Network Formation with Local Complements and Global Substitutes: - PowerPoint PPT Presentation

Network Formation with Local Complements and Global Substitutes: The Case of R&D Networks joint with Chih-Sheng Hsieh and Xiaodong Liu Department of Economics Vrije Universiteit Amsterdam † Department of Spatial Economics, VU Amsterdam, Netherlands. ‡ Centre for Economic Policy Research (CEPR), United Kingdom. § ETH Zurich, Swiss Economic Institute (KOF), Switzerland. 1/57 Michael D. König † , ‡ , § 26 th September 2018

Introduction to understand: Networks R&D collaborations , technology spillovers Behavior R&D expenditures , production choices 2/57 ▶ The many aspects that are governed by networks make it critical ▶ how networks impact behaviour (and vice versa), ▶ which network structures are likely to emerge , and ▶ how they afgect welfare in the society. ▶ We make three interrelated contributions to address these questions: (i) theory , (ii) econometrics and (iii) policy .

Contribution: Theory by making the network in Ballester at al. (ECMA, 2006) endogenous. consistent with the data. tend to be under-connected (with R&D policy implications). 1 A network exhibits nestedness if the neighborhood of a node is contained in the neighborhoods of the nodes with higher degrees. See e.g. König et al. (TE, 2014). 3/57 ▶ We provide the fjrst analytic characterization of both, ▶ equilibrium networks and ▶ endogenous production choices, ▶ Equilibrium networks are particular nested structures, 1 while the fjrms’ output levels and degrees follow a Pareto distribution , ▶ Our effjciency analysis further reveals that equilibrium networks

Contribution: Econometrics endogeneity of both, the network structure and (either continuous or discrete) action choices. 2 2 This generalizes previous works such as Mele (ECMA, 2017), where only the formation of the network was considered. 4/57 ▶ We provide the fjrst estimation framework that can handle the ▶ The analytic characterization allows us to design an estimation algorithm that can handle large network datasets . ▶ We estimate the model using a unique dataset on R&D collaborations matched to fjrm’s balance sheets and patents.

Contribution: Policy and identify the fjrm whose exit would have the largest impact; endogenizing Ballester at al. (ECMA, 2006). concentration). be subsidized . 3 3 E.g. EUREKA’s total subsidies for cooperative R&D accumulated to more than €37 billion in 2015. 5/57 ▶ We provide the fjrst (R&D) policy analysis with an endogenous network structure. ▶ The policy relevance is demonstrated with 3 examples: ▶ Shocks/Exit : We perform a dynamic key player analysis, ▶ Mergers & Acquisitions : We determine which mergers lead to welfare losses or gains (through effjcient R&D ▶ R&D Subsidies : We identify which collaborations should

Related Literature 2014 TE Belhaj et al. no competition/ no characterization endogenous 2017 WP Hiller random link decay no competition/ no linking cost endogenous TE endogenous König et al. Jackson none endogenous 2016 WP Chandrasekhar & none endogenous 2017 2017 no competition/ no characterization Authors Economic MS...Management Science, WP...Working Paper. Statistics, Applied of AAS...Annals Economics, of Journal RAND...RAND Behavior, and Snijders no characterization binary choice/ no competition / endogenous 2017 WP Badev no competition/ no characterization endogenous 2001 AAS ECMA Mele none 2014 2016 MS Bimpikis et al. endogenous exogenous 2014 GEB Belhaj et al. endogenous exogenous AER endogenous Bramoullé et al. endogneous exogenous 2006 ECMA Ballester et al. Action/Behavior Network Year Journal a exogenous endogneous König et al. WP 2010 RAND Westbrock none endogenous 2003 GEB Goyal & Joshi Moraga-Gonzalez endogenous exogenous c 2001 RAND Goyal & Jacquemin endogneous exogenous b 1988 AER D’Aspremont & endogneous exogenous 2015 6/57 a Note: ECMA...Econometrica, AER...American Economic Review, TE...Theoretical Economics, GEB...Games b An endogenous network is considered restricted to 2 fjrms. c An endogenous network is considered restricted to 4 fjrms.

The Model (1) (2) 7/57 ▶ The inverse demand for fjrm i producing quantity q i is ∑ p i = a − q i − b q j . j ̸ = i ▶ A fjrm i can reduce marginal costs c i by investing e i into R&D, or by benefjting from the R&D investment e j of its collaboration partner j : n ∑ c i = ¯ c i − αe i − β 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 .

8/57 collaboration. 4 Cf. Cohen & Klepper (EJ, 1996). (3) (4) Eq. (1) into Eq. (3) gives ▶ Firm i ’s profjt π i is then given by π i ( q , e , G ) = ( p i − c i ) q i − γe 2 i − ζd i , where γe 2 i is the cost of R&D, γ > 0 , and ζ ≥ 0 is a fjxed cost of ▶ Inserting marginal cost from Eq. (2) and inverse demand from n ∑ ∑ c i ) q i − q 2 a ij e j − γe 2 π i ( q , e , G ) = ( a − ¯ i − bq i q j + αq i e i + βq i i . j ̸ = i j =1 ▶ The FOC with respect to R&D efgort e i yields e i = λq i , 4 with α λ = 2 γ .

9/57 own concavity 5 Cf. Ballester et al. (ECMA, 2006). (6) local complementarity global substitutability (5) becomes 5 ▶ Denoting by η = a − ¯ c i , ν = 1 + λ ( λγ − α ) and ρ = λβ , Eq. (4) n n ∑ ∑ π i ( q , G ) = η i q i − νq 2 − bq i − ζd i . q j + ρq i a ij q j i � �� � j ̸ = i j =1 � �� � � �� � ▶ Proposition: The profjt function of Eq. (5) admits a potential function Φ: R n + × G n → R given by n n n n i ) − b q i q j + ρ ∑ ∑ ∑ ∑ ∑ ( η i q i − νq 2 Φ( q , G ) = a ij q i q j − ζm 2 2 i =1 i =1 i =1 j =1 j ̸ = i where m is the number of links in G .

Cournot Best Response Dynamics (links/output) arrive as a Poisson process. 6 (1838): 7 collaborations of the other fjrms as given (myopic). 8 6 Similar to Calvo models of pricing (Calvo, JME, 1983). 7 See Cournot (1838) and Daughety (2005). 8 Cf. Jackson & Watts (JET, 2002). 9 Cf. Kelly et al. (RDM, 2002) and Czarnitzki et al. (JIO, 2015). 10/57 ▶ We consider a Markov chain, where opportunities for change ▶ We follow the best response dynamics analyzed in Cournot ▶ Firms maximize profjts by taking the output levels and ▶ As R&D projects and collaborations are fraught with uncertainty , 9 we also introduce noise in this decision process.

consisting of one) of the following events happens: 11/57 ▶ The evolution is characterized by a sequence ( ω t ) t ∈ R + , ω t ∈ Ω , ▶ a vector of fjrms’ output levels q t ∈ Q n and ▶ a network of collaborations G t ∈ G n . ▶ Then, in a short time interval [ t, t + ∆ t ) , t ∈ R + , one (and only ▶ output adjustment , ▶ link formation or ▶ link removal .

Output Adjustment (7) Anderson et al., GEB, 2001, and McFadden, 1976). maximizing output level. 12/57 ▶ At rate χ > 0 a fjrm i receives an output adjustment opportunity. ▶ The profjt of fjrm i from choosing an output level q ∈ Q is then given by π i ( q, q − i , G ) + ε it . ▶ When ε it is i.i. type-I extreme value distributed with parameter ϑ , then 10 P ( ω t +∆ t = ( q, q − it , G t ) | ω t = ( q t , G t )) = e ϑπ i ( q, q − it ,G t ) χ Q e ϑπ i ( q ′ , q − it ,G t ) dq ′ ∆ t + o (∆ t ) , ∫ ▶ When ϑ → ∞ the noise vanishes and the fjrm chooses the profjt 10 That is a multinomial logistic function with choice set Q and parameter ϑ (cf.

Link Formation receives an opportunity to form a link. profjtable: 11 11 We have used the fact that 13/57 ▶ With rate λ > 0 a pair of fjrms ij which is not already connected ▶ The formation of a link depends on the marginal profjts plus a logistically distributed error term ε ij,t . ▶ The link ij is created is created only if both fjrms fjnd this P ( ω t +∆ t = ( q t , G t + ij ) | ω t − 1 = ( q , G t )) = λ P ( { π i ( q t , G t + ij ) + ε ij,t > π i ( q t , G t ) } ∩{ π j ( q t , G t + ij ) + ε ij,t > π j ( q t , G t ) } ) ∆ t + o (∆ t ) e ϑ Φ( q t ,G t + ij ) = λ e ϑ Φ( q t ,G t + ij ) + e ϑ Φ( q t ,G t ) ∆ t + o (∆ t ) . π i ( q t , G t + ij ) − π i ( q t , G t ) = π j ( q t , G t + ij ) − π j ( q t , G t ) = Φ( q t , G t + ij ) − Φ( q t , G t ) .

Link Removal opportunity to terminate their collaboration. 12 We have used the fact that 14/57 ▶ With rate ξ > 0 a pair of connected fjrms ij receives an ▶ The marginal profjts from removing the link ij are perturbed by a logistically distributed error term ε ij,t . ▶ The link ij is removed if at least one fjrm fjnds this profjtable: 12 P ( ω t +∆ t = ( q t , G t − ij ) | ω t = ( q , G t )) = ξ P ( { π i ( q t , G t − ij ) + ε ij,t > π i ( q t , G t ) } ∪{ π j ( q t , G t − ij ) + ε ij,t > π j ( q t , G t ) } ) ∆ t + o (∆ t ) e ϑ Φ( q t ,G t − ij ) = ξ e ϑ Φ( q t ,G t − ij ) + e ϑ Φ( q t ,G t ) ∆ t + o (∆ t ) . π i ( q t , G t − ij ) − π i ( q t , G t ) = π j ( q t , G t − ij ) − π j ( q t , G t ) = Φ( q t , G t − ij ) − Φ( q t , G t ) .