The Economics of Business Networks and Key Cities

■イベント 
：SOCIOECONOMIC NETWORKS AND NETWORK SCIENCE WORKSHOP
https://sites.google.com/view/socioeco-netsci-waseda2020

■登壇概要
タイトル：The Economics of Business Networks and Key Cities
発表者： 
DSOC R&D SocSci Group Takanori Nishida, Shota Komatsu, Juan Nelson Martínez Dahbura

▼Twitter
https://twitter.com/SansanRandD

Transcript

1. 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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2. ※ 掲載されている内容等は発表時点の情報です。
   ※ 公開に当たり、資料の⼀部を変更・削除している場合があります。
   

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3. Introduction
   

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4. 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))
   

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5. 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 !
   

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6. 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.
   

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7. 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.
   

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8. Methodology
   

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9. 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
   

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10. 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)
    

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

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12. 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.
    

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13. 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)
    

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14. 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.
    

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15. 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.
    

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16. 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
    

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17. Data
    

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18. 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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20. 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
    

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21. Results
    

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22. 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
    

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23. 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
    )
    

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24. 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
    

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25. 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
    

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26. 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(+, % )
    

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27. 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
    

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28. 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
    

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29. 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
    

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

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31. 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.
    

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32. Conclusion
    

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33. 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.
    

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34. 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.
    

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

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