An Introduction to Social and EconomicNetworks

Lecture 6

Michael D. Konig

University of ZurichDepartment of Economics

12–13 June 2017

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Policy Implications

▶ R&D Collaboration Networks▶ Social vs. Private Returns of R&D▶ Subsidizing R&D Efforts and Collaborations▶ Deregulation, Tax Benefits for Start-Ups and Cost of Entry

▶ Team Production and Coauthorship Networks▶ Rankings of Authors and Departments▶ Optimal Research Funding

▶ Networks in Conflict▶ Alliances and Rivalries between Militant Groups▶ Rent Dissipation and the Cost of War▶ Weapons Embargoes, Bilateral Reconciliation and Targeting of Groups

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R&D Networks: Theory, Empirics andPolicy Implications3

▶ R&D partnerships have become a widespread phenomenoncharacterizing technological dynamics, especially in industries withrapid technological development.1

▶ Firms have become more specialized on specific domains of atechnology and they tend to combine their knowledge with theknowledge of other firms that are specialized in different technologicaldomains.2

▶ Despite the importance of R&D collaborations for technological changeand economic growth, there is no comprehensive study of R&D policy(network design, subsidies) in such networked markets.

1John Hagedoorn. “Inter-firm R&D partnerships: an overview of major trends and patternssince 1960”. Research Policy 31.4 (2002), pp. 477–492.

2Martin L. Weitzman. “Recombinant Growth”. The Quarterly Journal of Economics 113.2(1998), pp. 331–360.

3Michael D. Konig, Xiaodong Liu, and Yves Zenou. “R&D Networks: Theory, Empirics andPolicy Implications”. CEPR Discussion Paper No. 9872 (2014).

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Contribution

▶ We study a structural model of R&D alliance networks where firmsjointly form R&D collaborations to lower their production costs whilecompeting on the product market.

▶ We provide a complete Nash equilibrium characterization, derive anefficiency analysis and determine the optimal R&D subsidy programthat maximizes welfare.

▶ We then structurally estimate our model using a unique panel of R&Dcollaborations and annual company reports.

▶ We use our estimates to analyze the impact of R&D subsidy programs,and study how temporal changes in the network affect the optimalR&D policy.

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The Model

▶ Firms can reduce their costs for production by investing into R&D aswell as by establishing an R&D collaboration with another firm.

▶ The amount of this cost reduction depends on the effort ei that a firmi and the effort ej that its R&D collaboration partners j ∈ Ni investinto the collaboration.

▶ Given the effort level ei ∈ R+, marginal cost ci of firm i is given by

ci = ci − ei − φ

n∑j=1

aijej , (1)

where aij = 1 if firms i and j set up a collaboration (0 otherwise) andaii = 0.

▶ The inverse demand function for firm i is

pi = αi − qi − ρ∑

j∈Mm,j =i

qj , (2)

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▶ We assume that R&D effort is costly. In particular, the cost of R&Deffort is an increasing function and given by Z = 1

2e2i .

4 Firm i’s profitπi is then given by

πi = (pi − ci)qi −1

2e2i . (3)

▶ Inserting marginal cost from Equation (1) and inverse demand fromEquation (2) into Equation (3) gives

πi = (αi − ci)qi − q2i − ρ

n∑j=1

bijqiqj + qiei + φqi

n∑j=1

aijej −1

2e2i , (4)

where bij ∈ {0, 1} is the ij-th element of the matrix B indicatingwhether firms i and j operate in the same market.

4C. D’Aspremont and A. Jacquemin. “Cooperative and noncooperative R&D in duopolywith spillovers”. The American Economic Review 78.5 (1988), pp. 1133–1137.

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Equilibrium Characterization

▶ From the FOC with respect to R&D effort, ∂πi∂ei

= qi − ei = 0, we find

that ei = qi.5

▶ From the FOC with respect to output, ∂πi∂qi

= 0, we obtain

qi = µi − ρ

n∑j=1

bijqj + φ

n∑j=1

aijqj , (5)

where

▶ ρ∑nj=1 bijqj is the product rivalry effect,

▶ φ∑nj=1 aijqj is technology (or knowledge) spillover effect,

▶ µi ≡ αi − ci is the ex ante heterogeneity in terms of firms (αi) andmarkets (ci).

▶ Then there exists a unique interior Nash equilibrium given by

q = (In + ρB− φA)−1µ. (6)

5W.M. Cohen and S. Klepper. “A reprise of size and R&D”. . The Economic Journal106.437 (1996), pp. 925–951.

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▶ Assume that there is only a single market and let ϕ ≡ φ1−ρ . Then there

exists a unique interior Nash equilibrium with output levels given by

q =1

1− ρ

(bµ (G,ϕ)− ρ∥bµ (G,ϕ) ∥1

1 + ρ(∥bu (G,ϕ) ∥1 − 1)bu (G,ϕ)

), (7)

where bµ(G,ϕ) is the µ-weighted Katz-Bonacich centrality6 defined by

bµ (G,ϕ) = (In − ϕA)−1 µ =∞∑k=0

ϕkAkµ.

▶ The coefficient a[k]ij in the (i, j) element of Ak counts the number of

walks of length k in G between i and j.

6Phillip Bonacich. “Power and Centrality: A Family of Measures”. American Journal ofSociology 92.5 (1987), p. 1170.

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Example

▶ Consider an industry composed of 3 firms and 2 sectors, M1 and M2,where firm 1 and 2, as well as firm 1 and firm 3 have an R&Dcollaboration, and firm 1 and 2 operate in the same market M1.

▶ Then the adjacency matrix A andthe competition matrix B are givenby

A =

0 1 11 0 01 0 0

,

B =

0 1 01 0 00 0 0

.1 2

3

M1

M2

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1 2

3

M1

M2 Π3

Π1

Π2

0.0 0.1 0.2 0.3 0.4 0.5 0.60.4

0.6

0.8

1.0

1.2

1.4

Ρ

Π

▶ Firm 1 enjoys higher profits due to having the largest number of R&Dcollaborations when competition is weak (small ρ), but its profits arefalling with increasing ρ, becoming smaller than the profits of firm 3 ifρ > φ.

▶ This result highlights the key trade off faced by firms between thetechnology spillover effect and the product rivalry effect (cf. Bloom etal. 2013).

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The R&D Subsidy Program

▶ An active government is introduced that can provide a (potentiallyfirm specific) subsidy, si ≥ 0, per unit of R&D.

▶ The profit of firm i can then be written as (cf. e.g. Hinloopen, 2001,2003; Spencer, 1983)7

πi = µiqi − q2i − ρqi∑j =i

bijqj + qiei + φqi

n∑j=1

aijej −1

2e2i + siei. (8)

▶ If we define net welfare as W (G, s) ≡W (G, s)−∑ni=1 eisi, then the

social planner’s problem is given by

s∗ = argmaxs∈Rn+W (G, s).

7J. Hinloopen. “Subsidizing R&D Cooperatives”. De Economist 149.3 (2001), pp. 313–345;Barbara J. Spencer and James A. Brander. “International R & D Rivalry and IndustrialStrategy”. The Review of Economic Studies 50.4 (1983), pp. 707–722.

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Optimal Subsidies

▶ The government (or the planner) is here introduced as an agent thatcan set subsidy rates on R&D effort (first stage) in a period before thefirms spend on R&D (second stage).

▶ The unique interior Nash equilibrium with targeted subsidies (in thesecond stage) is given by q = q+Rs, where R = M (In + φA),q = Mµ, equilibrium efforts are given by ei = qi + si and profits aregiven by πi = (q2i + s2i )/2.

▶ Further, if the matrix H ≡ In + 2(In −R⊤ (In + ρ

2B))

R is positivedefinite, the optimal subsidy levels (in the first stage) are given by

s∗ =2(H+H⊤

)−1 (2R⊤

(In +

ρ

2B)− In

)q.

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Empirical Implications – Data

▶ For the purpose of estimating our model we use the combinedThomson SDC and MERIT-CATI databases.8

▶ This database contains information about strategic technologyagreements, including any alliance that involves some arrangements formutual transfer of technology or joint research, such as joint researchpacts, joint development agreements, cross licensing, R&D contracts,joint ventures and research corporations.

▶ We use annual data about balance sheets and income statements fromStandard & Poor’s Compustat U.S. fundamentals database, and BureaVan Dijk’s Osiris database.

8M.A. Schilling. “Understanding the alliance data”. Strategic Management Journal 30.3(2009), pp. 233–260. issn: 1097-0266.

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Figure: The largest connected component of the R&D collaboration network with alllinks accumulated until the year 2005.

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Empirical Implications - Estimation

▶ Our empirical counterpart of the marginal cost cit of firm i fromEquation (1) at period t has a fixed cost equal to cit = η∗i − ϵit − xitβ,so that

cit = η∗i − εit − βxit − eit − φ

n∑j=1

aij,tejt, (9)

▶ xit is a measure for the productivity of firm i,▶ η∗i captures the unobserved (to the econometrician) time-invariant

characteristics of the firms, and▶ εit (i.i.d.) captures the remaining unobserved (to the econometrician)

characteristics of the firms.

▶ Denote by κt ≡ αt and ηi ≡ αm − η∗i , where κt captures a time fixedeffect due to exogenous demand shifters while ηi, which includes bothαm and η∗i , captures a firm fixed effect.

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▶ The econometric equivalent to the best response output level is

qit = φ

n∑j=1

aij,tqjt − ρ

n∑j=1

bijqjt + βxit + ηi + κt + ϵit, (10)

with an i.i.d. error term ϵit.

▶ Output qit is calculated using sales divided by country-year-industryprice deflators from the OECD-STAN database.

▶ The exogenous variable xit is the firm’s time-lagged R&D stock using aperpetual inventory method with a 15% depreciation rate,9 with R&Dtax credits as instruments.

▶ Equation (10) corresponds to a high-order Spatial Auto-Regressive(SAR) model with two spatial lags Atqt and Bqt.

10

9Bronwyn H Hall, Adam B Jaffe, and Manuel Trajtenberg. “Market value and patentcitations: A first look”. National Bureau of Economic Research, Working Paper No. w7741(2000).

10L. Lee and X. Liu. “Efficient GMM estimation of high order spatial autoregressive modelswith autoregressive disturbances”. Econometric Theory 26.1 (2010), pp. 187–230.

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Simultaneity of Product Quantities

▶ We use instrumental variables when estimating our outcome Equation(10) to deal with the issue of simultaneity of qit and qjt.

▶ We instrument∑nj=1 aij,tqjt by the time-lagged total R&D stock of all

firms with an R&D collaboration with firm i, i.e.∑nj=1 aij,txjt, and

instrument∑nj=1 bijqjt by the time-lagged total R&D stock of all firms

that operate in the same industry as firm i, i.e.∑nj=1 bijxjt.

▶ To allow for potential correlation in unobservables across firms (e.g.from unobserved R&D subsidies), the standard deviation of the IVestimator is estimated by the spatial heteroskedasticity andautocorrelation consistent (HAC) estimator.11

11Harry H. Kelejian and Ingmar R. Prucha. “HAC estimation in a spatial framework”.Journal of Econometrics 140.1 (2007), pp. 131–154.

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Endogeneity of the R&D Stock

▶ To deal with the potential endogeneity of the time-lagged R&D stock,we use supply side shocks from tax-induced changes to the user cost ofR&D to construct instrumental variables for R&D expenditures as inBloom et al. (2013).12

▶ Let wit denote the time-lagged R&D tax credit firm i received at timet− 1.

▶ We then instrument qa,it by the time-lagged total R&D tax credits ofall firms with an R&D collaboration with firm i, i.e.

∑nj=1 aij,twjt,

instrument qb,it by the time-lagged total R&D tax credits of all firmsthat operate in the same industry as firm i, i.e.

∑nj=1 bijwjt, and

instrument the time-lagged R&D stock xit by the time-lagged R&Dtax credit wit.

12Nicholas Bloom, Mark Schankerman, and John Van Reenen. “Identifying technologyspillovers and product market rivalry”. Econometrica 81.4 (2013), pp. 1347–1393.

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Endogenous Network Formation

▶ At is endogenous if there exists an unobservable factor that affectsboth the output, qit and the R&D alliance, aij,t.

▶ If the unobservable factor is firm-specific, then it is captured by thefirm fixed-effect ηi.

▶ If the unobservable factor is time-specific, then it is captured by thetime fixed-effect κt.

▶ However, it may still be that there are some unobservable firm-specificfactors that do vary over time and that affect the propensity of R&Dcollaborations and thus make the matrix At = [aij,t] endogeneous.

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▶ We consider IVs based on the predicted R&D alliance matrix, i.e.AtXt.

13

▶ We obtain the predicted link-formation probability aij,t from thelogistic regression of aij,t on:

▶ whether firms i and j collaborated before time t− s, where s is theduration of an alliance,

▶ whether firms i and j shared a common collaborator before time t− s,▶ the time-lagged technological proximity14 of firms i and j represented by

Pij,t−s and P 2ij,t−s,

▶ whether firms i and j are are in the same market, and▶ whether firms i and j are located in the same city.

13Harry H. Kelejian and Gianfranco Piras. “Estimation of spatial models with endogenousweighting matrices, and an application to a demand model for cigarettes”. Regional Scienceand Urban Economics 46 (2014), pp. 140–149.

14Adam B. Jaffe. “Technological Opportunity and Spillovers of R & D: Evidence from Firms’Patents, Profits, and Market Value”. The American Economic Review 76.5 (1986), pp.984–1001; Nicholas Bloom, Mark Schankerman, and John Van Reenen. “Identifying technologyspillovers and product market rivalry”. Econometrica 81.4 (2013), pp. 1347–1393.

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We then use the following step-wise procedure to estimate our model:15

▶ Step 1: Estimate a logistic link formation model. Use theestimated model to predict links. Denote the predicted adjacencymatrix by At and its elements by aij,t.

▶ Step 2: Estimate the outcome Equation (10) using∑nj=1 aij,txjt

and∑nj=1 bijxjt as IVs for

∑nj=1 aij,tqjt and

∑nj=1 bij,tqjt,

respectively.

15Cf. Harry H. Kelejian and Gianfranco Piras. “Estimation of spatial models withendogenous weighting matrices, and an application to a demand model for cigarettes”.Regional Science and Urban Economics 46 (2014), pp. 140–149; Bryan S. Graham. “Methods ofIdentification in Social Networks”. Annual Review of Economics 7.1 (2015), pp. 465–485.

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Estimation Results

Table: (Step 2) Parameter estimates from a panelregression of Equation (10) with IVs based on time-laggedtax credits. Model A includes only time fixed effects, whileModel B includes both firm and time fixed effects. Thedependent variable is output obtained from deflated sales.The estimation is based on the observed alliances in the years1967–2006.

Model A Model B

φ -0.0133 (0.0114) 0.0128* (0.0069)ρ 0.0182*** (0.0018) 0.0156** (0.0076)β 0.0054*** (0.0004) 0.0023*** (0.0006)# firms 1186 1186# observations 16924 16924Wald F 138.311 78.791

firm fixed effects no yestime fixed effects yes yes

*** Statistically significant at 1% level.** Statistically significant at 5% level.* Statistically significant at 10% level.

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Table: (Step 1) Link formation regression results.Technological similarity, fij , is measured using eitherthe Jaffe or the Mahalanobis patent similaritymeasures. The dependent variable aij,t indicates ifan R&D alliance exists between firms i and j at timet. The estimation is based on the observed alliancesin the years 1967–2006.

technological similarity Jaffe Mahalanobis

Past collaboration 0.5980*** 0.5922***(0.0150) (0.0149)

Past common collaborator 0.1161*** 0.1166***(0.0238) (0.0236)

fij,t−s−1 13.6120*** 6.0518***(0.6896) (0.3322)

f2ij,t−s−1 -20.1916*** -3.8699***

(1.7420) (0.4623)cityij 1.1299*** 1.1403***

(0.1017) (0.1017)marketij 0.8450*** 0.8559***

(0.0424) (0.0422)# observations 3,964,120 3,964,120

McFadden’s R2 0.0812 0.0813

*** Statistically significant at 1% level.** Statistically significant at 5% level.* Statistically significant at 10% level.

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R&D Subsidies – Welfare Impact

1990 1995 2000 2005year

0

0.5

1

1.5

2

2.5

3

3.5

W(G

,s∗)−

W(G

)W

(G)

[%]

1990 1995 2000 2005year

0

20

40

60

80

W(G

,s∗)−

W(G

)W

(G)

[%]

Figure: (Left panel) The percentage increase in welfare due to a homogeneoussubsidy, s∗, over time. (Right panel) The percentage increase in welfare due to(firm specific) targeted subsidies, s∗, over time.

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R&D Subsidies RankingsTable: Subsidies ranking for the year 1990 for the first 25 firms.

Firm Share [%]a num pat. d vPF Betweennessb Closenessc q [%] hom. sub. [%]d tar. sub. [%]e SICf Rank

General Motors Corp. 9.2732 76644 88 0.1009 0.0007 0.0493 6.9866 0.0272 0.3027 3711 1Exxon Corp. 7.7132 21954 22 0.0221 0.0000 0.0365 5.4062 0.0231 0.1731 2911 2Ford Motor Co. 7.3456 20378 6 0.0003 0.0000 0.0153 3.7301 0.0184 0.0757 3711 3AT&T Corp. 9.5360 5692 8 0.0024 0.0000 0.0202 3.2272 0.0156 0.0565 4813 4Chevron 2.8221 12789 23 0.0226 0.0001 0.0369 2.5224 0.0098 0.0418 2911 5Texaco 2.9896 9134 22 0.0214 0.0000 0.0365 2.4965 0.0095 0.0415 2911 6Lockheed 42.3696 2 51 0.0891 0.0002 0.0443 1.5639 0.0035 0.0196 3760 7Mobil Corp. 4.2265 3 0 0.0000 0.0000 0.0000 1.9460 0.0111 0.0191 2911 8TRW Inc. 5.3686 9438 43 0.0583 0.0002 0.0415 1.4509 0.0027 0.0176 3714 9Altria Group 43.6382 0 0 0.0000 0.0000 0.0000 1.4665 0.0073 0.0117 2111 10Alcoa Inc. 11.4121 4546 36 0.0287 0.0002 0.0372 1.2136 0.0032 0.0114 3350 11Shell Oil Co. 14.6777 9504 0 0.0000 0.0000 0.0000 1.4244 0.0073 0.0109 1311 12Chrysler Corp. 2.2414 3712 6 0.0017 0.0000 0.0218 1.3935 0.0075 0.0109 3711 13Schlumberger Ltd. Inc. 25.9218 9 18 0.0437 0.0000 0.0370 1.1208 0.0029 0.0099 1389 14Hewlett-Packard Co. 7.1106 6606 64 0.1128 0.0002 0.0417 1.1958 0.0047 0.0093 3570 15Intel Corp. 9.3900 1132 67 0.1260 0.0003 0.0468 1.0152 0.0018 0.0089 3674 16Hoechst Celanese Corp. 5.6401 516 38 0.0368 0.0002 0.0406 1.0047 0.0021 0.0085 2820 17Motorola 14.1649 21454 70 0.1186 0.0004 0.0442 1.0274 0.0028 0.0080 3663 18PPG Industries Inc. 13.3221 24904 20 0.0230 0.0000 0.0366 0.9588 0.0021 0.0077 2851 19Himont Inc. 0.0000 59 28 0.0173 0.0001 0.0359 0.8827 0.0014 0.0072 2821 20GTE Corp. 3.1301 4 0 0.0000 0.0000 0.0000 1.1696 0.0067 0.0070 4813 21National Semiconductor Corp. 4.0752 1642 43 0.0943 0.0001 0.0440 0.8654 0.0012 0.0068 3674 22Marathon Oil Corp. 7.9828 202 0 0.0000 0.0000 0.0000 1.1306 0.0060 0.0068 1311 23Bellsouth Corp. 2.4438 3 14 0.0194 0.0000 0.0329 1.0926 0.0060 0.0064 4813 24Nynex 2.3143 26 24 0.0272 0.0001 0.0340 0.9469 0.0049 0.0052 4813 25

a Market share in the primary 4-digit SIC sector in which the firm is operating. In case of missing data the closest year with sales data available has beenused.

b The normalized betweenness centrality is the fraction of all shortest paths in the network that contain a given node, divided by (n−1)(n−2), the maximumnumber of such paths.

c The closeness centrality of node i is computed as 2n−1

∑nj=1 2

−ℓij(G), where ℓij(G) is the length of the shortest path between i and j in the network G

(Dangalchev, 2006), and the factor 2n−1

is the maximal centrality attained for the center of a star network.d The homogeneous subsidy for each firm i is computed as e∗i s

∗, relative to the average homogeneous subsidy 1ns∗∑nj=1 e

∗j .

e The targeted subsidy for each firm i is computed as e∗i s∗i , relative to the average targeted subsidy 1

n

∑nj=1 e

∗js

∗j .

f The primary 4-digit SIC code of a firm in the database.

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Table: Subsidies ranking for the year 2005 for the first 25 firms.

Firm Share [%]a num pat. d vPF Betweennessb Closenessc q [%] hom. sub. [%]d tar. sub. [%]e SICf Rank

General Motors Corp. 3.9590 90652 19 0.0067 0.0002 0.0193 4.1128 0.0174 0.2186 3711 1Ford Motor Co. 3.6818 27452 7 0.0015 0.0000 0.0139 3.4842 0.0153 0.1531 3711 2Exxon Corp. 4.0259 53215 6 0.0007 0.0001 0.0167 2.9690 0.0132 0.1108 2911 3Microsoft Corp. 10.9732 10639 62 0.1814 0.0020 0.0386 1.6959 0.0057 0.0421 7372 4Pfizer Inc. 3.6714 74253 65 0.0298 0.0034 0.0395 1.6796 0.0069 0.0351 2834 5AT&T Corp. 0.0000 16284 0 0.0000 0.0000 0.0000 1.5740 0.0073 0.0311 4813 6Motorola 6.6605 70583 66 0.1598 0.0017 0.0356 1.3960 0.0053 0.0282 3663 7Intel Corp. 5.0169 28513 72 0.2410 0.0011 0.0359 1.3323 0.0050 0.0249 3674 8Chevron 2.2683 15049 10 0.0017 0.0001 0.0153 1.3295 0.0058 0.0243 2911 9Hewlett-Packard Co. 14.3777 38597 7 0.0288 0.0000 0.0233 1.1999 0.0055 0.0183 3570 10Altria Group 20.4890 5 2 0.0000 0.0000 0.0041 1.1753 0.0054 0.0178 2111 11Johnson & Johnson Inc. 3.6095 31931 40 0.0130 0.0015 0.0346 1.1995 0.0051 0.0173 2834 12Texaco 0.0000 10729 0 0.0000 0.0000 0.0000 1.0271 0.0055 0.0124 2911 13Shell Oil Co. 0.0000 12436 0 0.0000 0.0000 0.0000 0.9294 0.0045 0.0108 1311 14Chrysler Corp. 0.0000 5112 0 0.0000 0.0000 0.0000 0.9352 0.0052 0.0101 3711 15Bristol-Myers Squibb Co. 1.3746 16 35 0.0052 0.0009 0.0326 0.8022 0.0034 0.0077 2834 16Merck & Co. Inc. 1.5754 52036 36 0.0023 0.0007 0.0279 0.8252 0.0038 0.0077 2834 17Marathon Oil Corp. 5.5960 229 0 0.0000 0.0000 0.0000 0.7817 0.0039 0.0076 1311 18GTE Corp. 0.0000 5 0 0.0000 0.0000 0.0000 0.7751 0.0041 0.0073 4813 19Pepsico 36.6491 991 0 0.0000 0.0000 0.0000 0.7154 0.0035 0.0066 2080 20Bellsouth Corp. 0.9081 2129 0 0.0000 0.0000 0.0000 0.7233 0.0039 0.0063 4813 21Johnson Controls Inc. 22.0636 304 11 0.0027 0.0001 0.0159 0.6084 0.0021 0.0063 2531 22Dell 18.9098 80 2 0.0190 0.0000 0.0216 0.6586 0.0028 0.0061 3571 23Eastman Kodak Co 5.5952 109714 17 0.0442 0.0001 0.0262 0.6171 0.0023 0.0060 3861 24Lockheed 48.9385 9817 44 0.0434 0.0003 0.0223 0.6000 0.0028 0.0049 3760 25

a Market share in the primary 4-digit SIC sector in which the firm is operating. In case of missing data the closest year with sales data available hasbeen used.

b The normalized betweenness centrality is the fraction of all shortest paths in the network that contain a given node, divided by (n − 1)(n − 2), themaximum number of such paths.

c The closeness centrality of node i is computed as 2n−1

∑nj=1 2

−ℓij(G), where ℓij(G) is the length of the shortest path between i and j in the network G

(Dangalchev, 2006), and the factor 2n−1

is the maximal centrality attained for the center of a star network.d The homogeneous subsidy for each firm i is computed as e∗i s

∗, relative to the average homogeneous subsidy 1ns∗∑nj=1 e

∗j .

e The targeted subsidy for each firm i is computed as e∗i s∗i , relative to the average targeted subsidy 1

n

∑nj=1 e

∗js

∗j .

f The primary 4-digit SIC code of a firm in the database.

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Figure: The transition matrix Tij from the rank i in year t to the rank j in yeart+ 1 for the homogeneous subsidies ranking (left panel) and the targeted subsidiesranking (right panel) for the first 100 ranks.

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Summary & Conclusion

▶ We have developed a model where firms jointly form R&Dcollaborations (networks) to lower their production costs whilecompeting on the product market.

▶ We have identified the positive externalities in the network throughtechnology spillovers and the negative externalities of product rivalryfrom market competition.

▶ Using a panel of R&D alliances and annual reports, we have tested ourtheoretical results and showed that the magnitude of the technologyspillover effect is much higher than that of the product rivalry effect(i.e. net returns to R&D collaborations are strictly positive).

▶ Finally, we identified the firms that should be subsidised the most, andwe have drawn some policy conclusions about optimal R&D subsidiesfrom the results obtained over different sectors, as well as theirtemporal variation.

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Team Production and CoauthorshipNetworks17

▶ We build a micro-founded model for the output produced in scientificco-authorship networks.16

▶ Differently to previous works, we are able to characterize the interiorequilibrium when multiple agents spend effort in multiple, possiblyoverlapping projects, and there are interaction effects in the cost ofeffort.

▶ The equilibrium solution then allows us to study the impact ofindividual researchers on total research output (ranking), and theoptimal design of research funding programs.

16Coralio Ballester, Antoni Calvo-Armengol, and Yves Zenou. “Who’s Who in Networks.Wanted: The Key Player”. Econometrica 74.5 (2006), pp. 1403–1417; Antonio Cabrales,Antoni Calvo-Armengol, and Yves Zenou. “Social interactions and spillovers”. Games andEconomic Behavior 72.2 (2011), pp. 339–360; Matthew O. Jackson and Asher Wolinsky. “AStrategic Model of Social and Economic Networks”. Journal of Economic Theory 71.1 (1996),pp. 44–74.

17Hsieh Chih-Sheng et al. “Superstar Economists: Coauthorship networks and researchoutput”. Mimeo, University of Zurich (2013).

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▶ We develop a novel estimation framework in which agents canparticipate in many potentially overlapping projects, and thisparticipation is endogenously modelled.

▶ The allocation of agents into different projects is determined by amatching process that depends on both, the authors’ and projects’characteristics,18 while the effort levels are determined in the Nashequilibrium.

▶ We estimate this model using data for the network of scientificcoauthorships between economists registered in the Research Papers inEconomics (RePEc) author service.19

18Arun Chandrasekhar. “Econometrics of network formation”. In: The Oxford Handbook ofthe Economics of Networks. 2015, pp. 303–357; A. Chandrasekhar and M. Jackson. “Tractableand Consistent Random Graph Models”. Available at SSRN 2150428 (2012).

19http://repec.org/

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▶ We develop a novel ranking measure (for economists and theirdepartments) that quantifies the endogenous decline in research outputdue to the removal of an economist from the network (“key players”,“superstar” economists).20

▶ We find that the highest ranked authors are not necessarily the oneswith the largest number of citations, or coincide with other rankingmeasures used in the literature.

▶ However, this discrepancy is not surprising, as traditional rankings aretypically not derived from microeconomic foundations, and do not takeinto account the spillover effects generated in scientific knowledgeproduction networks.

20Yves Zenou. “Key Players”. Oxford Handbook on the Economics of Networks, Y. Bramoulle,B. Rogers and A. Galeotti (Eds.), Oxford University Press (2015); Fabian Waldinger. “Peereffects in science: evidence from the dismissal of scientists in Nazi Germany”. The Review ofEconomic Studies 79.2 (2012), pp. 838–861; Pierre Azoulay, Joshua Graff Zivin, andJialan Wang. “Superstar Extinction”. The Quarterly Journal of Economics 125.2 (2010),pp. 549–589.

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▶ Our model further allows us to solve an optimal research fundingproblem of a planner who wants to maximize total scientific output byintroducing research grants into the author’s payoff function.21

▶ A comparison of our optimal funding policy with the National ScienceFoundation (NSF) indicates that there are significant differences, bothat the individual and the departmental levels (e.g. NSF awards areuncorrelated with the number of coauthors).

▶ Our results highlight the importance of the coauthorship network indetermining the optimal funding policy, while it does not seem to havean effect on the research funding program by the NSF.

21Paula E Stephan. “The economics of science”. Journal of Economic literature (1996),pp. 1199–1235; Paula E. Stephan. How economics shapes science. Harvard University Press,2012.

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Production Function

▶ Assume that there are s ∈ P = {1, . . . , p} research projects (papers)and i ∈ N = {1, . . . , n} researchers (authors).

▶ Let the production function for project s be given by

Ys(G, es) =∑i∈Ns

αieis +β

2

∑i∈Ns

∑j∈Ns\{i}

eisejs, (11)

▶ where eis ≥ 0 is the research effort of agent i in project s, Ns ⊆ N isthe set of agents participating in project s, es is the stacked vector ofauthors’ effort levels participating in project s,

▶ αi ≥ 0 is the ability/skill of researcher i and

▶ β is a spillover parameter from complementarities between the researchefforts of coauthors.

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Payoffs

▶ The payoff of agent i is then given by

πi(G, e) =

p∑s=1

Ys(G, es)δis −1

2

p∑s,s′=1

ϕs,s′eiseis′δisδis′ (12)

where ns = |Ns| is the number of agents participating in project s, andwe have that ns =

∑ni=1 δis with δis ∈ {0, 1} indicating whether i is

participating in project s.

▶ This cost is convex if and only if the p× p matrix ϕ with elements ϕs,s′

is positive definite.

▶ The case of a quadratic cost includes the case of a convex total cost asa special case when ϕs,s′ = γ, and the case of a convex separable costwhen ϕs,s′ = γδs,s′ .

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Equilibrium Characterization

▶ Proposition Let the payoff function for each agent i = 1, . . . , n begiven by Equation (12), assume that

ϕss′ =

{γ, if s′ = s,

ρ, otherwise.

and let Γ be the symmetric (n× p)× (n× p) matrix with elements

Γis,jk =

ρδisδjk, if i = j, s = k,

−βδisδjk, if i = j, s = k,

0, otherwise,

(13)

with zero diagonal for i, j = 1, . . . , n, and s, k = 1, . . . , p. Further let δbe an (n× p) stacked vector with elements δis, α an (n× p) stackedvector with elements αis = αiδis and e an (n× p) stacked vector ofagent-project effort levels, eis. Then if the matrix γ diag(δ) + Γ isinvertible, the equilibrium effort levels are given by

e = (γ diag(δ) + Γ)−1 α. (14)

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Line Graph

▶ Definition: Given a graph G, its line graph L(G) is a graph such thateach node of L(G) represents an edge of G, and two nodes of L(G) areadjacent if and only if their corresponding edges share a commonendpoint in G.22

▶ The matrix Γ represents a weighted matrix of the line graph L(G) ofthe bipartite collaboration network G, where

▶ each link between nodes sharing a project has weight −β, and▶ each link between nodes sharing an author has weight ρ.

22Cf. e.g. Douglas B. West. Introduction to Graph Theory. 2nd. Prentice-Hall, 2001.

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Example

1 2 3

1 2

e11 e21 e12 e321

(e11e12

)

2(e210

)

3

2

(0e32

)

1

2

Figure: (Left panel) The bipartite collaboration network G of authors andprojects, where round circles represent authors and squares represent projects.(Right panel) The projection of the bipartite network G on the set of coauthors.

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e11 e12 e32

e21

−β

−βρ

Figure: The line graph L(G) of Equation (13) associated with the collaborationnetwork G, in which each node represents the effort an author invests intodifferent projects. Solid lines indicate nodes sharing a project while dashed linesindicate nodes with the same author.

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▶ The payoffs of the agents are given by

π1 = e11

(α1 +

β

2e21

)+ e21

(α2 +

β

2e11

)+ e12

(α1 +

β

2e32

)+ e32

(α3 +

β

2e12

)− γ

2e211 −

γ

2e212 − ρe11e12

π2 = e11

(α1 +

β

2e21

)+ e21

(α2 +

β

2e11

)− γ

2e221

π3 = e12

(α1 +

β

2e32

)+ e32

(α3 +

β

2e12

)− γ

2e232.

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▶ The matrix Γ with elements Γis,jk from Equation (13) is given by

Γ =

0 ρ −β 0 0 0ρ 0 0 0 0 −β−β 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 −β 0 0 0 0

.

▶ From Equation (14) we have that (γ diag(δ) + Γ) e = α, that is

γ 0 0 0 0 00 γ 0 0 0 00 0 γ 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 γ

+

0 ρ −β 0 0 0ρ 0 0 0 0 −β−β 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 −β 0 0 0 0

e11e12e21e22e31e32

=

α1

α1

α2

00α3

.

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▶ Computing the inverse, e = (γ diag(δ) + Γ)−1 α, then gives

e11 =(β − γ)(β + γ)(α2β + α1γ) + γ(α3β + α1γ)ρ

γ2ρ2 − (β2 − γ2)2,

e12 =(β − γ)(β + γ)(α3β + α1γ) + γ(α2β + α1γ)ρ

γ2ρ2 − (β2 − γ2)2,

e21 =(β − γ)(β + γ)(α1β + α2γ) + β(α3β + α1γ)ρ+ α2γρ

2

γ2ρ2 − (β2 − γ2)2,

e32 =(β − γ)(β + γ)(α1β + α3γ) + β(α2β + α1γ)ρ+ α3γρ

2

γ2ρ2 − (β2 − γ2)2. (15)

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e12

e11

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.2

0.4

0.6

0.8

1.0

β

e11,e

12

e12

e12

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.2

0.4

0.6

0.8

1.0

β

e11,e

12

Figure: Equilibrium effort levels from Equation (15) for agent 1 with α1 = 0.2,α2 = 0.1, α3 = 0.9, ρ = 0.05 (left panel), ρ = 0.25 (right panel) and γ = 1. Thedashed lines indicate the effort level for β = 0.

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Superstars, Key Players and Rankings

▶ We analyze the impact of the removal of individual authors from thecoauthorship network on overall scientific output.23

▶ The key author is defined by

i∗ ≡ argmaxi∈N

{p∑s=1

Ys(G)−p∑s=1

Ys(G−i)

}. (16)

▶ Further, aggregating researchers to their departments D ⊂ N allows usto compute the key department as

D∗ ≡ argmaxD⊂N

{p∑s=1

Ys(G)−p∑s=1

Ys(G\D)

}. (17)

23Fabian Waldinger. “Quality matters: The expulsion of professors and the consequences forPhD student outcomes in Nazi Germany”. Journal of Political Economy 118.4 (2010),pp. 787–831.

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Research Funding

▶ We consider a two-stage game:

▶ In the first stage, the planner announces the research fundingscheme z ∈ Rn+ that the authors should receive, and

▶ in the second stage the authors choose their research efforts, givenz.

▶ The optimal funding profile z∗ can then be found by backwardinduction.

▶ Consider the second stage. We assume that agent i ∈ N receivesresearch funding, zi ≥ 0, proportional to the output she generates:

πi(G, e, z) =

p∑s=1

Ys(G, es)δis−1

2

p∑s,s′=1

ϕs,s′eiseis′δisδis′+

p∑s=1

Ys(G, es)ziδis︸ ︷︷ ︸research funding

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▶ In the special case that all researchers obtain the same funding peroutput produced, one can show that the planner has to solve thefollowing problem (first stage)

z∗ = argmaxz∈R≥0

(

p∑s=1

Ys(G, z)︸ ︷︷ ︸total output

−n∑i=1

p∑s=1

δiszYs(G, z)︸ ︷︷ ︸total cost

), (18)

▶ where Ys(G, z) is the output of project s from Equation (11) witheffort levels given by Equation (14).

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Data

▶ The data used for this study makes extensive use of the metadataassembled by the Research Papers in Economics (RePEc) authorservice initiative and its various projects.24

▶ RePEc assembles the information about publications relevant toeconomics from 1900 publishers, including all major commercialpublishers and university presses, policy institutions and pre-printsfrom academic institutions.

▶ At the time of this writing, this encompasses 2.2 million records,including 0.75 million for pre-prints.

▶ We take the publication profiles of economists registered with theRePEc Author Service (49,000 authors), that includes what they havepublished and where they are affiliated.25

24http://repec.org/25https://authors.repec.org/

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▶ We get information about their advisors, students and alma mater, asrecorded in the RePEc Genealogy project.26

▶ We gather in which mailing lists the papers have been disseminatedthrough the NEP project.27 The latter have human editorsdetermining to which field new working papers belong.

▶ We make use of paper download data that is made available by theLogEc project.28

▶ We use citations to the papers and articles as extracted by the CitEcproject.29

▶ We use journal impact factors, author and institution rankings fromIDEAS.30

▶ We make use of the “Ethnea” tool at the University of Illinois toestablish the ethnicity of authors based on the first and last names.31

26https://genealogy.repec.org/27https://nep.repec.org/28http://logec.repec.org/29http://citec.repec.org/30https://ideas.repec.org/top/. For a detailed description of the factors and rankings, see

Zimmermann (2013).31http://abel.lis.illinois.edu/cgi-bin/ethnea/search.py

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Figure: The collaboration network among authors in the RePEc databaseconsidering only coauthored projects and dropping projects with zero impactfactor. A nodes’ size and shade indicates its degree.

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Estimating the Production Function

▶ Suppose there are n authors and p papers. Following Equation (11),the production function of paper s, with s = 1, . . . , p, is given by

Ys =

n∑i=1

δi,sei,sαi +β

2

n∑i=1

n∑j=1,j =i

δi,sδj,sei,sej,s + ϵs, (19)

▶ where δi,s is an indicator variable such that δi,s = 1 if author iparticipates in paper s and δi,s = 0 otherwise, ei,s is the effort ofauthor i put into paper s,

▶ αi is a measure of the productivity of author i which may be modelledby λxi with xi denotes a (k × 1)-vector of author characteristics, and

▶ ϵs is a project-specific random shock.

▶ The econometrician observes Ys, xi, and δi,s, but not ei,s and ϵs.

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Matching Process

▶ A problem with directly estimating Equation (19) is the potentialendogeneity of D.

▶ To address this endogeneity problem, we model the endogenousmatching process of author i to paper s by

δi,s = 1{ψi,s+ui,s>0},

where ψi,s denotes the matching quality between author i and paper sand ui,s is a random component.32

▶ We assume thatψi,s = c′i,sγ1 + γ2µi + γ3κs,

▶ where ci,s denotes a h× 1 vector of dyad-specific regressors, which is tocapture the homophily effect between the pair of author i and paper s.

▶ The variable µi represents author i’s unobserved characteristic; and κsrepresents paper s’s unobserved characteristic.

32Arun Chandrasekhar. “Econometrics of network formation”. In: The Oxford Handbook ofthe Economics of Networks. 2015, pp. 303–357; A. Chandrasekhar and M. Jackson. “Tractableand Consistent Random Graph Models”. Available at SSRN 2150428 (2012).

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▶ From the RePEc data we know the research field to reflect thesimilarity between authors and projects.

▶ We further treat the author in the project who ranks the highest inRePEc as the main author of the project, and construct the variableci,s between the main author s and author i according to theirsimilarities in

▶ gender,

▶ ethnicity,

▶ research fields, and

▶ whether they have an advisor-advisee relationship.

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▶ Assuming ui,s is i.i.d. type-I extreme value distributed, we obtain alogistic regression model for the matching process33:

logit(δi,s) = c′i,sγ1 + γ2µi + γ3κs. (20)

▶ The production function of Eq. (19) is

Ys =

n∑i=1

δi,sei,sαi+β

2

n∑i=1

n∑j=1,j =i

δi,sδj,sei,sej,s+κsη+vs, vs ∼ N (0, σ2v),

(21)where author’s productivity αi can be modelled by λxi + µiρ.

▶ The joint probability function of Y = (Y1, · · · , Yp) and D is

P (Y,D|x, c) =∫µ

∫κ

P (Y|D,x, c, µ, κ)P (D|c, µ, κ)f(µ)f(κ)dµdκ,

(22)

from which we can estimate the parameters θ = (β, ϕ, γ, λ, η, ρ) withthe author and paper latent variables, µ = (µ1, · · · , µn) andκ = (κ1, · · · , κp).

33Graham2014.

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Table: Estimation results.

Coauthored subsample Full sample

Model (I) Model (II) Model (I) Model (II)

Matching

Constant – -7.7896∗∗∗ – -9.1930∗∗∗

(0.1842) (0.1671)Same NEP – 0.5412∗∗∗ – 0.3494∗∗∗

(0.0562) (0.1175)Ethnicity – 1.1658∗∗∗ – 3.4429∗∗∗

(0.1441) (0.0857)Affiliation – 7.2436∗∗∗ – 7.0167∗∗∗

(0.4373) (0.4493)Gender – 0.0211 – 1.6455∗∗∗

(0.1737) (0.1482)Advisor-advisee – 7.5256∗∗∗ – 7.2347∗∗∗

(0.2462) (0.2126)Author effect – 1.0104∗∗∗ – 0.8884∗∗∗

(0.0801) (0.1991)Project effect – 0.0168 – -0.0046

(0.0818) (0.0504)

Sample size 773 1745

Note: Model (1) assumes an exogenous matching between authors andpapers, while Model (2) allows for an endogenous matching accordingto Equation (20).

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▶ Similarity of gender, ethnicity, and particularly the affiliation of thelead researcher and coauthors make collaborations more likely.34

▶ Similarities in the NEP fields apositively and significantly affectcollaborations.35

▶ Being in a Ph.D. advisor–advisee relationship also largely contributesto collaborations.

▶ The author’s latent variable shows a positively significant effect on theauthor-project matching.

34Richard B Freeman and Wei Huang. “Collaborating with people like me: Ethniccoauthorship within the United States”. Journal of Labor Economics 33.S1 (2015), S289–S318.

35Lorenzo Ductor. “Does Co-authorship Lead to Higher Academic Productivity?” OxfordBulletin of Economics and Statistics (2014).

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Table: Estimation results.

Coauthored subsample Full sample

Model (1) Model (2) Model (1) Model (2)

Output

β 0.6446∗∗∗ 0.6371∗∗∗ 0.6442∗∗∗ 0.6323∗∗∗

(0.0053) (0.0061) (0.0097) (0.0091)ϕ -0.0031 0.0032 -0.0018 -0.0107

(0.0037) (0.0052) (0.0056) (0.0060)Constant -1.4114∗∗∗ -0.9087∗∗∗ -1.3613∗∗∗ -1.3615∗∗∗

(0.2996) (0.1848) (0.4480) (0.2596)Log life-time citations 0.3838∗∗∗ 0.2174∗∗∗ 0.3738∗∗∗ 0.3283∗∗∗

(0.0541) (0.0403) (0.0789) (0.0565)Years after graduation -0.2334∗∗∗ -0.0881 -0.2051 -0.3804

(0.0870) (0.0768) (0.1414) (0.2650)Gender 0.3391∗∗ 0.2325 0.3428 0.2401

(0.1625) (0.1977) (0.2782) (0.2673)NBER connection 0.1942 0.9356∗∗∗ 0.2162 0.2850

(0.1202) (0.1480) (0.2070) (0.2314)Ivy League connection 0.2782∗∗∗ 0.0912 0.2271 0.3755∗∗

(0.1055) (0.1245) (0.1843) (0.1725)ρ – 0.8769∗∗∗ 1.3744∗∗∗

(0.0575) (0.0528)η – -1.0368 0.8087

(0.8525) (0.5770)

Sample size 773 1745

Note: Model (1) assumes an exogenous matching between authors and papers,while Model (2) allows for an endogenous matching according to Equation (20).

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▶ The spillover effect of efforts between coauthors (β), and thecongestion effect between projects (ϕ) have the expected signs,although only β is a significant predictor.

▶ Comparing Models (1) and (2), there exists an upward bias in thespillover effect β from assuming network exogeneity,

▶ Lifetime citations are a positive and significant predictor of researchoutput, and so is the female dummy (exogenous network case).

▶ Being affiliated with the NBER positively and significantly impactsresearch output.

▶ Having attended an Ivy League university also positively affects output(exogenous network case).

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Rankings for Individuals

Table: Ranking of the top-twenty five researchers.

Rank Name Projects Citations RePEc Ranka Output Lossb Institute

1 Reinhart, Carmen M. 5 17907 18 -12.04% Kennedy School of Government, Harvard University2 Bloom, Nicholas 11 3668 220 -11.93% Department of Economics, Stanford University3 van Reenen, John Michael 12 5835 79 -11.90% London School of Economics4 Rogoff, Kenneth S 5 20195 9 -11.82% Department of Economics, Harvard University5 Falk, Armin 4 4611 329 -10.43% Center for Economics and Neuroscience, University of Bonn6 Dohmen, Thomas Johannes 4 1951 1145 -10.42% Department of Economics, University of Bonn7 Schmitt-Groh, Stephanie 6 3534 499 -10.08% Department of Economics, Columbia University8 Uribe, Marti 6 4401 363 -10.07% NBER, Columbia University9 Angrist, Joshua D 6 7982 55 -9.85% Economics Department, MIT10 Black, Sandra E. 5 2681 585 -9.77% Department of Economics, University of Texas-Austin11 Demirguc-Kunt, Asli 4 8820 107 -9.73% Economics Research, World Bank Group12 Clark, Andrew 5 4926 365 -9.66% Paris School of Economics13 Coibion, Olivier 6 680 1821 -9.62% Department of Economics, University of Texas-Austin14 Devereux, Paul J. 5 1575 1152 -9.58% School of Economics, University College Dublin15 Huizinga, Harry P. 3 2172 778 -9.57% School of Economics, Tilburg University16 Reis, Ricardo 2 2279 409 -9.49% London School of Economics17 Mankiw, N. Gregory 2 11931 42 -9.49% Department of Economics, Harvard University18 Acemoglu, Daron 4 16324 5 -9.46% Economics Department, MIT19 Senik, Claudia 6 803 2935 -9.41% Paris School of Economics20 Gorodnichenko, Yuriy 4 1740 518 -9.36% Department of Economics, University of California-Berkeley21 Pischke, Jorn-Steffen 5 2756 550 -9.32% London School of Economics22 Wolfers, Justin 4 2598 658 -9.32% Economics Department, University of Michigan23 Kahn, Matthew E. 4 2211 352 -9.29% Department of Economics, University of Southern California24 Armstrong, Mark 6 2191 591 -9.28% Department of Economics, Oxford University25 Diebold, Francis X. 4 10946 96 -9.26% Department of Economics, University of Pennsylvania

a The RePEc ranking is based on an aggregate of rankings by different criteria. See Zimmermann (2013) for more information.b The output loss for researcher i is computed as

∑ps=1 Ys(G)−

∑ps=1 Ys(G

−i). See also Equation (16).

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Rankings for Departments

Table: Ranking of the top-ten departments.

Rank Department/School SizeRePEc OutputRanka Lossb

1 Department of Economics, Harvard University 10 1 -15.43%2 Kennedy School of Government, Harvard University 6 16 -12.84%3 Department of Economics, Stanford University 5 12 -12.54%4 Economics Department, Massachusetts Institute of Technology (MIT) 7 5 -11.69%5 National Bureau of Economic Research (NBER) 9 2 -11.57%6 Department of Economics, University of Texas-Austin 4 134 -11.52%7 Department of Economics, Princeton University 7 6 -10.84%8 Economics Research, World Bank Group 4 12 -10.83%9 Department of Economics, University of Pennsylvania 8 35 -10.58%10 Economics Department, University of Michigan 5 32 -10.35%

a The RePEc ranking is based on an aggregate of rankings by different criteria. See Zimmermann (2013) formore information.b The output loss for department D is computed as

∑ps=1 Ys(G)−

∑ps=1 Ys(G\D). See also Equation (17).

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Research Funding

▶ We compare our optimal research funding scheme z∗ of Equation (18)using the parameter estimates with funding programs beingimplemented in the real world.36

▶ We use data on the funding amount, the receiving economicsdepartment and the principal investigators from the EconomicsProgram of the National Science Foundation (NSF) in the U.S.37

▶ The National Bureau of Economic Research (NBER) received thelargest amount of funds totalling to 95,058,724 U.S. dollars, followedby the University of Michigan with a total of 57,749,679 U.S. dollars.38

36Paula E. Stephan. How economics shapes science. Harvard University Press, 2012;Gianni De Frajay. “Optimal Public Funding for Research: A Theoretical Analysis”. RANDJournal of Economics 47.3 (2016), pp. 498–528.

37See https://www.nsf.gov/awardsearch/.38L. Drutman. “How the NSF allocates billions of federal dollars to top universities”.

Sunlight foundation blog (2012).

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Research Funding for Individuals

Table: Ranking of the optimal research funding for the top-twenty five researchers.a

Name d Citations RePEc Rankb Institution NSF [0/00] Funding [%]c Rank

Dirk Bergemann 2 961 1039 Economics Department, Yale University 0.9060 6.4289 1Stephen Morris 2 3233 269 Department of Economics, Princeton University 2.1517 4.5837 2Nicholas Bloom 1 3668 220 Department of Economics, Stanford University 2.9818 4.1262 3Eric Leeper 2 3096 429 Department of Economics, Indiana University 0.4063 3.4586 4Joshua Angrist 2 7982 55 Economics Department, Massachusetts Institute of Technology (MIT) 2.5971 2.8433 5Todd Walker 2 471 3164 Department of Economics, Indiana University 0.3002 2.6012 6George-Marios Angeletos 3 1530 903 Economics Department, Massachusetts Institute of Technology (MIT) 0.5126 2.4224 7Guido Lorenzoni 3 698 1644 Department of Economics, Northwestern University 0.4632 2.4224 8Alessandro Pavan 3 703 1873 Department of Economics, Northwestern University 1.2122 2.4224 9Daron Acemoglu 2 16324 5 Economics Department, Massachusetts Institute of Technology (MIT) 0.8070 2.4069 10Sandra Black 1 2681 585 Department of Economics, University of Texas-Austin 0.5879 2.2748 11Kenneth Rogoff 1 20195 9 Department of Economics, Harvard University 1.1896 1.8469 12Thomas Holmes 1 1066 1083 Department of Economics, University of Minnesota 0.9731 1.7696 13Francis Diebold 1 10946 96 Department of Economics, University of Pennsylvania 1.0423 1.5833 14Donald Andrews 1 7343 43 Economics Department, Yale University 2.3043 1.5768 15Glenn Ellison 2 3031 420 Economics Department, Massachusetts Institute of Technology (MIT) 0.9729 1.5453 16Randall Wright 1 3830 200 School of Business, University of Wisconsin-Madison 1.4782 1.4518 17Yuriy Gorodnichenko 1 1740 518 Department of Economics, University of California-Berkeley 0.8387 1.4079 18Geert Bekaert 2 7239 178 Graduate School of Business, Columbia University 0.2738 1.3214 19Robert Hodrick 2 3984 474 Graduate School of Business, Columbia University 0.2910 1.3214 20Mark Rosenzweig 1 5257 99 Economic Growth Center, Economics Department, Yale University 0.8702 1.2468 21Gita Gopinath 1 947 1930 Department of Economics, Harvard University 1.8603 1.2020 22Harald Uhlig 1 3326 241 Department of Economics, University of Chicago 1.1066 1.1769 23Mario Crucini 1 1185 1554 Department of Economics, Vanderbilt University 2.1582 1.1339 24Mikhail Golosov 1 1016 1371 Department of Economics, Princeton University 0.7983 1.0749 25

a We only consider researchers that are listed as principal investigators in the Economics Program of the National Science Foundation (NSF) in the U.S. from 1976 to2016 and that can be identified in the RePEc database.b The RePEc ranking is based on an aggregate of rankings by different criteria. See Zimmermann (2013) for more information.c The total cost of funds,

∑ps=1 δiszYs(G, z), of researcher i with the optimal research funding scheme z∗ of Equation (18).

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Research Funding for Departments

Table: Ranking of optimal research funding for the top-ten departments.a

Department/School Size NSF [0/00] Funding [%]b Rank

Graduate School of Business, Columbia University 4 23.9521 10.2990 1Sloan School of Management, MIT 4 14.3698 8.4177 2Department of Economics, University of Texas-Austin 4 2.7044 6.4060 3Department of Economics, University of Minnesota 7 42.2463 6.3126 4Department of Economics, Vanderbilt University 5 4.8587 4.7536 5Economics Department, Yale University 4 22.7299 4.2365 6Economics Department, University of Rochester 4 5.3735 2.6427 7Department of Economics, Northwestern University 7 37.5792 2.5090 8Department of Economics, University of Chicago 9 20.5289 2.2148 9Economics Department, Georgetown University 7 2.2544 2.1254 10

a We only consider researchers that are listed as principal investigators in the Economics Programof the National Science Foundation (NSF) in the U.S. from 1976 to 2016 and that can be identifiedin the RePEc database.b The total cost of funds,

∑i∈D

∑ps=1 δisz

∗Ys(G, z), for each department D and researchers i ∈ Dwith the optimal research funding scheme z∗ of Equation (18).

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Figure: Pair correlation plot of the authors’ degrees, citations, total NSF awardsand the optimal funding policy. The Spearman correlation coefficients are shownfor each scatter plot.

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Conclusion

▶ We have analyzed the equilibrium efforts of authors involved inmultiple, possibly overlapping projects.

▶ We bring our model to the data by analyzing the network of scientificcoauthorships between economists registered in the RePEc authorservice.

▶ We rank the authors and their departments according to theircontribution to aggregate research output, and thus provide the firstranking measure that is based on microeconomic foundations.

▶ Moreover, we analyze various funding instruments for individualresearchers as well as their departments.

▶ We show that, because current research funding schemes do not takeinto account the availability of coauthorship network data, they areill-designed to take advantage of the spillover effects generated inscientific knowledge production networks.

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Future Work

▶ We can allow the returns of an author from participating in a projectto be split equally among the participants.39

▶ Instead of a convex cost, we can introduce a time constraint.40

▶ In work in progress we are extending our analysis to

▶ the Framework Programs of the E.U. and

▶ the research funding program of the Swiss National ScienceFoundation.

39Eugene Kandel and Edward P Lazear. “Peer pressure and partnerships”. Journal ofpolitical Economy (1992), pp. 801–817; Matthew O. Jackson and Asher Wolinsky. “A StrategicModel of Social and Economic Networks”. Journal of Economic Theory 71.1 (1996), pp. 44–74.

40Leonie Baumann. “Time allocation in friendship networks”. Available at SSRN 2533533(2014); Hannu Salonen. “Equilibria and centrality in link formation games”. InternationalJournal of Game Theory 45.4 (2016), pp. 1133–1151.

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Networks in Conflict: Theory andEvidence from the Great War of Africa41

▶ Many wars involve multiple actors with intricate webs ofalliances&rivalries:

→ Recent civil wars: Somalia, Uganda, Democratic Republic ofCongo, ...

→ In history: Peloponnesian War, Caesar’s Wars in Gaul,Thirty Years’ War, Napoleonic Wars, WWI, WWII ...

▶ Most existing formal theories focus on two player/coalition wars...

→ yet, this is a rare occurrence in the real world

→ alliances are often not unified coalitions; each participantretains its independent agenda and decision power (e.g.Warsaw insurrection; current rebellion in Syria; etc.).

41Michael D. Konig et al. “Networks and Conflicts: Theory and Evidence from Rebel Groupsin Africa”. Forthcoming in Econometrica (2016).

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▶ How does the network of military alliances and rivalries affect overallconflict intensity, destruction and death toll?

→ success at war hinges on allies’ and rivals’ actions;

→ each agent’s position in the network affects its incentive tofight more or less;

→ network externalities are a key driver of the escalation orcontainment of violence.

▶ Can network analysis be used as a guide for pacification policies?

→ Due to the externalities, pacifying a group affects theactions of all the other groups in a complex way.

→ A mis-designed intervention can result into a small decrease(or even an increase) in violence.

→ Network structure reveals which actors are the most criticalfor the escalation of violence

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Theory

▶ This paper combines insights from network theory with standardconflict theory tools (i.e. contest success function)

▶ A non-cooperative theory of strategic fighting taking as given thenetwork of alliances&enmities, with the purpose of fittingdisaggregated battlefield data

→ we postulate that each group’s operational performancehinges on two externalities with opposite signs: the fightingeffort of its allies and that of its enemies.

→ we obtain a closed form characterization of players’equilibrium fighting effort (related to a generalization ofBonacich centrality)

→ the theory predicts a mapping from the network structure tothe conflict intensity (rent dissipation)

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Empirics

▶ Empirical implementation

→ Dem. Rep. of Congo (”Great African War”) 1998-2010.Ideal setting (many fighting groups; rich network ofalliances&enmities)

▶ We perform a structural estimation based on the conditionscharacterizing Nash equilibrium

▶ Aim: estimate the fighting externalities and structural parameters

→ perform counterfactual pacification policies (welfareanalysis): the most destructive groups are not necessarilythe most active ones, but rather the most influential groupsthrough their alliance/enmity links

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Related Literature on Conflict

▶ Theoretical conflict literature studying alliances and conflict in settingswith 3 players, or sometimes with n identical players (Konrad, 2009,2011, Kovenock and Roberson 2012, Bloch, 2012).

▶ Conflict and collective action (why do masses follow?):Esteban and Ray 2008.

▶ Recent development literature using fine-grained geo-localised data onfighting events: Dube and Vargas (2013), Cassar et al. (2013), LaFerrara and Harari (2012), Michalopoulos and Papaioannou (2013),Rohner, Thoenig, and Zilibotti (2013), Yanagizawa-Drott (2012).

▶ Context and economic motives of DRC war: e.g.,Olsson and Congdon 2004; Lalji 2007; Carpenter 2012.

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Related Literature on Networks

▶ Generally linked to the literature on the economicsof networks (cf. e.g. Jackson and Zenou 2014;Acemoglu and Ozdaglar 2011; Jackson 2008).

▶ Franke and Ozturk (2009): agents choose their fightingefforts to attack their neighbors. No alliances.Focus on (low scale) specific networks.

▶ Hiller (2012): a model of network formation wherehaving more “friends” makes a player “stronger”

▶ Most previous work is theoretical.

▶ Exception: Acemoglu, Garcia-Jimeno and Robinson (2014)estimate a structural politico-economic model of public goodprovision using a network of Colombian municipalities.

▶ Key player analysis: Ballester et al. (2006), Liu et al. (2011),Lindquist and Zenou (2013). Focus is not on civil conflicts.

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The Model

▶ We consider a one period model with an exogenous network G ofGroups i ∈ N = {1, . . . , n} and a signed adjacency matrixA ≡ A+ −A−

aij ≡ a+ij − a−ij =

1, if i and j are allied

−1, if i and j are enemies

0, if relationship (i, j) is neutral.

▶ We assume:

1. aij = aji (reciprocity of alliance&enmity)2. alliance and enmity are mutually exclusive

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Contest Success Function (CSF)

▶ Payoff (utility) function: standard ratio-form (Tullock) contest successfunction:

πi = V︸︷︷︸territory

× φi∑nj=1 φj︸ ︷︷ ︸share

− xi︸︷︷︸fighting effort

▶ Group i’s fighting strength, φi, depends on its own fighting effort, xi,and (Generalization of the CSF) on that of its allies and enemies:

φi (xi, x−i,A) = xi + β

n∑j=1

a+ijxj − γ

n∑j=1

a−ijxj

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Discussion of assumptions

▶ Key assumptions: the allies’ (enemies’) fighting efforts increase(decrease) group i’s fighting strength

▶ Note: even allied groups compete one with another over V. Alliancesare no ”unitary” coalitions

▶ Rwanda and Uganda in the DRC war▶ Rebel forces in Syria

▶ The externalities through the fighting strength, ϕi,compound withthose already present in the CSF

▶ Not over-parametrized: the model spans from totally destructiveanarchy to a peaceful sharing without any rent dissipation (e.g. ourtheoretical example of a k−regular graph in the paper)

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Equilibrium Fighting Effort

▶ The First Order Conditions (FOC) yield, for all i = 1, 2, . . . , n:

∂πi (G,x)

∂xi= 0 ⇐⇒ φi =

1

1 + βd+i − γd−i

(1− 1

V

n∑j=1

φj

)n∑j=1

φj ,

where we assume that, for all i, βd+i − γd−i > −1.42

▶ Solving the system of n equations yields the equilibrium OP levels:

φ∗i (G) = Λβ,γ (G)

(1− Λβ,γ (G)

)Γβ,γi (G)× V, (23)

where

Γβ,γi (G) ≡ 1

1 + βd+i − γd−i, Λβ,γ (G) ≡ 1− 1∑n

i=1 Γβ,γi (G)

. (24)

42This condition is necessary and sufficient for the second order conditions to hold for allplayers.

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▶ Summing over i yields the total economy-wide OP level,

n∑i=1

φ∗i = Λβ,γ (G)× V, (25)

which in turn implies that

φ∗i∑n

j=1 φ∗j

=Γβ,γi (G)∑nj=1 Γ

β,γj (G)

(26)

▶ Γβ,γi is a measure of local hostility level capturing the externalitiesassociated with agent i’s first-degree alliance and hostility links.

▶ Λβ,γ is a measure of total OP in the network.

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Nash Equilibrium

▶ Assume that β + γ < 1/max{λmax(G+), d−max}, where λmax

(A±)

denotes the largest eigenvalue associated with the matrix A±. LetΓβ,γi (G) and Λβ,γ (G) be defined as in (24), and let

cβ,γ (G) ≡(In + βA+ − γA−)−1

Γβ,γ (G) (27)

be a centrality vector, whose generic element cβ,γi (G) describes thecentrality of agent i in the network.

▶ Then, there exists a unique Nash equilibrium with effort levels given by

x∗i (G) = Λβ,γ (G)(1− Λβ,γ (G)

)cβ,γi (G)× V, (28)

for all i = 1, . . . , n.

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▶ Moreover, the equilibrium OP levels are given by (25), and the payoffsare given by

π∗i (G) = πi (x

∗, G) = V (1− Λβ,γ(G))(Γβ,γi (G)− Λβ,γ (G) cβ,γi (G)

).

(29)

▶ Note, in particular, that the relative fighting efforts of any two agentsonly depends on their relative centrality in the network:

x∗i (G)

x∗j (G)=cβ,γi (G)

cβ,γj (G).

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Weak Spillovers

▶ As β → 0 and γ → 0, the centrality measure defined in Equation (27)can be written as

cβ,γ(G) = bΓβ,γ(G)(γ,G−) + bΓβ,γ(G)(−β,G

+) + Γβ,γ(G) +O (βγ) ,

where O (βγ) involves second and higher order terms.

▶ The (µ-weighted) Bonacich centrality with parameter α is defined as

bµ(α,G) ≡∞∑k=1

αkAkµ, (30)

as long as the invertibility condition |α| < 1/λmax(G) is satisfied.

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▶ Formally, the Bonacich centrality measures all walks arriving in i usingrivalry (alliance) connections, where walks of length k are weighted bythe geometrically decaying rival (alliance) externality γk (βk).

▶ In our contest game each Bonacich centrality gauges the networkmultiplier effect attached to rivalry or alliance.

→ bΓβ,γ(G)(γ,G− measures how much group i is

influenced by all its (direct and indirect) rivals.

→ bΓβ,γ(G)(−β,G+) measures how much group i isinfluenced by all its (direct and indirect) allies.

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Welfare Analysis

▶ The rent dissipation is equal to the total equilibrium fighting effort as ashare of the prize of the contest:

RDβ,γ(G) ≡ 1

V

n∑i=1

x∗i (G) = Λβ,γ(G)(1− Λβ,γ(G))

n∑i=1

cβ,γi (G).

▶ Since the aggregate welfare is

W β,γ(G) =

n∑i=1

π∗i (G) = V

(1− RDβ,γ(G)

),

then, minimizing rent dissipation is equivalent to maximizing welfare.

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Key Player

▶ The key player is defined as the agent whose removal triggers thelargest reduction in rent dissipation (cf. Ballester et al., 2006).Identifying the key player is important to determine which policyintervention can reduce fighting activity.

▶ Let G−i be the network obtained from G by removing agent i, then thekey player i∗ ∈ N = {1, . . . , n} ∪ ∅ is defined by

i∗ = argmaxi∈N

{RDβ,γ (G)− RDβ,γ

(G−i

)}, (31)

whereRDβ,γ(G) ≡

∑ni=1 x

∗i (G) = V Λβ,γ(G)(1− Λβ,γ(G))

∑ni=1 c

β,γi (G), and

x∗i (G) is the generic element of the vector x∗ (G) defined in Equation(28).

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Empirical Application to DRC

▶ We study the Second Congo War (”Great African War”), between 1998and 2010 (after the end of the 1996-97 conflict)

▶ Although the war is officially over since 2003, the fighting continues ona large scale.

▶ The deadliest conflict since World War II, with between 3 and 5million lives lost (Olsson and Fors, 2004; Autesserre, 2008).

▶ An emblematic conflict for the involvement of a large number (64) ofinter-connected domestic and foreign actors: ”Three Congolese rebelarmies, 14 foreign armed groups, and countless militias” (Autesserre,2008).

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Main Data Sources

▶ Network construction: Stockholm International Peace ResearchInstitute (SIPRI) data contains information on the mainalliances/rivalries in the DRC conflict.

▶ Violence measurement: ACLED (Armed Conflict Location EventsData) contains 4765 violent events in the DRC, 1998-2010

→ For each event, information over location, date and actors involved onthe two opposing sides

▶ IV of violence: Geolocalized rainfall measures from GPCC (grid of 0.5x 0.5 degree2 cell).

▶ Alternative network construction: Cederman, Buhaug and Rod (2009,JCR) panel of historical rivalries/alliances between ethnic groups in allAfrica, 1946-1996.

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LRA

UNITA

FAA/M...

Uganda

Hutu

Burundi J. Kab.

SPLA/M

Sudan

FNL

L. Kab.

ADF

RCD G...

FDLR

Rwand...

Mayi-...

CNDD-...

Zimba...

Chad

Hutu RCD K.

CNDP

MLC

DRC M...

UPC

Lendu ADFL

RCD

Namibia

FNI

Rwand...

FPJC

FRPI

Hema

Mutiny

ALIR

MRC

NALU

FLC

South...

DRC P...

PARECO

PUSIC

Rwand...

UPPS

BDK

Zambia

RUD

Enyele

Lobala

FRF

APCLS

Lendu

Un. M... F. DRC

Haut-...

Mayi-...

Mayi-...

Minem...

Bomboma

Masunzu

Wager...

CNDD-...

RCD N...

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Structural Equation

▶ Group i’s fighting strength, φi, depends on its own fighting effort, xi,and (Generalization of the CSF) on that of its allies and enemies:

φi (xi, x−i,A) = xi +

[β

n∑j=1

a+ijxj − γ

n∑j=1

a−ijxj

]+ Zitδ+ei + εit︸ ︷︷ ︸

shifters

▶ Structural shifters (Zit,ei + εit) are resp. observed and unobserved (bythe econometrician): group size, scale of operation, foreign affiliations,climatic shocks // weaponry efficiency, moral of troops, leadership

▶ This system of structural equations will be estimated to obtain (β, γ).

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▶ The system of FOC {∂πi/∂xi = 0}ni=1 allows us to characterizeequilibrium in a simple linear closed-form expression:

x∗i,t = −β∑j

a+ijx∗j,t + γ

∑j

a−ijx∗j,t − Zitδ+

Φ(1− Φ/V )

1 + βd+i − γd−i︸ ︷︷ ︸network feedback

− ei − εit

▶ Interpretation: Contest effect (enemies) and Free-riding effect (allies)

▶ The GE feedback is closely related to the concept of (Bonacich)centrality in the network: central players exert more efforts

▶ This system of structural equations will be estimated to obtain (β, γ).

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Identification Strategy

x∗i,t = −β∑j

a+ijx∗j,t + γ

∑j

a−ijx∗j,t − Zitδ︸︷︷︸

OBS.

+Φ(1− Φ/V )

1 + βd+i − γd−i− ei︸ ︷︷ ︸

FE

− εit

▶ Time-invariant unobserved heterogeneity → panel allows for group FE

▶ Endogeneity bias:

→ Reflection problem arising from network externalities [e.g.,Bramoulle et al. 2009; Zenou et al. 2013].

→ A’s effort depends on B’s effort, but B’s effort is in turnaffected by A’s effort, etc.

→ OLS yields inconsistent estimates

→ Needed: valid instruments (a set of exclusion restrictions)

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x∗i,t = −β∑j

a+ijx∗j,t + γ

∑j

a−ijx∗j,t − Zitδ + FEi − εit

▶ We use∑j a

+ijZjt and

∑j a

−ijZjt as excluded instruments (consistent

with our structural equation)

→ Zj,t : time-varying climatic shocks (rainfall) impactingfighting group ”homelands”. Rationale: exogeneous shockson income and military efficiency

→ So, the instruments are the weather conditions at t in thehomeland of group i′s friends and in that of its enemies.

→ Note: in the second-stage we control for weather conditionsin i’s own homeland.

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Geolocalized Violence in DRC

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Construction of group-level rain fallmeasures

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Baseline Regressions

Dependent variable: Total Fighting

(1) (2) (3) (4) (5) (6)

Tot. Fight. Enemies 0.08*** 0.08*** 0.06*** 0.08* 0.13** 0.09**(0.02) (0.02) (0.02) (0.05) (0.05) (0.04)

Tot. Fight Allies -0.03 -0.03 -0.04* -0.24* -0.18* -0.18**(0.03) (0.03) (0.02) (0.12) (0.11) (0.08)

Group FE, annual time dummies Yes Yes Yes Yes Yes YesControl for rainfall variables No Yes Yes Yes Yes YesAdditional controls No No Yes No No YesEstimator OLS OLS OLS IV IV IVSet of Instrument Variables n.a. n.a. n.a. Restricted Full FullObservations 832 832 832 832 832 832R-squared 0.339 0.343 0.420 0.196 0.254 0.367

Notes: An observation is a given armed group in a given year. The panel contains 64 armed groupsbetween 1998 and 2010. Robust standard errors allowed to be clustered at the group level in parentheses.Significance levels are indicated by * p < 0.1, ** p < 0.05, *** p < 0.01.

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Key Player Ranking

Table: Key player ranking for the first 35 actors in the Democratic Republic of the Congo (DRC) excluding governmentgroups.a The total number of groups is n = 85. The total number of alliances is m+(Gb) = 95, the total number ofconflicts is m−(Gb) = 111 and we have that

∑j φ

∗j (G

b) = 0.9891. Pearson correlation of fighting effort in the benchmark

with the reduction in the rent dissipation is 0.76.

Actor ∆RDβ,γk

(%)b φ∗k/

∑j φ

∗j (%) x∗k/RDβ,γ (%) Rank x∗k Rank ∆RD

β,γk

FDLR: Dem. Forc. for the Lib. of Rwanda 13.79 0.71 6.65 2 1Mayi-Mayi Milita 9.67 0.69 5.59 4 2Mil. Forc. of Rwanda 9.57 1.91 3.65 8 3Mil. Forc. of Uganda 7.71 0.93 4.34 6 4Lendu Ethnic Militia (DRC) 4.97 1.24 2.43 10 5Mil. Forc. of Rwanda 4.56 1.18 1.69 13 6RCD: Rally for Congolese Dem. 4.49 0.98 1.75 12 7Interahamwe Hutu Ethnic Militia 2.36 0.84 1.39 15 8RCD: Rally for Congolese Dem. (Goma) 2.36 6.90 8.67 1 9UPC: Union of Congolese Patriots 1.74 1.58 2.16 11 10Mil. Forc. of Zimbabwe 1.72 0.67 0.73 21 11Hutu Rebels 1.46 0.99 0.52 24 12Mil. Forc. of South Africa 0.80 0.91 0.28 32 13FAA/MPLA: Mil. Forc. of Angola 0.75 0.76 0.36 28 14Mayi Mayi Militia (PARECO) 0.72 0.68 0.37 26 15Mil. Forc. of Namibia 0.62 0.76 0.31 29 16PUSIC 0.54 1.33 0.26 33 17Former Mil. Forc. of Rwanda 0.45 0.79 0.24 34 18Mil. Forc. of Sudan 0.41 0.95 0.24 35 19Mil. Forc. of Burundi 0.27 1.20 0.29 30 20

a We have used the parameter estimates β = 0.1407 and γ = 0.0903 while setting V = 1.b The relative change in the rent dissipation is computed as ∆RD

β,γk

(%) =(RDβ,γ(Gb) − RDβ,γ(Gb\{k})

)/RDβ,γ(Gb), while the rent

dissipation in the original network Gb is RDβ,γ(Gb) =∑n

i=1 x∗i (G

b) = 474.4614 (with V = 1). A positive value of ∆RDβ,γk

thus indicatesa reduction in fighting, while a negative value indicates an increase in fighting.

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100 101

100

101FDLR

MAYIRWA-II

UGA

LENDURWA-I

RCD

INTERAH RCD-G

UPCZBWHUTU

SAF

ANG

MAYI-PNAM

PUSICEX-RWA

SUDBUR

Share in tot. fight., x∗k(G

b)/!n

j=1x∗j(G

b) [%]

Changein

rentdiss.

remov

ingk,∆RD

β,γ

k[%

]

1

1 5 10

5

10

Figure: The figure reports the relative change in the rent dissipation associatedwith the removal of each of the top 20 groups in the ranking of the key playeranalysis versus the respective share in total fighting before removal. Both axes arein log-scale. The red dashed line indicates the 45 degrees line.

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Conclusion

▶ New analysis on the role of alliance/rivalry networks in conflicts.

▶ Helps one to understand why violence may escalate or stay at a lowlevel.

▶ Structural estimation of the model.

▶ The keyplayer analysis enables us to identify the most destructivegroup: it is not necessarily the most active group.

→ implications for peacekeeping/pacification policies.

▶ The methodology can be exported to other war contexts.

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