Measuring Integration in the Network Structure: Some Suggestions on the Connectivity Index

Size: px

Start display at page:

Download "Measuring Integration in the Network Structure: Some Suggestions on the Connectivity Index"

Silvia Davis
5 years ago
Views:

1 Measurng Integraton n the Network Structure: Some Suggestons on the Connectvty Inde 1. Measures of Connectvty The connectvty can be dvded nto two levels, one s domestc connectvty, n the case of the physcal connectvty as covered n the report appears to focus on the domestc connectvty. The other s connectvty between the APEC economes. That s cross-board connectvty, a network measure. The network can be envsaged as a collecton of nodes, each of whch represents an economy. The structure of the network s gven by a lnk matr, denote t as L l n n,where a typcal element l 1 f there s a drect lnk gong from economy to economy ; otherwse, t s equal to zero. The actvty on each lnk of the network s measured n terms of the flow on the network, whch s summarzed n the matr n n. A typcal element, s the total flow from economy to economy, and s the flow n the other drecton from to (.e. transport networks are b-drectonal). Matr : n n2 1n 2n nn nn Note: (1) The cross-board connectvty s less nvolved as an ndcator n the report. Whereas for most economes, the domestc connectvty s farly advanced, the cross-board connectvty among them such as transnatonal roads, energy ppelnes, power grds and other nfrastructure s far less developed, whch s a weak lnk of the regonal connectvty and also a bottleneck for the regonal

2 development. Therefore a more balanced system of ndcators should be desgned to reflect the cross-board connectvty n the nde. (2) In order to reflect specfcally the connectvty between pars of economes, the raw connectvty measures data should be blateral level. For eample: UNCTAD presents Lner Shppng lateral Connectvty Inde (LSCI), whch ndcates a country par s ntegraton level nto global lner shppng networks. The LSCI s an etenson of UNCTAD s country-level Lner Shppng Connectvty Inde (LSCI) and based on a proper blateralzaton transformaton. The current verson of the LSCI ncludes 5 components. For any par of countres A and represented n the sample, the LSCI s based on: the number of transshpments requred to get from country A to country ; the number of drect connectons common to both country A and ; the geometrc mean of the number of drect connectons of country A and of country ; the level of competton on servces that connect country A to country ; the sze of the largest shps on the weakest route connectng country A to country. In order to establsh a unt free nde, all components are normalzed usng the standard formula: Normalzed_Value = (Raw - Mn(Raw)) / (Ma(Raw) - Mn(Raw)). The LSCI s computed by takng the smple average of the fve normalzed components. As a consequence, the LSCI can only take values between 0 (mnmum) and 1 (mamum). 2. Methodology and Technque A frst ntutve approach to connectvty s smply to use the total outflow or nflow from each node:. or. Such smple output ndcators obvously contan sgnfcant nformaton, but by defnton reman local rather than global, n the sense that they do not ncorporate nformaton from the full structure of the network. That s, they do not capture ndrect connectons, whch are of partcular mportance n physcal transport where connectng nodes are common. Nor do these types of measures reflect the nteractons among nodes. A more sophstcated approach, whch makes use of more nformaton from the matr, s to use concentraton ndces such as the Herfndhal or Thel ndces of the flows to and from a node n the network. The Thel nde s the entropy of the relatve weght of the outflows or nflows from node to the neghborng node s, and s gven by the followng epresson:

3 Thel _ Inde ln. ln These knds of concentraton ndcators have no dmenson. However, they do not ncorporate nformaton about the structure of the network. They are essentally local measures, because they only use nformaton from a sngle node. Relatve entropy measures are better n ths respect, snce they compare the composton of flows to or from a node to an average composton. The most commonly used s the ullback-lebler dstance, whch s a modfcaton of the Thel nde. In ths case, the reference composton should be the relatve weght of each node.. Clusterng s an mportant concept n network theory. The clusterng coeffcent of node s an ntutve measure of how well connected the nodes n the neghborhood of are. Ths number, comprsed between 0 and 1. Ths defnton apples equally to drectonal and non-drectonal networks; that s, a trangle s counted once for each drecton t can be run, k and k. A varant of ths defnton apples to weghted networks. It gves hgher weght to trangles wth hgher flows to the node: Cluster _ Inde k 1 k k k L y constructon, t not only ncludes nformaton about nteractons wth neghborng nodes, but also about nteractons between neghborng nodes. A Gravty-ased Defnton of Connectvty It needs develop a measure of connectvty n the APEC economes network, n the sense that t captures the full range of nteractons among all network nodes, even when there s no drect connecton between them, as n the Ar Connectvty Inde measurng. The generc b-proportonal gravty model takes the followng form: A where A s the repulsve potental of node, and s the attractve potental of node ; the flow s pushed from and pulled to. The blateral varable measures the nteracton between orgn and destnaton. The essence of the gravty nterpretaton of spatal nteracton models s a b-proportonal structure. The potentals are estmated from the requrement that row and column totals n the gravty model estmates must equal the total outflows or nflows of the nodes. Thus:. A or. A

4 As a consequence of the non-lnear nature of the model, the potental of a node does not depend upon ts own varables, but on every other nteracton n the network. In the trade lterature, a queston s addressed usng the concept of multlateral resstance (MR), whch corrects for orgn and destnaton nteractons wth the rest of the world. Let D be the pull eercsed by destnatons n the rest of the world on orgn node, and let O be the push eercsed by orgns n the rest of the world on destnaton node. We can then defne:.. AD O. D 1. D O O 1 A Total outflows are, thus, as epected roughly proportonal to total outflows/nflows of the orgn/destnaton multpled by an mpedance factor. Ths concluson s mantaned notwthstandng the correcton for the pull and push from the rest of the world, or adustment for multlateral resstance. A frst canddate for connectvty: C D The epresson apples to the connectvty of outflows, but permutng A,, D, and O gves the correspondng value for nflows. Ths epresson can be nterpreted n two ways. Frst, connectvty s equal to the average mpedance, weghted by the potental of each partner. An alternatve nterpretaton s that the numerator summarzes the pull or push of all partners, and the denomnator represents the mamum possble pull or push. The denomnator n equaton ecludes an economy s own potental from the sum. Ths choce leads to some nconsstency. Hence a consstent defnton of connectvty should also nclude an economy s own contrbuton to push and pull. D. C A Ths mproved defnton amounts to ncludng n the flow matr a dagonal term, whch corresponds to the effectve flow between each economy and tself wth an mpedance of one. For a symmetrc defnton of connectvty, we can take the geometrc average of the connectvty of as orgn and destnaton. Ths approach gves:

5 C A A A 1 2 The constructon produces a consstent defnton of connectvty, whch s rooted not only n the topology of the network, but also n a fundamental understandng of spatal nteractons among the nodes. Under ths defnton, connectvty s a non-dmensonal number between zero and one. An economy s connectvty depends not only on ts neghbors, but also on all of the nteractons among the other economes n the network (ust as multlateral resstance depends on trade costs across all potental tradng partners). Note: To mplement the model emprcally, we need estmates of the potentals (the A and terms n equaton). They can be consstently obtaned by usng orgn and destnaton fed effects, as n much of the trade lterature. Jean-Franços Arvs and en Shepherd estmate an Ar Connectvty Inde (ACI) for They derve the potental terms (A and ) as fed effects usng a Posson estmator. In the contet of ar transport, t posts that the blateral mpedance s a functon of dstance, or equvalently tme of flght, wth a modfcaton of the shfted logarthmc functon: ~ A ep f ( d ) where the dependence of dstance s gven by a shfted log: f ( d) a log( a d) log( a) In ths epresson, the constant a represents the natural scale of the network. The ntutve nterpretaton of ths scale s that there s a fed mnmum cost n the nteracton between nodes, or n the contet of ar transport the tme to take off and land when movng from termnal to termnal. The prmary queston for mplementng the shfted log estmator n dstance s the choce of scale parameter a. To do ths, they adopt a grd search approach and run a seres of fed effects Posson regressons. The value of the log-lkelhood s mamzed at appromately a Introduce more canddate ndcators For nstance, physcal connectvty relates to nfrastructure assets such as power generaton, transmsson, and dstrbuton systems, transportaton or communcatons networks, and water and santaton systems. However, the hard or vsble component must be combned wth some soft nfrastructures, whch nclude polces and regulatons. y some defnton, socal, organzaton or regulatory nsttutons can also

6 be consdered as nfrastructure (often referred to as soft nfrastructure to dfferentate t from hard physcal nfrastructure). Connectvty ndces as a systemc framework consst of hard and soft components. The soft nfrastructure must also support the hard nfrastructure to ensure that the rght m and synergy of the two can provde completely connectvty nde (even n sub-level ndces). Note: The energy nde system can be epanded and refned by addng data of power supply grd, ol and gas ppelne. The port nde can be ncluded for evaluatng the connectvty n the physcal connectvty pllar. The border management and the degree of ntegraton of the customs, such as the degree of mutual recognton of two economy s customs documents, proof materals etc., can be used for measurng nsttutonal connectvty. The educaton and tranng ndcators, such as the echange of the number of foregn students, can be ncluded n the people-to-people connectvty pllar.

Steps for Computing the Dissimilarity, Entropy, Herfindahl-Hirschman and. Accessibility (Gravity with Competition) Indices

Steps for Computing the Dissimilarity, Entropy, Herfindahl-Hirschman and. Accessibility (Gravity with Competition) Indices Steps for Computng the Dssmlarty, Entropy, Herfndahl-Hrschman and Accessblty (Gravty wth Competton) Indces I. Dssmlarty Index Measurement: The followng formula can be used to measure the evenness between