. After this long and comprehensive debate, ABBGH reconcile the opposite lines of thought finding an inverted-u relationship between innovation and competition. They state that when there is very low competition, profits before and after innovating are not so different, hence there is not too much incentive to innovate when firms have similar costs. In an unleveled sector, if the leader innovates the follower keeps the technology distance because of spillovers, thus the leader does not have incentive to innovate. Due to that, low competition industries will be most of the time neck-and-neck where any increase in the competition level leads firms to innovate in order to escape from it (escape-competition effect). When there is too much competition, the follower s profit after innovating is not so different to pre-innovation profit, consequently there is not much incentive to innovate in the unleveled case. For neck-and-neck firms, any innovation would give more profit than if they remain leveled. Therefore, too high competition leads industries to be unleveled most of the time, while any decrease in the level of competition increases the follower s profit if it innovates (Schumpeterian effect). However, Correa (1) finds that the ABBGH inverted-u relationship between innovation and competition is the result of mixing two different regimes. Using the same ABBGH dataset, he finds that there is a structural brake produced by the establishment of the Court of 1 Geroski (199) uses the extent of market penetration by entrants, the market share of imports, the relative number of small firms (measured by number of employees), the within period percentage change in concentration, the market share of exiting firms and the five firm market concentration ratio, as indicators of rivalry.

3 Appeals for the Federal Circuit in the United States (CAFC). After considering this break into account, he finds a monotonic positive relationship between innovation and competition before the establishment of the CAFC and no relationship after. A recurrent issue regarding innovation-competition relationship models is that it does not take into account that industries can exhibit memory in the process of innovation. Hausman et al. (1984) and Hall et al. (1986) find that contemporaneous research intensity is correlated with past research intensity, giving support to the memory assumption. In my model, a firm can obtain knowledge during the process of innovation. This knowledge is completely appropriable and it can be used as an input to innovate in the next period. Since under the Schumpeterian context the leader firm does not have incentives to innovate, the memory prize encourage the laggard firms to devote more efforts to research, shortening the length that the industries remain unleveled. As a result, industries will be most of the time neck-and-neck where the escape-competition effect dominates. The rest of the paper is organized as follows. Section proposes a theoretical model which assumes that firms follow a short-memory process. Section 3 develops the methodology to define whether the innovation process has memory or is memoryless, and to show the empirical relationship between innovation and competition for both memory and memoryless industries. Section 4 concludes. Theoretical Memory Model Following ABBGH I assume that there are two firms, where n k,l m denotes the research intensity of a firm which is m technological steps away from its competitor at time t and was k steps away from its rival at time t t; and l takes the value S if the firm succeeded to innovate at time t t or F if it failed. As in ABBGH, a firm cannot be more than one step ahead of its opponent, since the latter can copy the leader s previous technology whenever it innovates. Therefore, the leader s research intensity is zero as it cannot obtain additional value from innovating. Consequently, a firm can be in three possible levels, one step ahead, neck-and-neck and one step behind, these states are denoted by the sub(super)scripts 1, and respectively. As in ABBGH and Aghion et al. (1), h represents the copy rate or R&D spillovers. The leader obtains profit π 1 and neck-and-neck π, while the follower does not gain any profit. Neck-and-neck s profit π can also be expressed as π 1 (1 δ), δ [.5, 1], where δ is the product market competition parameter. The higher the value of δ, the more competitive the industry is. Assuming Bertrand competition, the firms equally share the monopoly profits, π 1, with maximum level of collusion δ =.5. By the contrary, firms receive zero profits when competition reaches its maximum level at δ = 1. The research cost of a firm is given by (nk,l m ). The research intensity of a rival firm is denoted as n k,l m and a symmetric Nash equilibrium turns to n k,l = n k,l when firms are and were neck-and-neck. Aghion et al. (1) relax this assumption, assuming that there is no bounding for the distance between the leader and the follower. However, they find that there is no closed-form solution for the research equilibrium and the steady state industry structure. 3

4 .1 The memory parameters and Bellman equations The model presented in this section is constructed assuming that changes in the relative position (leader, neck-and-neck and follower) can only occur after innovating. Hausman et al. (1984) and Hall et al. (1986) empirically find that contemporaneous R&D investment depends on previous investment. Therefore, I assume whenever a firm improves its relative position at time t t, a value λ, which increases the probability of innovating at time t, will be generated under the process, where λ >. When a firm innovates, but does not improve its relative position, it obtains a value, φ, which also increases the probability of innovating at time t; where φ >. After time t, both λ and φ depreciate completely, i.e. memory lasts for only one period; after that, any advantage completely disappears. The memory values of rival firms are denoted as λ and φ. The memory parameters λ and φ represent the knowledge obtained via the innovation process. I assume that this knowledge lasts only one period. This assumption is useful to make the model tractable. Doraszelski (3) develops a model to study how knowledge accumulation affects the firms behavior. In his model, knowledge has a cumulative effect over current research, therefore there is no restriction about the length of lag. However, his model does not allow for an analytic solution. In section 3 I give empirical support to the short-memory assumption. The value function of each firm is given by the current profit flow, the discounted expected value of the firm after investing in R&D and the cost of investing in R&D. The discount factor e r t can be expressed as (1 t) for t to be small. From this, we can also have that ( t). For the case of unleveled industries, the leader profits flow is π 1 t, while the follower s profit is zero. Since the leader does not invest in R&D, the expected value of an unleveled firm after the follower invest in R&D is given by the follower s probability to innovate (n k + h) t. For the same reason only the follower incurs in R&D cost. After the follower invest in R&D there are two possible outcomes: (i) both the leader and the follower continue in the same position with value functions V 1 1 with value functions V 1 and V and V respectively, or (ii) the leader is caught up by the follower respectively. Therefore, the value function for the leader who was a leader in the previous period can be written as V1 1 = π 1 t + (1 r t) [ (n + h) tv 1 + [1 (n + h) t]v 1 1 ] ; for the leader who was neck-and-neck in the previous period V1 = π 1 t + (1 r t) [ (n + h) tv 1 + [1 (n + h) t]v1 1 ] ; for the follower who was follower in the previous period { V = max n (1 r t) [ (n + h) tv + [1 (n ] (n + h) t]v and for the follower who was neck-and-neck in the previous period { V = max (1 r t) [ (n n + h) tv + [1 (n + h) t]v 4 ) ] (n ) t ; t.

5 For neck-and-neck industries, the firm s profit flow is π t. The expected value of a neck-and-neck firm, which was also neck-and-neck in the previous period and failed to innovate, is a function of its own research intensity n,f and the rival s research intensity n,f. In the case that the neck-and-neck firm succeeded to innovate in the previous period, the expected value is a function of the research intensities n,s and n,s, and the memory parameters φ and φ obtained in the innovation processes. For neck-and-neck firms which were unleveled in the previous period, the expected value of the firms is a function of the research intensities and the memory parameter λ obtained by the firm which was a follower the previous period. For any of the neck-and-neck firm there are four possible outcomes after they invest in R&D: (i) Succeeding to innovate while the rival fails with a value function V1, (ii) Failing to innovate while the rival succeeds with a value function V,S, (iii) both succeeding to innovate with a value function V and (iv) both failing to innovate with a value function V,F. Therefore, the value function for the neck-and-neck firm that was also neck-and-neck in the previous period and failed to innovate, as well as its rival, is { [ V,F = max π t + (1 r t) n,f n,f tv1 + n,f tv + (n,f + n,f ) tv,s +[1 (n,f + n,f ) t]v,f ] (n,f ) t ; for the neck-and-neck firm, which was also a neck-and-neck in the previous period but succeeded to innovate, i.e. both firms innovated in the previous period, { [ V,S = max π t + (1 r t) (n,s n,s + φ) tv1 + (n,s + φ) tv +(n,s + φ + n,s + φ) tv,s + [1 (n,s + φ + n,s + φ) t]v,f for the one which was a follower in the previous period { [ V = max π t + (1 r t) n +[1 (n + λ + n 1 ) t]v,f and for the one which was a leader { [ V 1 = max π t + (1 r t) n 1 +[1 (n 1 + n + λ) t]v,f ] (n,s ) (n + λ) tv1 + n 1 tv + (n + λ + n 1 ) tv,s ] (n ) t ; n 1 tv1 + (n + λ) tv + (n 1 + n + λ) tv,s ] (n1 ) t After simplifying the value functions, the annuity values can be expressed as rv 1 1 = π 1 + (n + h)(v 1 V 1 1 ); 5. t ;

6 rv,f = max n,f rv = max n { rv1 = r t [ π 1 + (n + h)(v 1 V1 1 ) ] + (1 r t)rv 1 { rv = max (n n + h)(v V ) (n ) ; { [ ] r t (n + h)(v V ) (n ) 1 ; + (1 r t)rv π + n,f (V1 + V,S V,F ) + n,f (V + V,S V,F ) (n,f ; ) ; (1) { [ rv,s = max r t π + (n,s n,s + φ)(v1 + V,S V,F ) + (n,s + φ)(v + V,S () V,F ) (n,s ) ] + (1 r t)rv,f ; { [ rv = max r t π + (n n + λ)(v1 + V,S V,F ) + n 1 (V + V,S V,F ) (3) (n ) ] + (1 r t)rv,f ; { [ rv 1 = max r t π + n 1 (V n V,S V,F ) + (n + λ)(v + V,S V,F (n1 ) ] +(1 r t)rv,f. First-order conditions can be formulated as ) (4) n = V V ; (5) n = V V ; (6) n,f = V 1 + V,S V,F ; (7) n,s = V 1 + V,S V,F ; (8) n = V 1 + V,S V,F ; (9) n 1 = V 1 + V,S V,F. (1) From (5) and (6) we can see that the research intensity of a follower which was a follower in the previous period is the same one of the follower which was neck-and-neck. This is due to the fact that the leader does not innovate and it is not possible to be a follower after innovating, thus the value function of the leader is the same whether it was a leader or neck-and-neck the 6

7 previous period and the value function of the follower is the same whether it was a follower or neck-and-neck the previous period. From (7), (8), (9) and (1); we can also observe that each type of neck-and-neck firms has the same level of research intensity. This is because the knowledge, λ or φ, obtained in the previous period, is independent of the research intensity in the current time, thus it does not affect the marginal decision to research in the actual period. Therefore, notation is simplified as n = n n and n,f = n,s = n = n 1 n. After rearranging, we can see a system of two equations and two variables (the research intensities), which can be written as follows = 1 φ t 1 φ t (V 1 V,F ) φ t,f (V V ) n ; 1 φ t = π 1 (1 δ) t + (1 r t)v,f n t(v 1 V ) + 3 n t + λn t r + h n n r r ; where [ V 1 r + h + n = π 1 (1 δ) π 1(λ t + n ) r(r + h + n ) + (n + λ t)(n + h) r + h + n + 3 n + λn t r V,F = 1 [ {π 1 (1 δ) r + λn t + n r + h rλ t r n r + h + n + n ( n r + n r + h n ) r ] + 3 n + n ( n r + h + n n ) n (n + h) V 1 ; r r r + h + n V 1 = π 1 + (n + h)v 1 ; r + h + n V = n r (n + h). Notice that it is not possible to have analytical solutions for the research intensities n and n. Therefore, I proceed to solve the steady state and then to have a numerical solution for both the research equations and the aggregate flow of innovations. ] ;. Steady state In this model, as we can see in figure 1, there are four different states. The firms can be unleveled with probability µ 1 ; neck-and-neck, having been neck-and-neck and failed to innovate in the previous period, with probability µ,f ; neck-and-neck, having been neck-and-neck and succeeded to innovate in the previous period, with probability µ,s ; and neck-and-neck, having been unleveled in the previous period, with probability µ 1. An unleveled industry can become a neck-and-neck after the follower innovates, thus the outflow is equal to (n + h) tµ 1. Since the state of an unleveled industry can be originated by a neck-and-neck state which was neck-and-neck and failed to innovate in the previous period, 7

8 Figure 1: Steady State a neck-and-neck which was neck-and-neck and succeeded to innovate in the previous period or a neck-and-neck that was unleveled in the previous period, the inflow of this case is given by n tµ,f + (n + φ) tµ,s + (n + λ) tµ 1. A neck-and-neck industry, which was also neck-and-neck and failed to innovate in the previous period, can continue to be neck-and-neck after both firms innovate or become unleveled, thus the outflow is 4n tµ,f. In order to become a neck-and-neck that was neck-and-neck and failed to innovate in the past, industries must have been neck-and-neck, hence the inflow is (n + φ) tµ,s + (n + λ) tµ 1. A neck-and-neck industry, which was neck-and-neck and succeeded to innovate in the previous period, can continue to be neck-and-neck after both fail to innovate or become unleveled, hence the outflows are 4(n +φ) tµ,s. To become a neck-and-neck that was neck-and-neck and succeeded to innovate in the previous period, industries must have been neck-and-neck, thus the inflow is n tµ,f + (n + λ) tµ 1. Finally, a neck-and-neck industry, which was unleveled before, can become to an unleveled or a neck-and-neck state which was neck-and-neck and either succeeded or failed to innovate in the previous period, thus the outflow of this state is 3(n + λ) tµ 1. Since to become a neck-and-neck having been unleveled before can only be produced by an unleveled state, the inflow is (n + h) tµ 1. In the steady state the outflows must be equal to the inflows, thus we have the following 8

9 equations From (11) and (1) we have and from (13) we have that µ 1 (n + h) = n µ,f + (n + φ)µ,s + (n + λ)µ 1 ; 4n µ,f = (n + φ)µ,s + (n + λ)µ 1 ; (11) 4(n + φ)µ,s = n µ,f + (n + λ)µ 1 ; (1) 3(n + λ)µ 1 = (n + h)µ 1. (13) µ,s = n + λ (n + φ) µ1 ; (14) µ,f = n + λ n µ 1 ; (15) µ 1 = 3(n + λ) n + h µ1. (16) From (14), (15), (16) and the fact that in the steady state µ 1 + µ,f + µ,s + µ 1 = 1, we have µ 1 = µ,f = µ,s = µ 1 = 6n (n + φ) n (n + λ)[6(n + φ) + (n + h)] + (n + φ)(n + h)(4n + λ) ; (17) (n + h)(n + φ)(n + λ) n (n + λ)[6(n + φ) + (n + h)] + (n + φ)(n + h)(4n + λ) ; (18) n (n + h)(n + λ) n (n + λ)[6(n + φ) + (n + h)] + (n + φ)(n + h)(4n + λ) ; (19) n (n + φ)(n + h) n (n + λ)[6(n + φ) + (n + h)] + (n + φ)(n + h)(4n + λ). () Since the aggregate flow of innovations (AI) is given by the sum of the outflows, from (17), (18), (19) and () we have AI = (n + φ)(n + h)[3n + (n + λ)(5n + )] n (n + λ)[6(n + φ) + (n + h)] + (n + φ)(n + h)(4n + λ). Replacing the research intensities n and n, we have the aggregate flow of innovations as a function of competition, memory, R&D spillovers and profit parameters. Since the research intensities do not have an analytical solution, subsection.4 shows the relationship between the aggregate flow of innovation and competition, using a numerical solution. 9

10 .3 The memory effect The memory parameters λ and φ have a direct effect over the neck-and-neck s value functions. However, the leader s value function depends on the value function of the neck-and-neck firm which was the leader in the previous period and therefore the memory parameters also have an effect over the leader s value function. Since in this model the knowledge obtained by the innovation process does not affect the marginal research s decision, i.e. n,f = n,s = n = n 1 n ; from equations (1), (), (3) and (4), we can notice that whenever λ = φ =, the annuity value rv,f = rv,s = rv = rv 1. Hence, n = V,F V and n = V 1 V,F, which is equivalent to the ABBGH model. As the knowledge λ obtained by the neck-and-neck firm which was a follower previously gives this firm an advantage to innovate again and earns the monopoly profit, the value V is larger than the value V,F of the neck-and-neck firm which was neck-and-neck and failed to innovate. Therefore, we should expect that the research intensity of the follower n in the memory model would be larger than in the memoryless (or ABBGH) model..4 Innovation and competition relationship In order to solve this model and compare the results with the memoryless model we have to follow the condition identified in ABBGH which satisfies the inverted-u relationship. First, I assume that the leader s profit π 1, the interest rate r and the time interval t are given. It is denoted φ = απ 1, λ = βπ 1, and h = γπ 1. Now, ABBGH define + γ π 1 x 3 + γ π 1, x 1 + γ π 1, x + γ π 1. The inverted-u pattern holds whenever x < x < x. Therefore, in order to construct the benchmark model I assume that α =.8, β =.4, γ =.18, π 1 = 5, r =.1 and t =.1, parameters which satisfy the inverted-u condition. Figure shows the relationship between the aggregate flow of innovations and the competition parameter for both the memory and the memoryless model. Subfigure a exhibits a clear positive relationship between innovation and competition. We can also notice that the aggregate flow of innovations level is higher (at any level of competition) in the memoryless model than in the memory model. As we can see in figure 3, the memory model also shows the Schumpeterian and escapecompetition effects. As displayed in subfigure 3a, more innovation decreases the level of research intensity of the follower firm. However, even at the maximum level of competition the research 1

11 (a) Memory Model (b) Memoryless Model Figure : Innovation and Competition intensity is still much higher than the research intensity of the neck-and-neck firm, as we can see in subfigure 3b. (a) Follower Research Intensity (b) Neck-and-Neck Research Intensity Figure 3: Research Intensity This is because whenever the follower innovates it will be in a better position than its rival when they will be neck-and-neck, since the former follower obtained the memory value λ after innovating while its rival s probability of innovating depends just on the research intensity. Since at any level of competition the research intensity of the follower is much higher than the neck-and-neck research intensity, the follower firm quickly catches up with its rival and the firms will be most of the time neck-and-neck, where the escape-competition effect dominates over the Schumpeterian effect. From ABBGH, the Schumpeterian effect will dominate over the whole interval whenever x x. Therefore, with the same assumptions of the benchmark model but now with γ =., we can see the outcome in figure 4. Although in the memoryless model the Schumpeterian effect 11

12 dominates in the whole interval, in the memory model the relationship between innovation and competition is still positive. (a) Memory Model (b) Memoryless Model Figure 4: Schumpeterian Domination Figure 5 shows the case when the knowledge parameters, λ and φ, increase. The solid line shows the benchmark model when α =.8 and β =.4, while the dash-dot line displays the aggregate flow of innovation when α = β =.5. As we can see in subfigure 5a, the level of the aggregate flow of innovations increases with an increase in the memory. However, there is no perceptible change in the slope of the curve. We can also notice from subfigures 5b and 5c that an increase in the memory parameters increase the research intensity at the unleveled state, but it has almost no effect at the neckand-neck state. As the memory prize increases, the follower firm invest more in R&D since if it innovates the advantage over its rival will be higher, thus the probability to innovate again and become the leader is also higher. (a) Aggregate Flow of Innovations (b) Follower Research Intensity (c) Neck-and-Neck Research Intensity Figure 5: Increasing the Memory 1

13 .5 Robustness of the model In this subsection I check whether the qualitative results of the model are affected by the other parameters. Since this paper studies how competition affects innovation when there is memory in the process, I do not intend to analyze the effect that the other parameters have over the model. Figure 6 shows how the memory model changes when increasing the interest rate. The solid line is the benchmark model (r =.1), while the dash-dot line considers an interest rate of 1%. We can see that there is no qualitative change. (a) Aggregate Flow of Innovations (b) Follower Research Intensity (c) Neck-and-Neck Research Intensity Figure 6: Increasing the Interest Rate Figure 7 shows the case when decreasing the copy rate or R&D spillovers. As the former graphic, the solid line is the benchmark model with γ =.18 and the dash-dot line displays a lower copy rate with γ =.8. We can also see that there is no qualitative change, but this time the slope of the aggregate flow of innovations is higher with a lower copy rate. (a) Aggregate Flow of Innovations (b) Follower Research Intensity (c) Neck-and-Neck Research Intensity Figure 7: Decreasing R&D Spillovers 13

14 3 Empirical Relationship between Innovation and Competition 3.1 Data To perform the empirical model, I use the Correa and Ornaghi (14) database. The dataset is constructed merging firm-level data from Standard & Poor s Compustat and NBER Patent Data Project. Then, the data are merged with industry-level data from BLS, EU KLEMS Growth and Productivity Data, and US International Trade Commission imports data at 4 digits SIC level. These data include 1,359 manufacturing firms, divided across 3 industries, covering the period From Compustat, the data retrieved include sales S, gross capital K, and operating profits OP. Following ABBGH, firm i profitability at time t is defined as where r is the cost of capital. 3 indicating larger profitability. 4 π it = OP it rk it S it, (1) π it can take any value from zero to one, with higher values Competition c jt is computed measured as the unweighted average profitability across all firms in industry j as c jt = 1 1 π it, () n jt where n jt is the number of firms in industry j at time t, with c jt [, 1], and where higher values of index c jt indicates higher competition in the industry. 5 The total number of patents granted by firm i at time of patent application t, P it, is retrieved from the NBER Patent Data Project. 6 In order to capture the quality of patents, I also use citations received by patents. Following ABBGH and Correa and Ornaghi (14), innovation intensity is measured by the simple average number of patents measured as: P jt = 1 P it, i j n jt i j and the average number of patents weighted by citations and constructed as: P CI jt = P jtci jt CI t, where CI jt denotes the average number of citations received by those patents and CI t the average number of citations received by all other patents at the same year. One of the major problems to estimate the effect of competition on innovation when using patents as a measure of innovation and profitability as a measure of competition is the mutual 3 As well as in ABBGH and Correa and Ornaghi (14), I assume that r is equal to It is assumed that π = when firms have negative profits. 5 As in ABBGH and Correa and Ornaghi (14), it is used the unweighted average profitability as it is not possible to observe market share given that many firms in the sample compete in international markets and Compustat covers only publicly traded companies. Since the empirical model includes industry effects, identification comes from variation of profitability measure over time. In this context, the simple average is less sensitive to changes in the sample due to attrition, i.e., entry and exit of firms. 6 See Hall et al. (1) for more information about the patent data and Correa and Ornaghi (14) about the financial and patent information merge procedure. The NBER Patent Data Project gives information until 6. However, since both patents and citations are affected by a truncation problem as they reach the last years of the data, as in Correa and Ornaghi (14), I use patents and citations until year 1. 14

15 causality. As well as in Correa and Ornaghi (14), I use tariff rates and productivity indices of EU countries as instruments to address this problem. Tariff rates T jt are computed as the ratio of the import duties collected by US authorities divided by the (free-on-board) value of imports in each industry. I also use Canada and Mexico specific tariff rates, denote as T Can,jt and T Mex,jt, respectively. Industry productivity statistics of EU countries consist on labor productivity for France LP F ra, jt and Germany LP Ger, jt. 3. Defining memory and memoryless innovation processes As shown in the previous section, the theoretical model predicts a positive relationship between innovation and competition when innovation follows a memory process, while the relationship can be positive, negative or inverted-u when the innovation process is memoryless. In order to test this prediction, it is necessary to identify the type of process of each industry. Since Hausman et al. (1984) find that the negative binomial specification allows for overdispersion, a problem which may arise when using a Poisson regression, it is employed an autoregressive model with drift and year trend, estimating the negative binomial regression { k P jt = exp ς j + λ j t j + ς js P j,t s + ε jt, where ς j is the drift for industry j, t j is the time trend of industry j and P j,t s is the patent variable at the s lag. Following Hayashi () to determine the memory in each industry, the sequential rule is used to test s=1 H : ς jk =, (4) H 1 : otherwise. The test begins with k = 5 (five-lags model). After testing significance of the last lag, it is dropped if not significant and the test is repeated recursively until j = 1. If the null hypothesis is rejected at least for one lag at 5% significance level, the industry is defined as memory process. There are 77 memory process industries and 146 memoryless process industries. Among the research intensive memory industries we can identify: Chemicals and Allied Products (8), and Aircraft and Parts (37); while among the research intensive memoryless industries we can identify: Computer and Office Equipment (357), and Electronic and Other Electrical Equipment (36). 15

16 3.3 Innovation and competition relationship As in ABBGH and Correa and Ornaghi (14), I assume that the innovation process is a function of competition such that, I jt = exp β + β 1 c jt + β c jt + φˆv jt + α j D j + γ t D t + u jt, (5) j t where I jt is specified by either the patents vector P jt or the patents weighted by citations vector P CI jt, ˆv denotes the vector of residuals from the regression of competition c jt on instruments T jt, T Can,jt, T Mex,jt, LP F ra, jt, and LP Ger, jt. The sums represent industry and time effects respectively. Given the mutual causality problem between innovation and competition, and that it is assumed a non-linear relationship between innovation and competition, I use the control function approach. I propose the following first stage for this approach c jt = ζ T jt +ζ 1 T Can,jt +ζ T Mex,jt +ζ 3 LP F ra, jt+ζ 4 LP Ger, jt+ j ψ j D j + t φ t D t +v jt, (6) where the residual v captures any variation in competition that is not explained by the instruments, and the industry and time effects. Table 1 displays the outcome of the first-stage regression defined in equation (6). The sixth column of of table 1 shows the F -statistic of the joint hypothesis that the coefficients instruments are equal to zero. Since the F -statistic is 1.5, it satisfies the Staiger and Stock (1997) condition to rule out the problem of weak instruments. I also perform a Hansen test, giving a J-statistic of 1.87, failing to reject the null hypothesis that the instruments are exogenous at any conventional level of significance. Table 1: Competition and Instruments Tariff Tariff Rate Tariff Rate LP LP F -statistic Observations Rate Canada Mexico Growth Growth (Growth) (Lag) (Lag) Germany France (.31) (.688) (.71) (.5) (.5) 1.5 [.] 3,633 Industry and time effects are included. Robust standard errors are given in parentheses. () significant at the 1% level. P -values are given in square brackets. The Hansen J-statistic computed in a linear model fails to reject the null hypothesis that instruments are valid (J-statistic=1.87 and p-value=.74). Following Hausman et al. (1984), I perform a negative binomial regression for equation (5). In the case of negative binomial regressions I use random industry effects, since the negative binomial regression with a large number of fixed effects may drive inconsistent estimators. The outcome of these regressions is displayed in table. The seventh column of this table shows the χ -statistic of the joint hypothesis that both competition and competition squared coefficients 16

17 are equal to zero. We can notice that in the case of the memory sample, the null hypothesis is rejected at any conventional level of significance for any specification. However, in the case of the memoryless sample, the null hypothesis is failed to be rejected when using patents and instrumental variables. Memory Table : Innovation and Competition Competition Competition Control Industry Year χ -statistic Observations Squared Function Effects Effects P Yes Yes ,383 (4.357) (.5565) [.4] P Yes Yes 41. 1,383 (5.34) (.8636) (1.945) [.] P CI Yes Yes ,383 (5.784) (.9789) [.1] P CI Yes Yes ,383 Memoryless (5.939) (3.651) (.639) [.] P Yes Yes 6.37,354 ( ) (1.178) [.414] P Yes Yes 4.,354 ( ) (1.6161) (4.645) [.1356] P CI Yes Yes 15.7,354 (1.9993) (1.43) [.5] P CI Yes Yes 8.,354 Standard errors in parentheses. (.1176) ( ) (3.6187) [.165] Figure 8 shows that for the memory sample the relationship between innovation and competition is monotonically positive either using patents or patents weighted by citations. Therefore, we can see the innovation-competition relationship follows a similar pattern than the theoretical memory model, where the escape-competition effect dominates in the whole interval. Figure 9 shows the innovation and competition relationship for the memoryless sample. Although that figure 9b show a positive relationship between innovation and competition, we already know that there is no statistically significant relationship between innovation and competition for that specification, since the χ -statistic when testing the joint hypothesis that both competition and competition squared coefficients are equal to zero is 4.. In the case of the other specifications, there is always an inverted-u relationship between innovation and competition as predicted by the memoryless model. 17

18 (a) Patents (b) Patents IV (c) PCI (d) PCI IV Figure 8: Innovation and Competition - Memory. Figures 9a and 9b refer to patents, and figures 9c and 9d refer to citation-weighted patents. Figures 9a and 9c refer to estimates without including the control function ˆv, and figures 9b and 9d show the competition-innovation relationship when including the control function ˆv. 4 Conclusions This paper analyzes the relationship between innovation and competition when the research activity follows a memory process. We have seen that whenever memory is assumed, there is a positive relationship between innovation and competition. A follower firm has very high incentive to innovate, even in a highly competitive environment, since the memory obtained after innovating increases its probability to innovate again and become a leader. Therefore, industries will be most of the time neck-and-neck where the escape-competition effect dominates. We have also seen that empirical evidence supports this positive relationship when considering that industries follow a memory process. However, in the case of industries which follow a memoryless process, we do not find this positive relationship but an inverted-u relationship as predicted by some theoretical models. Both this paper s and ABBGH models assume that the leader cannot stay more than one step ahead of its rival. One extension for this model is to assume that the leader can be more than one step ahead from the follower, but binding the distance to a certain level. One the 18

19 (a) Patents (b) Patents IV (c) PCI (d) PCI IV Figure 9: Innovation and Competition - Memoryless. Figures 9a and 9b refer to patents, and figures 9c and 9d refer to citation-weighted patents. Figures 9a and 9c refer to estimates without including the control function ˆv, and figures 9b and 9d show the competition-innovation relationship when including the control function ˆv. assumption of this paper is that knowledge obtained through innovating is independent from the current period s research, thus this knowledge does not affect the marginal decision to invest in research. If this assumption is modified, the research intensities of the neck-and-neck who was leader, the neck-and-neck who was follower, neck-and-neck who failed to innovate and neck-andneck who succeeded to innovate in the previous period, will be different. It would be interesting to test whether this modification changes the outcome of the model. 19

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