The Economics of Business Networks and Key Cities Sansan, Inc. DSOC R&D SocSci Group Takanori Nishida, Shota Komatsu, Juan Nelson Martínez Dahbura Special Thanks to Yusuke Inami (Keio University)

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Introduction

Data Strategy and Operation Center Question - Which cities are the “key players” in business networks? Why is it interesting? 1. Potentially valuable for policy making 2. Contribute to the empirical literature on the effects of networks in economics, with a focus on “key players” (e.g., Lee et al. (2020))

Data Strategy and Operation Center Definition of the “Key Player” - The key player in a network is the agent whose removal from the network leads to the largest reduction in the total equilibrium level of economic activity (Ballester et al., 2006) !∗ = arg max ) (+∗ , − +∗(,.) )) - +∗(,) is the total output under the network , - +∗ ,.) is calculated using the network without city !

Data Strategy and Operation Center Why not just picking the highest degree node? - Social-interaction effect: the performance of a node has an effect on its neighbors (spillovers). - Identifying the social-interaction effect is not simple: neighbors perform similarly because they are connected (spillovers)? or do they connect because they perform similarly (homophily)? - Contextual effect: the characteristics of the neighbors may affect the nodeʼs output. - When you remove a node, the rest of the network may rewire. - You need to consider what the network will look like after removing a given node.

Data Strategy and Operation Center Challenges 1. How to estimate the social-interaction effect separately from other effects? - We address this issue by applying an instrumental variables (IV) strategy. 2. How to calculate key-player centrality, taking network formation into account? - We calculate key-player centrality both with and without the assumption that when one node is removed from a network, the rest of the network does not change.

Methodology

Data Strategy and Operation Center Econometric Model - The econometric model can be written as ! = #$! + &' 1) + *&+ + , *&- + . - ! : level of economic activity - $ : adjacency matrix (which cities are connected with which) - * : city characteristics such as population - , * : average exogenous characteristics of other connected cities. , *0 ≔ ∑3 403 *3 / ∑3 403. We are interested in consistently estimating the parameters, especially #, which measures the impact of the total economic activity of other connected cities on that of your city. social-interaction effect contextual effects

Data Strategy and Operation Center What prevents us from estimating the parameters? There are three factors that make it difficult to estimate the social-interaction effect. 1. Simultaneity of output - Cities’ economic activities are interdependent. 2. Network formation through homophily - Like attracts like – if the economic activity of your city is high, it is likely that your city becomes connected with other cities with high level of economic activity. Then the economic activity of your city affects that of other cities. 3. Common factors that cause cities in the same network to behave in a similar manner (correlated effects)

Data Strategy and Operation Center What prevents us from estimating the parameters? Social-interaction effect Homophily Simultaneity of output Common factors

Data Strategy and Operation Center How to solve the problem?: Simultaneity - Bramoullé, Djebbari, and Fortin (2009) suggest an IV-based estimation strategy using exogenous characteristics of friends of friends. - Construct an IV matrix ! = [1% , ', ( ', )1% , )', ) ( '] - Then we can consistently estimate the parameters using the moment condition + !, - − /)- − 01 1% − '02 − ( '03 = 0 given that the adjacency matrix ) is exogenous, which is difficult to assume.

Data Strategy and Operation Center How to solve the problem?: Endogeneous adjacency matrix - Kelejian and Piras (2014) show that we can consistently estimate the social-interaction effect by replacing the observed adjacency matrix ! with the predicted adjacency matrix " ! based on predetermined covariates. - To predict the adjacency matrix, we estimate the following logit model: Pr %&' = 1 = exp(./ + 1&' .2 ) 1 + exp(./ + 1&' .2 ) - 1&' is homophily measures (difference in population, same prefecture, cosine similarity of industry)

Data Strategy and Operation Center How to solve the problem?: Endogeneous adjacency matrix - Using the predicted adjacency matrix, we can construct IV matrix ! " = [1& , (, ) * (, ) +1& , ) +(, ) + ) * (] - Then we can consistently estimate the parameters by the two-stage least squares (2SLS) or the generalized method of moments (GMM) using moment conditions - ! ". / − 1+/ − 23 1& − (24 − * (25 = 0 - Note that the consistency of the estimators of network formation parameters does not affect consistency of 2SLS/GMM estimator.

Data Strategy and Operation Center How to solve the problem?: Correlated effects - The best way to deal with common shocks in the same network is to include network fixed effects. - Our setting does not allow us to include such network fixed effects. - We include prefecture dummies, ordinance-designated city dummies, and their contextual effects to account for as many common shocks to certain groups of cities as possible.

Data Strategy and Operation Center Summary of parameter estimation 1. Estimate Pr($%& = 1) by logit and get the predicted adjacency matrix 2. Using the predicted adjacency matrix, construct the IV matrix, * 3. Estimate the parameters of the following model by 2SLS/GMM + = ,-+ + /0 11 + 2/3 + 4 2/5 + 6 social-interaction effect contextual effects

Data

Data Strategy and Operation Center Data: City-to-City Business Networks - Business card exchanges between Eight users - Only exchanges that happened during 2017 - Based on firmsʼ addresses printed on business cards, we can identify how many business cards are exchanged between cities. - We construct a network of cities: - Including only connections between users with addresses in Tokyo, Kanagawa, Saitama, and Chiba Prefectures - If there is at least one business card exchange between two cities, they are “connected”. *We used anonymized log data of network ties in 2017 from Eight — a Japanese Business card management app provided by Sansan, Inc.Using data that is anonymized within the permission scope of the “Eight Service Terms of Use” is analysed only statistically.

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Data Strategy and Operation Center Data: Outcome Variable and City Characteristics - Annual commercial sales of goods in cities during 2015 - Proxy for the level of economic activity in cities - From the Ministry of Internal Affairs and Communication (MIAC) - This was collected in 2015, and we assume that the values did not change very much over time. - Covariates - Population (2014 Economic Census, MIAC） - Percentage of people working in each industry (2015 National Popultion Census, MIAC) - Prefecture dummy - Ordinance-designated city (政令指定都市) dummy

Results

Data Strategy and Operation Center Results: Estimated Social-Interaction Effect Dependent variable: log(Annual commercial sales of goods) 2SLS w/ predicted G GMM (1) (2) Social-interaction effect 0.002169 *** 0.002115 *** (0.000383) (0.000234) Control variables Yes Yes Contextual variables Yes Yes Observations 248 248

Data Strategy and Operation Center Finding the Key Player - Using the estimated parameters, we can determine which city is the key player: ! "∗ $ = 1' ( )' − + ,$ -. ( + 01 1' + 3 + 0. + 4 3 + 05 ) - Then calculate the key-player centrality for each city: ! "∗ $ − ! "∗($-7 )

Data Strategy and Operation Center Score Without Contextual Effects Prefecture City Name Tokyo Chiyoda-ku Tokyo Chuo-ku Tokyo Minato-ku Tokyo Shinjuku-ku Tokyo Shibuya-ku Tokyo Taito-ku Tokyo Shinagawa-ku Tokyo Koto-ku Tokyo Bunkyo-ku Tokyo Ota-ku

Data Strategy and Operation Center Score With Contextual Effects Prefecture City Name Saitama Omiya-ku Tokyo Setagaya-ku Tokyo Shinjuku-ku Kanagawa Kanagawa-ku Kanagawa Nishi-ku Chiba Funabashi-shi Saitama Kawaguchi-shi Kanagawa Kohoku-ku Chiba Chuo-ku Tokyo Hachioji-shi

Data Strategy and Operation Center Simulating Changes in the Network - So far we assume that the network does not change if a node is removed. In the short term this is reasonable. In the long term, business activity can migrate to other cities. - We relax this assumption by estimating the network formation process employing a simple Exponential Family Random Graph (ERGM) model. - An ERGM models the probability of a network as an exponential function of some sufficient statistics: the number of edges, the number of triangles, reciprocity, etc. P" # = % ∝ exp(+, % )

Data Strategy and Operation Center ERGM Model Definition And Results - We employ an ERGM similar in spirit to the gravity model in Economics. - Larger nodes (population) that are close to each other are more likely to be connected. - Our model: ! " = ℎ(edges, population, distance) Dependent variable: Network Number of Edges 3.821 *** (0.104) Total Population 0.008 *** (0.0001) Distance -1.466 *** (0.026) Akaike Inf. Crit. 27,701.110 Bayesian Inf. Crit. 27,726.100

Data Strategy and Operation Center ERGM-based Score Prefecture City Name Tokyo Setagaya-ku Saitama Kawaguchi-shi Saitama Omiya-ku Saitama Chuo-ku Chiba Midori-ku Tokyo Shinjuku-ku Kanagawa Nishi-ku Tokyo Suginami-ku Saitama Urawa Saitama Kawagoe-shi

Data Strategy and Operation Center Again, Degree Centrality is Not All This is because of the Contextual Effect! Add the contextual effect and the relation breaks Now remove the invariant network assumption Without contextual effects the score equals the degree centrality

Data Strategy and Operation Center Top Sellers are Not Necessarily Key Players

Data Strategy and Operation Center Interpretations - The top cities in the ranking, calculated based on key-player centrality, are not necessarily the most economically active ones. - One hypothesis that led to this result might be: - A city in an economic cluster (e.g., the 23 wards of Tokyo) receives a lower rank because even if it were removed from the network, its functions could be covered by the surrounding cities. - A hub city that is connected to economic clusters (e.g., Omiya) couldnʼt be substituted, if removed, by its surrounding cities, resulting in a significant spread of impacts across the network.

Conclusion

Data Strategy and Operation Center Conclusion - We attempt to identify the “key cities” in a geographic business network - We estimate parameters including the social-interaction effect, considering reverse causality and confounding factors. - The key cities are not necessarily the most economically active ones, after accounting for the social-interaction and contextual effects.

Data Strategy and Operation Center References - Ballester, C., Calvó-Armengol, A., & Zenou, Y. (2006). “Who's who in networks. Wanted: The key player.” Econometrica, 74(5), 1403-1417. - Bramoullé, Y., Djebbari, H., & Fortin, B. (2009). Identification of peer effects through social networks. Journal of econometrics, 150(1), 41-55. - Kelejian, H. H., & Piras, G. (2014). “Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes.” Regional Science and Urban Economics, 46, 140-149. - Lee, L. F., Liu, X., Patacchini, E., & Zenou, Y. (2020). “Who is the key player? A network analysis of juvenile delinquency.” Journal of Business & Economic Statistics, 1-9.

Data Strategy and Operation Center Virtual Cards Takanori Nishida Shota Komatsu Juan Martínez

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