R&D Networks: Theory, Empirics and Policy Implications Michael - PowerPoint PPT Presentation

R&D Networks: Theory, Empirics and Policy Implications Michael D. König, Xiaodong Liu and Yves Zenou NBER SI 2016 Innovation 19 th July 2016

Motivation R&D policy (network design, subsidies) in such networked Economics 113.2 (1998), pp. 331–360. . The Quarterly Journal of 2 Martin L. Weitzman. “Recombinant Growth” patterns since 1960” 1 John Hagedoorn. “Inter-fjrm R&D partnerships: an overview of major trends and markets. change and economic growth, there is no comprehensive study of technological domains. 2 knowledge of other fjrms that are specialized in difgerent technology and they tend to combine their knowledge with the with rapid technological development. 1 characterizing technological dynamics, especially in industries 2/30 ▶ R&D partnerships have become a widespread phenomenon ▶ Firms have become more specialized on specifjc domains of a ▶ Despite the importance of R&D collaborations for technological . Research Policy 31.4 (2002), pp. 477–492.

Contribution fjrms jointly form R&D collaborations to lower their production costs while competing on the product market. an effjciency analysis and determine the optimal R&D subsidy program that maximizes welfare. R&D collaborations and annual company reports. programs, and study how temporal changes in the network afgect the optimal R&D policy. 3/30 ▶ We study a structural model of R&D alliance networks where ▶ We provide a complete Nash equilibrium characterization, derive ▶ We then structurally estimate our model using a unique panel of ▶ We use our estimates to analyze the impact of R&D subsidy

The Model by (2) (1) n 4/30 R&D as well as by establishing an R&D collaboration with another fjrm. ▶ Firms can reduce their costs for production by investing into ▶ The amount of this cost reduction depends on the efgort e i that a fjrm i and the efgort e j that its R&D collaboration partners j ∈ N i invest into the collaboration. ▶ Given the efgort level e i ∈ R + , marginal cost c i of fjrm i is given ∑ c i = ¯ c i − e i − φ a ij e j , j = 1 where a ij = 1 if fjrms i and j set up a collaboration (0 otherwise) and a ii = 0. ▶ The inverse demand function for fjrm i is ∑ p i = ¯ α i − q i − ρ q j , j ∈M m , j ̸ = i

5/30 n 2 e 2 duopoly with spillovers” 3 C. D’Aspremont and A. Jacquemin. “Cooperative and noncooperative R&D in whether fjrms i and j operate in the same market. 2 e 2 (4) (3) 2 e 2 from Equation (2) into Equation (3) gives n ▶ We assume that R&D efgort is costly. In particular, the cost of R&D efgort is an increasing function and given by Z = 1 i . 3 Firm i ’s profjt π i is then given by π i = ( p i − c i ) q i − 1 i . ▶ Inserting marginal cost from Equation (1) and inverse demand ∑ ∑ π i = (¯ α i − ¯ c i ) q i − q 2 i − ρ b ij q i q j + q i e i + φ q i a ij e j − 1 i , j = 1 j = 1 where b ij ∈ { 0 , 1 } is the ij -th element of the matrix B indicating . The American Economic Review 78.5 (1988), pp. 1133–1137.

Equilibrium Characterization n 106.437 (1996), pp. 925–951. . The Economic Journal 4 W.M. Cohen and S. Klepper. “A reprise of size and R&D” c i ). where (5) 6/30 n ▶ From the FOC with respect to R&D efgort, ∂π i ∂ e i = q i − e i = 0, we fjnd that e i = q i . 4 ▶ From the FOC with respect to output, ∂π i ∂ q i = 0, we obtain ∑ ∑ q i = µ i − ρ b ij q j + φ a ij q j , j = 1 j = 1 ▶ ρ ∑ n j = 1 b ij q j is the product rivalry efgect, ▶ φ ∑ n j = 1 a ij q j is technology (or knowledge) spillover efgect, ▶ µ i ≡ ¯ α i − ¯ c i is the ex ante heterogeneity in terms of fjrms α i ) and markets ( ¯ ( ¯

7/30 and (8) output levels given by (7) (6) ▶ Let λ PF ( A ) be the largest eigenvalue of A and denote by µ = min { µ i | i ∈ N} and µ = max { µ i | i ∈ N} , with µ < µ . ▶ If ( { }) − 1 ρ + φ < max λ PF ( A ) , m = 1 ,..., M { ( |M m | − 1 ) } max ρ m = 1 ,..., M { ( |M m | − 1 ) } < 1 − φλ PF ( A ) , max hold, then there exists a unique interior Nash equilibrium with q = ( I n + ρ B − φ A ) − 1 µ .

8/30 Journal of Sociology 92.5 (1987), pp. 1170–1182. there exists a unique interior Nash equilibrium with output levels given by . American 1 5 Phillip Bonacich. “Power and Centrality: A Family of Measures” of walks of length k in G between i and j . defjned by φ ▶ Assume that there is only a single market and let ϕ ≡ 1 − ρ . Then ( ) ρ ∥ b µ ( G , ϕ ) ∥ 1 q = b µ ( G , ϕ ) − 1 + ρ ( ∥ b u ( G , ϕ ) ∥ 1 − 1 ) b u ( G , ϕ ) , (9) 1 − ρ where b µ ( G , ϕ ) is the µ -weighted Katz-Bonacich centrality 5 ∞ ∑ b µ ( G , ϕ ) = ( I n − ϕ A ) − 1 µ = ϕ k A k µ . k = 0 ▶ The coeffjcient a [ k ] ij in the ( i , j ) element of A k counts the number

Example 1 3 2 1 0 0 0 0 0 1 0 1 0 0 0 9/30 0 given by 1 R&D collaboration, and fjrm 1 and 2 operate in the same market 1 1 0 0 the competition matrix B are ▶ Consider an industry composed of 3 fjrms and 2 sectors, M 1 and M 2 , where fjrm 1 and 2, as well as fjrm 1 and fjrm 3 have an M 1 . ▶ Then the adjacency matrix A and M 2    ,  A =   M 1   . B =

1 2 Bloom et al. 2013). the technology spillover efgect and the product rivalry efgect (cf. 10/30 3 1.4 M 2 1.2 Π 3 1.0 Π 0.8 Π 1 0.6 Π 2 0.4 M 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Ρ ▶ Firm 1 enjoys higher profjts due to having the largest number of R&D collaborations when competition is weak (small ρ ), but its profjts are falling with increasing ρ , becoming smaller than the profjts of fjrm 3 if ρ > φ . ▶ This result highlights the key trade ofg faced by fjrms between

The R&D Subsidy Program n and Industrial Strategy” pp. 313–345; Barbara J. Spencer and James A. Brander. “International R & D Rivalry . De Economist 149.3 (2001), 6 J. Hinloopen. “Subsidizing R&D Cooperatives” the social planner’s problem is given by 2 e 2 11/30 2001, 2003; Spencer, 1983) 6 ▶ An active government is introduced that can provide a (potentially fjrm specifjc) subsidy, s i ≥ 0, per unit of R&D. ▶ The profjt of fjrm i can then be written as (cf. e.g. Hinloopen, ∑ ∑ π i = µ i q i − q 2 i − ρ q i b ij q j + q i e i + φ q i a ij e j − 1 i + s i e i . (10) j ̸ = i j = 1 ▶ If we defjne net welfare as W ( G , s ) ≡ W ( G , s ) − ∑ n i = 1 e i s i , then s ∗ = arg max s ∈ R n + W ( G , s ) . . The Review of Economic Studies 50.4 (1983), pp. 707–722.

Optimal Subsidies R is 2 B given by positive defjnite, the optimal subsidy levels (in the fjrst stage) are 2 B 12/30 that can set subsidy rates on R&D efgort (fjrst stage) in a period before the fjrms spend on R&D (second stage). ▶ The government (or the planner) is here introduced as an agent ▶ The unique interior Nash equilibrium with targeted subsidies (in the second stage) is given by q = ˜ q + Rs , where R = M ( I n + φ A ) , ˜ q = M µ , equilibrium efgorts are given by e i = q i + s i and profjts are given by π i = ( q 2 i + s 2 i ) / 2. ( I n − R ⊤ ( )) I n + ρ ▶ Further, if the matrix H ≡ I n + 2 H + H ⊤ ) − 1 ( 2 R ⊤ ( ) ) ( I n + ρ s ∗ = 2 − I n ˜ q .

Empirical Implications – Data Thomson SDC and MERIT-CATI databases. 7 agreements, including any alliance that involves some arrangements for mutual transfer of technology or joint research, such as joint research pacts, joint development agreements, cross licensing, R&D contracts, joint ventures and research corporations. from Standard & Poor’s Compustat U.S. fundamentals database, and Burea Van Dijk’s Osiris database. 7 M.A. Schilling. “Understanding the alliance data” . Strategic Management Journal 30.3 (2009), pp. 233–260. issn : 1097-0266. 13/30 ▶ For the purpose of estimating our model we use the combined ▶ This database contains information about strategic technology ▶ We use annual data about balance sheets and income statements

Figure: The largest connected component of the R&D collaboration network with all links accumulated until the year 2005. 14/30

Empirical Implications - Estimation n econometrician) characteristics of the fjrms. time-invariant characteristics of the fjrms, and (11) 15/30 Equation (1) at period t has a fjxed cost equal to ▶ Our empirical counterpart of the marginal cost c it of fjrm i from c it = η ∗ ¯ i − ϵ it − x it β , so that ∑ c it = η ∗ i − ε it − β x it − e it − φ a ij , t e jt , j = 1 ▶ x it is a measure for the productivity of fjrm i , ▶ η ∗ i captures the unobserved (to the econometrician) ▶ ε it (i.i.d.) captures the remaining unobserved (to the α m − η ∗ ▶ Denote by κ t ≡ ¯ α t and η i ≡ ¯ i , where κ t captures a time fjxed efgect due to exogenous demand shifters while η i , which α m and η ∗ includes both ¯ i , captures a fjrm fjxed efgect .