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SPATIAL ANALYSIS OF TELECOMMUNICATION FLOWS:
LITERATURE REVIEW AND CONCEPTUAL FRAMEWORK
Jean-Michel Guldmann 1
Department of City and Regional Planning
The Ohio State University
Columbus, Ohio 43210
2 Correspondence to: Jean-Michel Guldmann, Department of City and Regional Planning,
The Ohio State University, 298 Knowlton Hall, 275 West Woodruff Avenue, Columbus,
Ohio 43210, USA. Tel: 614/292-2257; FAX: 614/292-7106; E-Mail:
Guldmann.1@osu.edu.
1. INTRODUCTION
Telecommunication systems carry information over space, in the same way as
transportation systems carry goods and people. In both cases, these movements are
necessary to complete economic and social transactions, and can be viewed as derived
demands. Telecommunication flows analysis may therefore provide empirical insights into
the patterns of spatial interactions between individuals, businesses, cities, regions, and
countries. Various modeling techniques have been used, with real-world data and at
various geographical scales, by economists, geographers, and other social scientists to
better understand these patterns. The purpose of this chapter is to critically review the
literature dealing with telecommunication flows, focusing on both modeling techniques
and empirical applications and results. This review is organized along different
geographical scales: local, regional, and international. The modeling techniques include:
(1) aggregate, discrete choice, and spatial interaction (gravity) models; and (2) network
and hierarchies analyses, using graph theory, Markov chains, and multivariate and
clustering techniques. A general spatial modeling framework is then proposed, within
which the existing models can be nested, and which can provide the theoretical basis for
further analyzing the structure of telecommunication flows and the spatial impacts of
telecommunication technologies.
2. TELECOMMUNICATIONS AT THE LOCAL SCALE
From an infrastructural perspective, the basic telephone spatial unit is the wire
center (WC), a territory including a central office building housing one or more switches,
and to which all subscribers located in the WC are connected via access lines. In rural
areas, a WC may include several villages and small towns, whereas metropolitan areas
cover several WCs. Access is defined as connection to the central office. However, local
usage may take place over several WCs in large urban areas, and is, at least in the U.S.,
generally characterized by a flat monthly rate. Local usage may extend to areas adjacent to
an urban area, making up an extended calling area. The concept of community of interest
is used to delineate such extensions.
Telephone flow studies at the local level can be classified into two categories: (1)
local access, and (2) local use. Access studies try to explain variations in the level of
residential connections to the network, using individual household census data derived
from public-use micro samples, or census data aggregated at the tract level. Local usage
studies try to relate residential usage variables (numbers of calls, conversation minutes,
average call duration) to price, income, and various socio-economic and demographic
variables gathered through small-scale surveys.
2.1. Local Telephone Access
Access studies use various qualitative choice models (linear probability, logit,
probit), with:
AC
i = f(Ti , Xi), (1)
where ACi is either the probability that a given household i has telephone access, or the
percentage of households with access in a given area i , Ti a vector of telephone
characteristics, including price, and Xi a vector of household socio-economic
characteristics. Perl (1978) uses a sample of 36,703 households from the 1970 Census of
Population, and matches these data with monthly service and installation charge data from
AT&T. He finds that demand for access is positively related to income, age and education
of the household head, and negatively to household size, unemployment and rurality, with
less access for negro- and female-headed households. Bodnar et al. (1988), using a sample
of 34,262 households from the 1985 Canadian census, test variables similar to Perl's, with,
in addition, dummy variables related to home ownership and size, type of occupation,
recency of residence, degree of urbanization of household location, and identification of
Canadian provinces. Taylor and Kriedel (1990) use 1980 census data on 8423 census
tracts, which, they argue, allow for a better interfacing of census and rate data. Indeed, the
location of micro sample households is only identified in the case of areas with 100,000+
people, which may include several WCs with different local rates. In addition to the usual
household size, ethnicity, mobility, age and employment variables, Taylor and Kriedel use
both income mean and variance, as well as dummy variables related to the availability of
various local service tariffs. All these studies suggest a very low, but non-null, price
elasticity.
2.2. Local Telephone Usage
The general form of local usage models is:
LU
i = g(Ti , Xi) (2)
where LUi is the usage (calls, minutes) by household i over a specific period , Ti a vector of
telephone characteristics, including price, and Xi a vector of household socio-economic
characteristics. The few local usage studies done prior to 1980 have been reviewed and
criticized by Taylor (1980). Additional studies have been published since then, all
designed to assess the effects of usage sensitive pricing on different population groups.
Infosino (1980), using a sample of 1000 households spread over 18 WCs in Metropolitan
Los Angeles and Cincinnati, and the results of a mail survey, relates individual household
calling rates to such variables as race, sex of head of household, and size and income of
household. He obtains R2 around 0.35. In addition, Infosino develops WC models,
relating the wire center calling rate to census data such as the average household size, the
fraction of black and Spanish households, and to the telephone station density, obtaining
higher R2 than for the individual household models. This appears to be the only local usage
study using census data. Brandon (1981) reports results of a study of 513 households in
Chicago, relating the Box-Cox transforms of the number of calls, the average duration, and
the total conversation time, to the number of males and females in different age classes,
dummy variables related to income levels, ethnicity, employment status of head of
household and spouse, occupation, length of residency, and various interaction terms.
However, the estimated models turn out to have poor explanatory power (R2 =
0.05460.195). Brandon computes census-derived variables for each WC, by matching WC
boundaries with census tract and block boundaries, but these variables are not used in the
models. Brandon and Infosino study the effects of demographics on telephone usage under
an unchanging tariff. In contrast, in the study by Park, Mitchell, Wetzel, and Alleman
(1983) with data from the GTE Illinois Experiment, around 640 households spread over 3
WCs are monitored over 6 months, subject to a flat rate during the first three months, and a
measured rate during the last three. Their numbers of monthly calls are related to
demographic variables gathered through a survey and telephone interviews, as well as to
dummy variables related to the service tariff. The results suggest that, after introduction of
measured service rates, larger households reduce their numbers of calls more than smaller
households, and older households do so more than younger households. Under both tariffs,
the number of calls increases with household size and number of teenagers, and the age of
the household head. In a related study with the same data, Park, Wetzel, and Mitchell
(1983) show that calling patterns vary seasonally, with a higher telephone use in winter
than in summer, clearly pointing to the influence of the weather.
Another approach to local calling analysis involves the application to a sample of
individual households of nested multinomial logit models of choice of local service option
and local calling pattern characterized as a portfolio of numbers of calls and average call
durations by time of day and distance zone (Train et al. 1987, 1989). The general form of
the model is:
P
is = f(Yis) (3)
where Pis is the probability for a household to select service option s and calling portfolio i,
and Yis a vector of factors characterizing the service (e.g., tariff) and the household
(income, number of telephones). Because of the extremely large number of possible
portfolios, a random selection of portfolios is used to estimate the models. For instance, in
Train et al. (1989), 3 distance bands, 3 types of days, and 24 hours per day, are considered,
making up 216 potential portfolios. However, this approach can only deal with a few
mileage ranges, and the characteristics of the destination points and their geographical
locations cannot be accounted for.
3. TELECOMMUNICATIONS AT THE REGIONAL SCALE
The scope of the regional scale has changed over time, but always involves a toll
rate system accounting for calling distance, time of day, and duration. Before the
divestiture of the Bell System (1984), a region, in the U.S., could encompass a state, a set
of adjacent states, or the whole nation. Since divestiture, the U.S. territory has been
subdivided into LATAs (Local Access and Transportation Area), within which inter-city
toll service is provided by a monopolistic local exchange company (e.g., Baby Bell), while
inter-LATA service is provided by long-distance companies (e.g., AT&T). Most
post-divestiture studies focus on intra-LATA service, as inter-LATA data have become
unavailable due to competitive and proprietary reasons.
Telephone flow studies at the regional level can be classified into two major
categories: (1) demand models, which try to explain variations in the flows themselves,
whether aggregate or point-to-point, as functions of price, socio-economic, and locational
variables; and (2) inter-city network flow models, which use flow data to better understand
the organization and functioning of urban systems.
3.1 Telecommunications Demand Modeling
3.1.1. Aggregate Toll Models
Aggregate models consider the total number of toll calls within a given territory
(state, LATA), without distinguishing their origins and destinations. Early, pre-1980,
models are variations of the distributed-lag model,
M
t = f( Mt-1, Xt , Pt , Tt ) (4)
where Mt is the total number of intrastate toll messages in year t, Xt the state per capita
income, Pt a price variable, and Tt the number of telephone stations, with generally no
distinction between residential and business calls (Taylor 1980). These studies suggest
mean price elasticities of -0.21 and -0.67 for the short and long runs, and mean income
elasticities of 0.39 and 1.33 for the same horizons. Mahan (1979) regresses the logarithm of
expenditures on long-distance toll calls by 934 households on local service charges,
number of household members, gender and age distribution variables, family income,
distance to family members outside the calling area, and various dummy variables for race,
education of household head, size of local calling area, and employment status. No toll
price variable is considered, and an R2 of 0.35 is obtained. Using state-level data, Griffin
(1982) introduces in an MTS (Message Toll Service) call model, estimated with pooled
quarterly data over the period 1966-78 in 5 southwestern states, the number of subscribers
and its square (the externality effect) and lagged advertising, income, and price variables.
Duncan and Perry (1994), using intra-LATA toll call monthly time series over the period
1986-1990 from GTE California, regress both deflated revenues and minutes of use on
population, real income, and nonagricultural employment, obtaining a price elasticity of
-0.38. Call data are aggregated over mileage bands, times of day, and both residential and
business users. Griffin and Egan (1985) analyze the substitutions between WATS (Wide
Area Toll Service) and MTS for business intercity communications, using a translog cost
function for the business sector, with, as costs determinants, the prices of MTS and low-
and high-usage WATS service. Their results point to MTS and high-usage WATS
own-price elasticities of -0.36 and -0.86. The elasticity of WATS demand with regard to
MTS price is estimated at 0.82. Finally, Guldmann (1993), using an intra-LATA toll call
data base, wherein callers and callees are identified by their SIC code, builds an
eleven-sector table of calls, showing the numbers of calls and conversation minutes from
each sector to each sector, including the residential sector. The analysis of these tables
points to major patterns and clusters of interactions, and to the extent of calling reciprocity.
These intersectoral flows are linked to sectoral employment data, leading to a
telecommunication forecast model using employment forecasts as an input.
3.1.2. Standard Point-to-Point Spatial Interaction Models
The following models can be set within the framework of spatial interaction
(gravity) modeling, wherein flows Xij between origin and destination nodes (i,j) are
functions of the sizes and characteristics of these nodes, that determine their
propulsiveness Vi and attractiveness Wj, and of the friction factors that inhibit movement,
Rij, with:
X
ij = F(Vi,Wj, Rij) (5)
Point-to-point telephone flow models have been developed by both geographers
and economists. However, both streams of studies have somewhat ignored each other, with
geographers emphasizing the effects of distance and place size/centrality, and economists
focusing on price and income effects.
The earliest geographical study of intercity telephone flows appears to be that of
Hammer and Iklé (1957), who regress the total number of telephone calls, in both
directions, between pairs of cities, on the airline distance and the respective numbers of
subscribers. A similar gravity model is estimated by Leinbach (1973), using telephone
flow data for West Malaysia and regressing the number of intercity messages on distance
and the modernization scores of the origin and destination cities, as obtained from a
principal component analysis of various socio-economic data. In addition, he estimates
similar models for 16 originating exchanges separately, and then demonstrates a
significant relationship between the distance coefficient and the distance of the exchange
from a modernization core located close to the capital, Kuala Lumpur, the closer the
exchange to the core the lesser the effect of distance. Leinbach thus provides convincing
evidence of the influence of the spatial structure on telecommunication flows, Hirst (1975),
using telephone call data for Tanzania, shows that combining the distance variable with a
dummy variable that discriminates between dyads that do and do not include the capital
city, Dar Es Salaam, leads to significant improvements in the explanatory power of the
gravity model, with no need for mass variables any longer. This result suggests that the use
of population size as a mass variable may be inadequate for developing countries, because
it does not discriminate well in terms of socio-cultural patterns, political power, and the
type of economic activities in an urban system in early stages of development. Rossera
(1990) and Rietveld and Janssen (1990), using intra-Switzerland and international
Dutch-originating call data, introduce the concept of barriers into gravity-like models via
dummy variables (e.g., linguistic differences). Finally, Fisher and Gopal (1994) use
artificial neural networks to estimate a model of Austrian interregional telephone flows,
where the independent variables are the regional products of the origin and destination, and
the interregional distance. The neural approach provides a gain of 6% in the R2 over the
standard gravity model OLS estimation.
In the economic studies stream, Larsen and McCleary (1970) regress residential
and business interstate toll calls on income, price, and the volume of interstate mail.
Deschamps (1974) regresses intercity calls in Belgium on the numbers of subscribers in
both cities, the income at the origin city, the toll rate, and dummy variables representing
distance ranges, language commonality, the location of a provincial capital, and an index
of sociological proximity defined as the ratio of the commuters between the two cities to
their total population. The distance coefficients are all negative and increase with distance,
while the sociological proximity and language coefficients are positive and highly
significant. Pacey (1983) estimates a model similar to Deschamps’ (1974), but is not able
to separate distance and price effects. Both studies obtain price elasticities around -0.24 for
aggregate residential and business calls. Guldmann (1992), using regional toll calls,
estimates separate residential and business models, for both messages and minutes, with
the effects of prices and distance successfully separated. The models with the highest R2
include second-order terms for the destination size and distance variables. The price
elasticities are equal to -0.31 and -0.54 for residential and business calls, and to -1.43 and
-1.79 for residential and business minutes. The distance elasticities are slightly below -1.0
for calls and around -0.6 for minutes. In addition, conversation time sharing models are
estimated for the different rate periods, following Kohler and Mitchell (1983). If MTijt is
the flow (minutes) during rate period t, and MTij the minutes over all periods from WC i to
WC j, then the share considered is SHijt = MTijt/MTij. In the case of period 1 (day), the
model estimated is:
SHij1 = b0 + b1lnMTTj + b2lnDij + b3ln(Pij1/Pij3) + b4ln(Pij2/Pij3), (6)
where Pijt is the price variable for period t, Dij the distance between i and j, and MTTj the
total flow ending at j.. Combining the aggregate and time-sharing models allows for
computing cross-price elasticites, and thus for assessing substitution effects across rate
periods.
3.1.3. Point-to-Point Spatial Interaction Models with Reverse Flows
Another, more recent, stream of point-to-point models has been initiated by the
seminal paper by Larson et al. (1990), who extend the basic theory of telephone demand,
presented in Taylor (1980), by using reverse traffic (from j to i) as a determinant of the
traffic from i to j. Their theoretical framework is briefly summarized. Two economic
agents, a and b, have utility functions of the form U(X,I), where X is the usual composite
good, and I the "information" good, which is produced through a production function of the
form:
I = f(Q
ab,Qba), (7)
where Qab and Qba are the directional telephone flows between a and b. Two extreme cases
of information exchange are: (1) perfectly reciprocal calling patterns, where agents return
messages in direction proportion to the quantity received; and (2) once a given amount of
information has been transferred, there is no need for further communication. Each agent
is assumed to maximize its utility subject to its income constraint and its information
production constraint, leading to a Nash equilibrium, with:
Qab = W( p, q, Ma, Qba ), (8)
Q
ba = Z ( p, q, Mb, Qab), (9)
where M is the income, p the price of the composite good, and q the price of telephone
service. Larson et al. (1990) analyze high-density intra-LATA toll routes consisting each
of a large metropolitan area (A) and a relatively small suburb or town (B). No information
is provided on the geographical location of these routes, or their length. Traffic flow from
A to B is taken as a function of telephone rates, income, market size expressed as the
product of the populations at A and B, and traffic from B to A, with route-specific
intercepts (i.e., dummy variables), but route length is not an explanatory variable. The
estimated price elasticities are around -0.75. The call back (reverse traffic) coefficient is
estimated at 0.75 for the A-to-B equation, and at 0.67 for the reverse one. This approach is
implemented by Appelbe et al. (1988) in their analysis of Canadian interprovincial flows.
Using long-distance direct-dial MTS data from the six Telecom Canada member
companies, they regroup inter-provincial routes by mileage band, and combine these bands
with two rate periods (full and discount). Then, for each combination, they estimate
point-to-point models, with, as dependent variables, the deflated revenues. The
independent variables include price, income, size of the originating market (the numbers of
residential and business access lines), and the reverse traffic. The call back coefficients
range from 0.38 to 0.72. Similar models are estimated by Guldmann (1998), who analyzes
intersectoral regional toll flows, with the economy disaggregated into four sectors
(Manufacturing, Trade, Services, and Households). Using intra-LATA toll call data, where
callers and callees are identified by their SIC codes, he estimates the following system of
equations:
lnXkilj = a0 + a1lnXljki + a2lnDij + a3lnPkilj + a4lnNCOki + a5lnNCDlj (10)
lnXljki = a0 + a1lnXkilj + a2lnDij + a3lnPljki + a4lnNCOlj + a5lnNCDki (11)
where Xkilj is the flow from sector k located in wire center (WC) i to sector l located in WC
j, Dij the distance between the central offices of the two wire centers, Pkilj the average toll
price from (k,i) to (l,j), NCOki the total outflow from (k,i), and NCDlj the total inflow to
(l,j). The last two variables are measures of the sizes of the origin and destination markets.
The models are estimated for both calls and conversation seconds. As in all previous
studies, the results point to the often significant role of the reverse flow, however with
strong variations from one intersectoral interaction to another. The bidirectional price
elasticities vary between -0.125 and -0.656 for calls, and between -1.114 and -2.193 for
minutes. The effect of distance is also always negative, and, in most cases, highly
significant. As distance is taken as proxy for transportation costs, this negative cross-price
elasticity suggests a complementarity between the transportation and telecommunication
inputs to all production processes. Using the same data, Guldmann (1999) models
inter-city total flows (minutes), accounting for both reverse flows and the effects of the
spatial structure. He tests alternative forms of competing destinations (Fotheringham,
1983) and intervening opportunities (Stoufer, 1960) factors, in terms of both their spatial
definition and their distance exponent. He concludes that the spatial structure has an effect
on telecommunication flow patterns, confirming the earlier results of Leinbach (1973) and
Hirst (1975). The effect is competitive, at the destination, providing a model explanatory
gain of 7.5% (up from 64.2% without such a factor).
In all the previous studies, simultaneous equation estimation procedures are used.
In order to analyze the welfare implications of extending local calling areas, Martins-Filho
and Mayo (1993), departing from this estimation approach, account for the reverse traffic
effect by estimating the correlation of the flows of transposed exchanges. They use data
for 4 major Tennessee metropolitan areas to regress point-to-point calls on (1) a price
variable measuring the cost of a three-minute duration call, (2) a market size variable equal
to the product of the numbers of subscribers at the two points, and (3) dummy variables
representing different distance ranges. The call back effect is estimated around 0.40. The
distance effects are negative and significant, and the price elasticity range from -1.18 to
-1.54.
3.1.5. Distance-Stratified Models
Calls are divided into several categories on the basis of time, distance, and other
factors, and regression models are estimated for the number and average duration of calls
in each category. However, the problem with that approach is that it may involve a very
large number of equations, and it may be very difficult to allow for the full set of
cross-elasticities and other constraints across equations. Gatto et al. (1988) model AT&T
MTS interstate residential demand by developing systems of 5 interdependent demand
equations corresponding to alternative ways of placing a call (direct dial-DD-evening, DD
day, DD night, operator-assisted calls, and person-to-person) for each of the 48 states and
for five mileage bands (1-30, 31-124, 125-430, 431-925, 926-3000), each equation relating
the number of messages per access line to price and income variables. They use the
Random Coefficient Regression (RCR) approach, which appears to provide more
reasonable estimates (e.g., price elasticities and cross-elasticities with the right sign) than
the Seemingly Unrelated Regression (SUR) approach (Zellner 1962), primarily because
cross-equations restrictions are to apply only stochastically. Gatto et al. assume that
calling patterns are independent across mileage bands. If this hypothesis were rejected, the
joint estimation of 25 equations would be necessary. De Fontenay and Lee (1983) analyze
residential calls between British Columbia and Alberta. Second-order, translog-type
models, allowing for variable elasticities, are estimated for various mileage bands by
regressing call minutes on price and income, with price elasticities ranging from -1.12 to
-1.65. Cameron and White (1990) use a sample of 26,672 long-distance calls originating
from British Columbia, and regress call duration on rate, distance, and several dummy
variables characterizing the call (time-of-day, business, collect, credit card,
person-to-person, etc.). They find that call duration decreases with price and when the call
is placed person-to-person or with a card, and increases with distance (a result similar to
Pacey's 1983) and when the call is placed as collect and in the evening or night. Finally,
the discrete logit model approach reviewed in the context of local usage (Section 2.2) has
been recently used by Train (1993) to estimate a price elasticity of -0.39 for intra-LATA
toll calls by GTE-California residential customers.
3.2. Information Flows and the Urban Hierarchy
Various inter-city flows (e.g., migration, commuting, freight, telephone) have been
used to analyze regional settlement structures, uncover central place hierarchies, delineate
functional and nodal subregions, and identify regional disparities (e.g., core-periphery).
Telephone flows, which depend upon the socio-economic structure, size, and
interdependencies of the regional urban network, are considered the best single criterion by
which to grasp the urban system in its totality. Interestingly, Christaller (1966) uses the
number of telephone stations per person to develop a hierarchy of centers among Southern
Germany’s cities in 1933, to illustrate his central place theory (CPT), and Green (1955)
uses telephone call data to define the common boundary of the hinterlands of New York
City and Boston. In this section, we review several studies that attempt to uncover urban
hierarchies and network structures, based on inter-city telephone linkages. The approaches
may be regrouped into three categories: graph theory, Markov chains, and multivariate and
clustering methods
3.2.1 Graph Theory
Nystuen and Dacey (1961) pioneer the graph theory approach, and apply the
concept of dominant or primary linkage to the analysis of a 40x40 matrix of inter-city
telephone calls in the state of Washington. Each place i is assigned to that place j to which
it sends its largest flow (i.e., xij>xik, kj), provided that j is larger in size than i, where size
is measured by the total incoming flow. Each such place j is defined as the central place or
nodal point for the places assigned to it. This network of nodal points and largest flows is
the skeleton of the urban hierarchy in the entire region. Central cities are the terminal
nodes in this hierarchy, i.e., they are not assigned to any other node. The basic problem is
that all the lesser flows are ignored, and thus much information in the interaction matrix
[xij] may be wasted. This approach is also applied by Dietvorst and Wever (1977) and
Clayton (1974, 1980). Puebla (1987) extends the method with a multiple linkage
approach.
Rouget (1973) analyzes the telephone flows between the 34 centers of the
Bourgogne-Franche Comté region of France, using the concept of power of a node. If xij is
the flow from i to j, and xi the total flow from i, then node i is said to dominate node j if
(xij/xi) < (xji/xj), and if the relative difference between these two ratios is at least 10%. Only
ratios higher than 1% are used to define relations of dominance or symmetrical influence.
If i dominates j, then 2 arcs are assigned to the i6j linkage, and none to j6i. If there is a
symmetrical influence between i and j, then 1 arc is assigned to each direction. Let M =
[mij] be the matrix of the resulting numbers of arcs, and Mk the matrix obtained by
multiplying M k times by itself, with Mk = [pjj], and pjj the number of distinct paths of
length k (i.e., with k arcs) running from i to j. Rouget then defines measures of power of
nodes, based on the mij and pij. For instance, the influence of node i on all other nodes is
defined as:
Β(i) = ∋jmij + ∋j∋kpij (12)
Rouget then ranks centers according to the index Β(i), with 8 centers with a score greater
than the regional average, and 3 centers accounting for 75% of the group’s total score.
Rouget also presents an alternative ranking method, based on the pseudo Grundy function,
that assigns the centers to 9 hierarchical levels.
A third graph-theoretic approach, implemented by Fischer et al. (1993) with
Austrian interregional telephone flows, is based on the iterative proportional fitting
procedure (IPFP) in conjunction with a hierarchical clustering procedure based on the
concept of strong components of a directed graph. The IPFP standardizes the interaction
matrix so that the sums of all rows and all columns are equal. The entry (i,j) of this
standardized matrix represents a measure of the functional relationship from i to j. Next, a
directed graph is built hierarchically, based on the strength of the (i,j) entries of the matrix,
leading to the formation of clusters of nodes linked by paths of directed arcs.
3.2.2 Markov Chain
The use of Markov chains, pioneered by Brown et al. (1970) and Brown and
Holmes (1971) in their studies of migration and journey-to-work flows, is applied to
telephone flow data by Hirst (1975) and Dietvorst and Wever (1977) to delineate
functional regions and urban hierarchies. The approach is based on accepting the
interaction matrix [Xij] itself as representing the structure of the interaction phenomenon,
without implying any causal structure, and on computing the probabilities Pij of interaction
from location i to location j, with:
Pij = Xij/∋jXij, (13)
where Xij is the observed flow from i to j. The next step is to solve a recursive system of
linear equations (Hillier and Lieberman 1968, Chapter 13) to compute the probabilities f(n)
that the first passage time from state i to state j is equal to n. It is then possible to compute
a Mean First Passage Time MFPTij for any couple of places i and j, which serves as an
index of functional distance. The MFPTij can be viewed as a nonspatial measure of
proximity between regions i and j: the lesser this distance, the greater the level of
interaction. The average MFPT for a given destination can be viewed as a measure of its
overall accessibility and centrality in the urban hierarchy. Then, using clustering
algorithms, destinations can be grouped according to the MFPT, thus providing a
delineation of functional regions and an urban hierarchy.
Applying the MFPT method to inter-city calls in Tanzania, Hirst (1975) assigns the
19 towns to 4 urban hierarchy levels. Dietvorst and Wever (1977) also apply the MFPT
method to 8 annual telephone flow matrices, from 1967 to 1974, and show that the
hierarchical structure of the 21 districts displayed a significant degree of stability, with no
change in the ranking of the 7 most central districts. However, their MFPTs increase with
time, pointing to a weakening of their dominating position, while the MFPTs for the
majority of the other districts decline, suggesting that they are coming to occupy a less
peripheral situation in the information exchange system.
3.2.3 Multivariate and Clustering Methods
Central place structures are also delineated by using multivariate analysis
techniques applied to matrices containing standardized measures of flows between places,
with functional groupings indicated by factor loading patterns.
Illeris and Pederson (1968) use factor analysis to delineate places with a high
degree of centrality, and their zones of influence, using telephone flows between 62
districts in Denmark. The factor loadings are interpreted as places that have similar
destination profiles, and the scores of the places designate the places that send messages to
these receivers. Factor 1 shows a very high score in the Copenhagen district and low
positive or negative scores in all other districts, and thus represents the calls from
Copenhagen to the rest of the country. The influence zones of the 7 major centers are
delineated, the maximum factor weight determining, for each district, the hinterland to
which it is assigned. Descubes and Martin (1982) also use factor analysis to delineate
major centers and zones of influence in Alsace, France, based on inter-city telephone
flows. The results point to a strongly polarized structure, with three major centers
(Strasbourg, Colmar, Mulhouse) that dominate 140 of the 173 districts.
Clark (1973) uses principal component analysis to delineate urban linkages in
Wales in 1958 and 1968, based on long-distance communication data. He also uses
canonical correlation and a step-wise grouping procedure to measure the changes in the
linkages from 1958 to 1968, pointing to a trend where increasingly more distant areas
become involved within the spheres of influence of the major centers, thus suggesting that
urban and regional growth is the product of the intensification of connections between
previously poorly linked areas. Clayton (1980) also uses principal component analysis to
delineate, among 66 Western Massachusetts communities, the major organizing nodes and
their dependent satellite places, based on inter-city calls.
Finally, cluster analysis is also used to analyze spatial structures. Clayton (1974),
using message flows between 36 toll centers in New England, clusters the lines and
columns of the interaction matrix into groups so as to maximize the difference between
separate groups and to simultaneously minimize the difference between the members of
any group. Rows are grouped based on their role as origins of messages to all other places
in the system (similar divergence profiles), and columns are grouped based on their role as
collectors of messages (similar convergence profiles). Another hierarchical clustering
procedure, the Intramax, is implemented by Fischer et al. (1993) with Austrian telephone
flows. The strength of the interaction is measured by the difference between observed and
expected flows, where the latter are based on the product of the observed marginal
frequencies divided by the overall total. Nodes are then aggregated based on pairwise
comparisons of their relative strength of interaction.
3.2.4 Comparative Analyses
Some of the studies discussed in the previous sections involve a comparison of the
hierarchies obtained with different methods. Illeris and Pedersen (1968) use nodal data, (1)
wholesale trade employment, and (2) the occurrence of 16 central functions, to create
central place hierarchies, which are compared with the hierarchy derived from the factor
analysis of inter-district telephone flows. The 4 major centers turn out to be the same in all
3 approaches, but the positions of the following medium-level towns depend upon the
measure selected. The nodal analysis tends to assign high positions in the hierarchy to
towns located in densely populated regions near major metropolitan centers, while factor
analysis tends to space centers far apart, each dominating its own hinterland, but located
outside the influence fields of other centers. Clayton (1974) compares the applications of
(1) Nystuen’s and Dacey’s graph-theoretic approach, (2) principal component analysis,
and (3) cluster analysis, to telephone flows in New England, concluding that the three
methods yield patterns of spatial organization with a high degree of similarity. Dietvorst
and Wever (1977) compare the application of (1) Nystuen’s and Dacey’s approach, and (2)
the Markov chain MFPT approach, to telephone flows in the Netherlands, concluding that
the network derived from the MFPT approach displays considerably greater stability over
the years. Clayton (1980), using the frequencies of occurrence of 60 tertiary and
quaternary functions in 89 places in Western Massachusetts, applies principal component
analysis to these data to derive a hierarchy with five levels of central places. He concludes
that there is convergence between this hierarchy and the ones derived by applying (1)
Nystuen’s and Dacey’s approach, and (2) principal component analysis, to inter-city
telephone flow data. Finally, Fischer et al. (1993) compare the application of (1) a
graph-theoretic IPFP-based approach, and (2) the Intramax procedure, to Austrian
telephone flows, pointing to the superiority of the Intramax approach because it leads to the
spatial groupings of nodes with more intra-group and less inter-group interactions.
3.2.5 Combined Hierarchical and Spatial Interaction Analyses
Camagni and Salone (1993) test the hypothesis that the central place theory (CPT)
paradigm of linkages between cities in a region is no longer sufficient to explain
contemporary regional structures, and must be complemented by the new paradigm of city
networks, made of specialized and complementary centers interconnected through market
interdependencies, and synergies. The hypothesized new spatial order simplifies vertical
relationships between cities and complicates, instead, their horizontal relationships.
Camagni and Salone use telephone flows among the 157 districts of the Lombardy, Italy,
region in 1990, and assume that a network relationship exists between 2 centers if the
actual telephone flows significantly exceed the interaction expected on the basis of a
doubly-constrained gravity model. The results show that such networks do exist, but are
not ubiquitous, and do not substitute for the traditional CPT form of spatial organization.
Networks are discovered within the metro area of Milan, shaping its emerging polycentric
structure, and within sub-regional industrial districts. They conclude that the two
organization forms should be viewed as complementary rather than mutually exclusive.
4. TELECOMMUNICATIONS AT THE INTERNATIONAL SCALE
The country is the basic spatial unit at the international scale, and all studies involve
country-to-country telephone flows. The models used to explain these flows are
structurally similar to the regional spatial interaction models. However, the selected
explanatory variables are significantly different, involving trade, tourism, and language
and cultural commonalities.
4.1. Country-to-Country Standard Gravity Models
Early econometric models of international telecommunication demand generally
include separate equations for telephone, telegraph, and telex services. Most of these
models were developed in the 1970s, when telephone service was not as dominant as it is
today. Lago (1970), making use of 73 observations on telecommunication flows between
the U.S. and 23 countries over the period 1962-1964, regress the number of telephone
messages between the U.S. and country i in year t, on the volume of trade between the U.S.
and country i, the U.S. investment in country i, the value of U.S. travel expenditures to
country i, the U.S. population whose parents came from country i, the number of
telephones in country i, a dummy variable related to use of radio circuits, the speed of
service (all connections were operator-assisted), the number of common hours during a
working day schedule between the U.S. and country i, the price of a 3-minute call, the cost
per telegram word, the telex cost for 3 minutes, and the monthly rental cost of leased
telegraph circuit service between the U.S. and country i. Similar equations are estimated
for telegraph and telex services. Lago's results show that (1) time commonality,
foreign-parentage population, and number of telephone sets are insignificant variables, (2)
trade, tourism, and U.S. investment abroad are significant variables for telephone service,
and (3) the own-price elasticity of telephone service is greater than one, with no
substitutions with the other services. Telegram service turns out closely related to trade,
and very vulnerable to telex service. Naleszkiewicz (1970) estimates similar equations
while regrouping destination (from the U.S.) countries according to their economic
development status and considering four categories of explanatory variables: (a) flows of
capital between countries, proxied by foreign assets and liabilities; (b) flows of goods and
services, measured by imports, exports, national income, and gross national product
(GNP); (c) country wealth, measured by money supply, demand for deposits, etc.; and (d)
country industrialization, measured by industrial production. Yatrakis (1972), using the
numbers of calls over 46 international routes in 1967, estimates models similar to Lago's
and Naleszkiewicz's, while including additional explanatory variables such as: the average
fare of a first-class airline round trip, the percentages of a country GDP attributable to the
extractive and manufacturing sectors, the number of ships of 1000 tons capacity registered
with the origin country, government expenditures as a percentage of the GDP, the average
annual dividends paid and received on foreign investments, the numbers of emigrants to
and immigrants from all destination countries, the percentage of the population living in
urban centers, and measures of language similarity and spatial contiguity among the pairs
of interacting countries. The last two variables turn out to be highly significant. All the
previous studies involve simple regression (OLS).
More sophisticated is the slightly later work of Rea and Lage (1978), who use the
error component regression model to deal with cross-section time-series data on the
number of outgoing messages from the U.S. to 37 major countries over the period 1964-73.
While their equations are, in general, similar to the previous ones, and their results also
point to a price-elastic demand (-1.8) for telephone service, they conclude, in contrast to
earlier work, that the value of total trade (exports + imports) between the U.S. and the
foreign country is not a significant variable. Fiebig and Bewley (1987) use the Box-Cox
transformation in the estimation of a lagged model for telephone traffic between Australia
and ten foreign countries, where the number of paid minutes for outgoing telephone traffic
is regressed on the real GDP of Australia, a telephone price index, the bilateral trade, and
the short-term migrations. A lagged endogenous variable is used to capture habit
formation and inertia effects, and also provides a way to distinguish between short-term
and long-term elasticities. Tests regarding the optimal Box-Cox parameters suggest that
the double-log functional form is acceptable, while the linear one is not. Bewley and
Fiebig (1988) further analyze Australia-originating international telephone calls by
modeling how the numbers of calls and conversation minutes are shared among the
following three services: (1) direct dialing, (2) operator-connected station-to-station, and
(3) operator-connected person-to-person. This is the first study to analyze substitution
among services for international telecommunications. Rietveld and Janssen (1990), mixing
462 observations on interregional calls within the Netherlands (22 districts) and 27
observations on international calls between the Netherlands and foreign countries, estimate
gravity models where the explanatory variables are the district/country gross domestic
products, the origin-destination distance, and dummy variables characterizing 11
individual and groups of foreign countries, intended to measure the barrier effect of
borders. This is the first time that a distance variable is introduced into such a model. It
turns out to be highly significant, with an elasticity of -1.23. The coefficients of the
dummy variables are negative and, in most cases, significant, pointing to barrier effects.
Focusing on the 27 international calls observations only, they use both distance and the
cost of calling in the same model, but the coefficient of distance becomes insignificant, due
to the high correlation between these variables. Hackl and Westlund (1995), departing
from the traditional assumption of constant price elasticity, show that the demand for
telecommunications between Sweden and its major trading partners (Germany, U.K., U.S.,
Denmark, Finland, Norway) is best described by time-varying coefficient equations
estimated with the moving local regression technique and with monthly data over the
period 1976-1990. In addition to price, the relevant explanatory variables include trade
volume and industrial production indices for Sweden and the foreign countries.
4.2. Country-to-Country Gravity Models with Reverse Flows
A second stream of study involves accounting for callback effects. Acton and
Vogelsang (1992), analyzing the annual telephone traffic between the U.S. and 17 West
European countries over the period 1979-1986, and borrowing from Larson et al. (1990),
incorporate the phenomenon of call stimulation or substitution by including the return
telephone flow in their estimated equations. However, instead of using a simultaneous
equation approach, they estimate a reduced form of the equation, where the demand for
calls (minutes) from the U.S. to a foreign country is a function of the originating and
terminating prices of both telephone and telex services, the U.S. and foreign country gross
domestic products (GDP), the number of European telephones, trade volumes, and the
composition of production in the destination country (agriculture, restaurants and hotels,
transportation, banking and financial services, manufacturing), and country-specific
dummy variables to capture other effects. The results indicate that the own-price and GDP
variables are significant, but that cross-price and trade and telephone equipment variables
are not. Appelbe and Dineen (1993) report on the results of a similar approach to
Canada-Overseas MTS demand. Using quarterly data for the period 1988 to 1991, they
analyze calling patterns between Canada and the U.K., France, Italy, Holland, Germany,
Hong Kong, Japan, Australia, and the Carribbean, using a 4-quarter lag for prices and a
3-quarter lag for income. Other variables include retail sales and access lines. They report
a low callback effect coefficient of 0.10. Sandbach (1996) estimates an origin-destination
model with traffic data on 154 routes between developed countries and in both directions.
The non-price variables include the numbers of lines in the origin and destination
countries, the GDP per capita in the origin country, the time difference between countries,
the inverse of distance, and dummy variables related to language commonality and the
Germany-Turkey routes (picking up the impact of the German guest worker community).
The price variables include the price of an outgoing call, and the difference between
incoming and outgoing call prices, to capture call stimulation and reversal effects.
However, these effects are not statistically significant, probably because of the relatively
low level of price disparity. Garin-Munoz and Perez-Amaral (1998) estimate demand
functions for outgoing telephone traffic from Spain to 27 African and Oriental countries
over the period 1982-1991. The explanatory variables include the minutes of incoming
traffic, the price of an outgoing call, the volume of trade between Spain and the foreign
country, and the number of tourists in Spain from this country. They use instrumental
variables to control for the simultaneity between outgoing and incoming calls. The
incoming calls, price, and tourists variables turn out to be significant, but the trade variable
is not. Finally, Karikari and Gyimah-Brempong (1999), using traffic data between the U.S.
and 45 African countries over the 1992-1996 period, implement a simultaneous equations
approach and regress the number of calls in one direction on the lagged traffic in this
direction, the return traffic, the price of an outgoing call, the GDP per capita, the volume of
trade, the differential in outgoing and incoming prices, and the product of the number of
households, as a measure of the community of interest.
5. THEORETICAL FRAMEWORK
The previous review points to a diversity of approaches in analyzing
telecommunication flows. However, their theoretical foundations are limited, which
hinders the development of more comprehensive methodologies. The purpose of this
section is to outline a theoretical framework within which these approaches can be nested,
and which can point to new research directions. This framework extends the concept of
information function proposed by Larson et al. (1990).
The focus is on a simple model of the firm, where the information generated by
two-way telecommunication exchanges are linked to basic input and output transactions.
Consider firm A that sells its output Q to firm B. Firm A buys two inputs: materials, M,
from firm C, and labor, L, from residential area R. Delivered pricing is assumed to take
place, wherein the seller of goods or labor incurs transportation costs. Let PQ , PM , and PL
be the competitive market prices of Q, M, and L, and tAB the unit transportation cost of Q
from firm A to firm B. Let Q=f (M, L) be the production function of firm A. The standard
problem of firm A is to select the values of Q, M, and L that maximize its profit,
ΑA = PQQ - PMM - PLL - tABQ, (14)
subject to the production function constraint. To extend this basic model, consider the
telecommunication exchanges (flows) that may take place between the four parties (A, B,
C, R) to complete the above transactions: F= (FAB, FBA, FAC, FCA, FAR, FRA ). Each flow
may be viewed, in turn, as a multidimensional vector, including voice, data, and video
subflows, with possible substitutions among them. However, for the sake of presentation
clarity, each flow is treated as unidimensional. These flows are constrained by the
telecommunication infrastructure available at each location (e.g., large data transmissions
are easily handled via fiber optic cables, but much less so over copper cables). Let T=(TA,
TB, TC, TR) be a vector of exogenous variables (e.g., types and numbers of access lines and
switching channels, capacity of transmission trunks, microwave channels, coaxial and
fiber optic cables) characterizing the state of the telecommunication infrastructure at A, B,
C, and R. The completion of the transaction between A and B (sale of Q) requires a certain
amount of information, I, that is function of the individual information exchanges FAB and
FBA, and the available telecommunication technologies TA and TB, with:
I
AB = g(FAB, FBA, TA, T B). (15)
The relationship between transaction and related information is next expressed by an
information constraint:
g
Q (Q, IAB) = gQ (Q, FAB, FBA,TA,TB) = 0 (16)
Similar information constraints apply to the M and L transactions, with: gM (M, FAC, FCA,
TA, TC) = 0 and gL(L, FAR, FRA, TA, TR) = 0. Let Pij be the unit price of
telecommunications from i to j. The expanded profit function of firm A now accounts for
the costs of the telecommunication flows initiated by A, with:
ΑA = PQQ - PMM - PLL - tABQ - PABFAB - PACFAC - PALFAL (17)
Firm A selects (Q, M, L, FAB, FAC, FAR) to maximize (17) subject to the production and
information constraints. The derived input demand functions have, as arguments, (1) the
market-determined prices of the output and all inputs, (2) all the reverse
telecommunication flows, the amounts of which are determined by agents B, C, and R, and
(3) the telecommunication infrastructure variables T. Let P and RF be the vectors of prices
and reverse flows associated to firm A: P = (PQ, PM, PL, tAB, PAB, PAC, PAL), and RF =
(FBA, FCA, FLA). The optimal telecommunication flow from A to B is then expressed as:
F
AB = hAB ( P, RF, T ) (18)
Similar demand functions would be derived for FAC and FAL, as well as for all the flows
initiated by B, C, and R, leading to a Nash equilibrium for all flows. The above model of
firm A could be extended to include (1) several distinct markets for Q, including other
firms as well as final (residential) markets, (2) several sources of inputs (e.g., capital,
energy, other materials), and (3) several labor inputs differentiated by skills. Such
considerations would expand the price and reverse flow vectors, but would not modify the
basic structure of Eq. (18). Further extensions arise when more than one transaction take
place between two parties, e.g., firm A sells some of its output to firm B, but also buys as
input some of the output of firm B. Two distinct telecommunication demand functions for
flows from A to B would then be associated to these two transactions, but only the sum of
these flows would actually be observed. Finally, note that the model could be easily
modified to include other modes of communication, such as snail mail and face-to-face
contacts (implying business travel), accounting for their costs and possible substitutions
for telecommunications. A similar model can be formulated for a household, which
engages in social transactions with other households, sells its labor to firms, and purchases
goods and services from firms, while maximizing its utility function subject to income,
time, and information constraints, leading to similar information demand functions.
Because of lack of space, it is not presented here.
The respective locations of firms and households are prime determinants of the
costs/prices of the transportation and telecommunication services they require. It is
assumed that the general model (18) is applicable to clusters of similar households and
firms located at distinct sites. Define FKiLj as the total flow from sector K at location i, to
sector L at location j, with:
F
KiLj = ∋ k,(K,i) ∋ Ρ,(L,j) FkΡ , (19)
where FkΡ is the telecommunication flow from agent k to agent Ρ. It is reasonable to
assume that FKiLj is a function of the vectors of reverse flows, RF, prices, P,
telecommunication infrastructure T , and some measures of the sizes and characteristics of
sectors (K,i) and (L,j), S, with:
F
KiLj = f( RF, P, S , T ) (20)
Equation (20) encompasses all the point-to-point models reviewed in Section 3 and
4. In these models, the reverse flows vector RF only includes the flow FLjKi . However,
Eq. (20) suggests that other return flows F**Ki might be included in RF, which would
require the formulation and estimation of larger and more complex systems of
simultaneous equations. The price vector P generally includes some telecommunication
price(s) and distance, which can be taken as proxy for the cost of transportation. However,
Eq. (20) suggests that the prices of other goods and services might be included in P. While
such location-specific prices are generally unavailable, their spatial variations are related
to the spatial organization and location of activities, i.e., the spatial structure. Guldmann
(1999) represents the first systematic attempt to account for the spatial structure, and
further research in this direction should be useful. While all the mass variables are
subsumed in vector S, none of the reviewed studies accounts for infrastructure variables T.
This is also an area for further research.
The urban hierarchy models reviewed in Section 3.2 focus on the aggregate
inter-city flows
F
ij = ∑K ∑L FKiLj (21)
Strong determinants of the flows Fij are likely to be the mix and size of the economic
activities at i and j (mass vector S), and the telecommunication infrastructure (vector T).
The hierarchy models may be helpful to uncover changes in the urban system resulting
from economic restructuring and the use of information technologies. The framework
made of Eqs. (20) and (21) may help further understand these changes.
Finally, the firm’s profit maximization and consumer’s utility maximization
behavioral models can also be used to analyze the impacts of telecommunications on the
socio-economic system. Consider, for instance, a producer services (PS) firm located at
time t1 in the CBD of a metropolitan area, where it maximizes its profit Α1,CBD under the
prices P1 and telecommunication infrastructure T1 vectors. Let F1,CBD be the vector of
telecommunication flows generated by and terminating at this CBD firm (see Eq. 18).
Consider next a later period t2 when CBD real estate costs have increased significantly,
while the costs of telecommunication services and clerical labor in an edge city (EC) are
much lower than those in the CBD. Further, fiber optics cables are now available in the
EC, which allows for easy telecommunications with customers located in the CBD, thus
reducing the need for face-to-face contact travels. Given the prices P2 and
telecommunication infrastructure T2 vectors at time t2 , the firm PS will decide to relocate
to the EC if it can achieve a higher profit than by remaining in the CBD, that is:
Α2,EC ( P2 , T2 ) > Α2,CBD ( P2 , T2) (21)
If PS moves to EC, we can expect a pattern of telecommunication flows F2,EC different
from the one that was associated to the CBD location, F1,CBD , in particular intense flows
between the EC and the CBD. A similar comparative analysis could be applied to a worker
considering telecommuting. If, after accounting for the time saved by not commuting, the
ability to deal with personal/family duties, but also the social isolation and lack of working
interactions, the worker derives a higher utility by telecommuting, UT , than by
commuting, UC , then he/she will telecommute (provided, of course, that the employer
agrees to this arrangement). Thus, changes in telecommunication flows and infrastructure
may be linked to changes in the location of economic activities and households, and the
proposed framework should provide guidance for empirical analyses of these relationships.
6. CONCLUSIONS
The social sciences literature dealing with telecommunication flows has been
reviewed, classified along different geographical scales (local, regional/national, and
international), with an emphasis on the methodologies used to analyze the empirical data,
and on the nature of the results. There is no claim to exhaustiveness, and the reader might
usefully consult Taylor (1980, 1994) for further references and descriptions. However, to
the best of our knowledge, the studies reviewed here are representative, and should
provide, together with the theoretical framework presented in Section 5, a good basis for
further empirical research on telecommunication flows. Understanding the spatial
structure of these flows and their relationships to the socio-economic spatial structure is
likely to become more and more critical in the information economy.
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