A Spatial Analysis for Telecommunications: Estimates of Demand Elasticities in European Union

Christos Agiakloglou* and Sotiris Karkalakos** * Department of Economics, University of Piraeus, Piraeus, Greece ** Department of Economics, University of Cyprus, Nicosia, Cyprus

Abstract In this paper we try to identify and evaluate the role of geography in telecommunications. We use a spatial econometric framework, since this approach is particularly useful in studying spatial patterns, to estimate a demand function for telecommunications in European Union, emphasizing the geographic and economic characteristics of this demand behavior. Our results provide evidence that spatial correlation is considered to be an important factor which affects demand elasticities for telecommunications.

Keywords: Price elasticities, telephone traffic demand, spatial dependence. JEL classification: C21, C22, C23, L96

Corresponding addresses: *Karaoli & Dimitriou 80, Piraeus 18534, Greece. Tel.: +30-210-414-2290, Fax.: +30-210-414-2290, E-mail [email protected]. ** P.O. Box 20537, CY-1678 Nicosia, Cyprus. Tel: +30-5722-892-405, E-mail: [email protected].

1. Introduction

The telecommunications sector has received an increasingly attention in the economic literature over the last few years and a large volume of theoretical and empirical work has been published in this area trying to analyze its market performance. The two essential components of this research interest are the demand for telecommunications and the market structure. Indeed, the demand for international telecommunications services has increased tremendously as a result of the expansion of the economic activities of many multinational organizations, as well as of international tourism and at the same time the telecommunication market has moved to a more deregulated market structure, following the rules established by the Regulatory Authority. In this environment, several important elements of any market behavior, such as price practicing, demand elasticities, innovations and market share are more important now than before and they are playing a major role in any firm's daily activity. Several

research

papers

have

examined

the

performance

of

the

telecommunication market. For example, Kiss and Lefebvre (1987) applied a variety of telecommunications cost models to American firms, where Laffont and Tirole (1993 & 2000) have focused their research on regulatory framework models on how to make regulation more efficient. In fact, they concluded that a good regulatory framework requires cost and demand information. A study also by Gasmi et al., (1999) indicates that despite efficiency gains from regulatory schemes, consumers might experience significant loses. Therefore, in order to understand the impact of regulatory reforms in the economy, it is very important to analyze telecommunications demand, since estimates of price elasticities are essential in measuring social welfare level attained by the

2

regulatory environment.

Indeed, determining demand behavior for international

telecommunications services it not only important for the operating companies, but it is important also for their Regulator Authority. Operating companies need to know demand elasticities in order to set their market targets, the quality of services and their profit goals over some period of time. Meanwhile, regulators need also to know these estimates to control market behavior and to prevent any unfair action against smaller firms. In this lieu, several empirical studies, such as Appelbe et al. (1988), Bewley and Fiebig (1988), Acton and Vogelsand (1992), Hackl and Westlund (1995), Perez Amaral et al. (1995), Sandbach (1996), Garin Munoz and Perez Amaral (1996 & 1998), Wright (1999), Madden and Savage (2000) and Agiakloglou and Yiannelis (2005) have tried to estimate price elasticities for international telecommunications demand for different countries based on time series data. This paper aims to analyze the extent to which price elasticities of demand for telecommunications differ between broad groups of countries classified according to geographic, social and economic criteria. To accomplish this, spatial econometrics analysis in employed to obtain empirical evidence of the differences in demand parameter estimates between European countries, using data published in Eurostat statistics, a European Union publication.

The final estimates derived for the

elasticities will indicate the degree of diversification of these elasticities across Europe. The theoretical framework of how to obtain the demand reaction function is presented on section two, whereas section three discusses the various spatial econometrics models and the definitions of spatial weights. Section four describes the variables used in the regression analysis and section five presents the final results. The concluding remarks are discussed in section six.

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2. Theoretical Framework

The demand for international telecommunications of a country i is defined as the amount of calling time used during some period of time, where the calling time is distributed over different distances. Let m(d, g, t) denote the expected calling time in distance zone d, with g denoting the local economic characteristics, such as, for example, per capital income and population density and t is the time period. In all cases, we consider that there are D distance zones, so d = 1, 2, …, D, G local economic characteristics distinguished in the tariff, so g = 1, 2, …, G, and T time periods, so t = 1, 2, …, T.

The demand then m(d, g, t) of international

telecommunications will be a function of the price q(d, g, t) per minute of calling time in distance zone d with characteristics g, as well as of prices p(d, g, t) of composite goods in the complete The estimation procedure will take into account the fact that the tariff has "two dimensions" meaning that the price per minute of a long distance call differs both across points in time (t) and across distance zones (d), given local economic characteristics (g). In that sense, a consumer who considers making a zone d call and has to decide at which time t to make that call, takes prices for type d calls at various points in time into account as well as the distance zone d. In addition, the consumer takes also into account prices in other distance zones. However, the consumer cannot substitute a call to person i in one distance zone for a call to person j in another distance zone as a result of a price change in one of these zones. Therefore, the longer the distance the higher the price per minute must be and this gives us the opportunity to measure the price sensitivity of calls from cross sectional data with a fixed tariff.

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Suppose there is a continuum of potential economic agents, whose preferences for telephone calls are measured by a parameter ρ with distribution function B(ρ) and density b(ρ) in [ρlow, ρhigh]. The parameter ρ is related to the income and geographic location of the agent and the distribution of consumer types is consider as public information. Given a customer of type ρ, an economic agent derives utility when making a number of calls to each of the other subscribers (information) and a vector of composite goods. Information is produced from incoming and outgoing calls. Therefore, assuming that there is only a long distance traffic route with endpoints i and j and that the agent i is located at country i, then the agent’s optimization problem is constructed in the following way. First, the utility function Ui of the agent located at point i is defined as: U i ( ρ , X i , Ci , Gi ) = ρ ui ( X i , Gi ) + k ( ρ )Ci − qi (d , g , t )

(1)

with U´(.) > 0 and U´´(.) < 0, where Gi is the vector of country specific economic characteristics, Xi is the vector of composite goods (i.e., x1, x2, …, xn), ui is the utility function only as a function of Xi and Gi, k ( ρ ) is the coefficient which depicts the type of customer and Ci is the information produced as a function of the telephone traffic m, i.e., Ci = f ( mij , m ji )

(2)

where mij and mji represent telephone traffic from country i to country j and from country j to country i respectively. Furthermore, agent i has an income Ii to spend for international calls defined as: I i = h( pi , qi , X i , mij )

(3)

where pi is the vector of all prices (i.e., p1, p2, …, pn) of the composite goods Xi and qi is the price for the long distance call.

5

Hence, the utility maximization problem of an economic agent for an outgoing call quantity based on the income constraint should satisfy the following first-order conditions:

ρ u x − λh x = 0 k (ρ ) f

mij

− λh

mij

(4) =0

(5)

where superscripts denote partial derivatives. Equations (4) and (5) simply imply that: u x = k (ρ )

hx h

mij

f

mij

(6)

which suggests that he general form of the traffic demand function will be: mij = H ( X i , pi , qi , I i , m ji )

(7)

Following Park et al. (1983) approach and assuming that the demand elasticity for calling time is proportional to price and that there are no cross price effects, we will obtain the following specification: m( d , t ) = ad bt e −ϕ q ( d ,t ) e −ψ p ( d ,t )

(8)

for the expected demand in zone d at time t. Taking into account that the traffic demand is also affected by the country’s specific economic characteristics, equation (8) becomes in a stochastic form as follows: ε

m(d , g , t ) = ad bt e−ϕ q ( d , g ,t ) e−ψ p ( d , g ,t ) e d ,g ,t

(9)

where εd,g,t is the error term defined as the difference between the sample mean and the moment mean of the demand at time t, distance zone d and country i with economic characteristics g. The model specification of the demand function using spatial econometrics will be presented in the next section and the exact type of the model will be determined using spatial diagnostic tests (statistics).

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3. Model Selection and Spatial Weights

Perhaps the most interesting feature in dealing with spatial data is the autocorrelation in space. Observations that are in close in spatial proximity tend to be more similar than is expected for observations that are more spatially separated. In fact, the term spatial autocorrelation refers to the coincidence of attribute similarity and locational similarity as discussed by Anselin (1988 and 2002). That means that the presence of spatial effects is an important issue in quantitative analysis and an analyst should estimate spatial econometrics models to incorporate these effects. These models as well as the criteria of spatial weights are presented in this section along with the spatial test statistics used to determine the type of spatial effects and therefore the type of the spatial model used in the regression analysis.

3.1 Spatial Models

The classical regression analysis requires that a linear functional form can adequately enough describe the relationship between a set of variables. This functional form can be presented in the following regression model: y i , t = x i , t β + ε i ,t

(10)

where yi,t represents some dependent variable of interest at year t being a linear function of some covariates xi,t, β is the vector of coefficients that is going to be estimated and εi,t is the error term, satisfying the standard regression assumptions, meaning that it is identically independently normally distributed with mean zero and constant variance and it not related to the values of the covariates.

7

Clearly, the assumption of linearity is not that important since some other nonlinear models can be applied in econometrics as well as in spatial econometrics to determine the existence of another type of relationship. The most crucial assumption is the one that requires the covariates to be independent of the error process. If this assumption is violated, due to the presence of spatial effects, then a different estimation procedure must be applied and a different model must be constructed to incorporate these spatial effects. The two models considered in the literature are the spatial error model and the spatial autoregressive model.

Spatial Error Model

The spatial error model, also knows as spatially lagged error model, is an extension of the linear regression model (10) by incorporating the spatial autocorrelation problem of the errors, meaning that “errors” εi,t in unit i are related to “errors” εj,t in nearby units j, where j ≠ i. The model is defined as: y i ,t = xi ,t β + ε i ,t + λwi′ε i ,t

(11)

where λ is the spatial parameter that is actually estimated in this model and wi′ is the vector of the spatial weights to indicate how “close” the other j observations (j ≠ i) are to unit i. Hence, if λ = 0, model (11) reduces to the standard non-spatial linear regression model (10). If however λ ≠ 0, OLS estimation is still consistent, but the reported standard errors will be not computed properly and therefore estimated β will be inefficient.

This problem can be fixed reasonably well by GLS estimation,

8

although in some cases complication may require full maximum likelihood estimation. 1

Spatial Autoregressive Model

The spatial error model corresponds to the time-series serially correlated errors model. The spatial autoregressive model, also knows as spatial lag model, corresponds to the time-series lagged dependent in space variable model. In this model, the dependent variable is affected by the values of the dependent variable in nearby units, with “nearby” suitably defined. It differs from the spatially lagged error model in the sense that both the error term and the covariates in nearby units have impact on the current unit (since it is the current values of the other y’s, suitably weighted, that impact the dependent variable). The spatial autoregressive model using time-series-cross-section data can be presented as follows: y i ,t = xi ,t β + kwi′ y i ,t + ε i ,t

(12)

where k is the spatial parameter and wi′ is the vector of the spatial weights. Actually, the difference between models (11) and (12) is whether the spatial effect arises from the errors or from the dependent variable. As in the case of model (11), if k is zero there will be no spatial effect. Without the spatial term kwi′ y i ,t this equation would be easy to estimate provided the error process shows no temporal correlations, so that the

1

The log-likelihood for the spatial model is complicated since it involves the log of the determinant |I − λW|, which is an nth order polynomial that can be very time consuming to evaluate. Ord (1975) showed that this determinant could be written as a function of the product of the eigenvalues wi of the connectivity matrix W, |I− λW| = Л(1 −λwi). The eigenvalues wi can be determined prior to optimization, which allows writing the likelihood for the model in a form that can be easily be estimated. For further econometric details on the spatially lagged error model see Anselin (1988).

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lagged y is independent of the error process. Recent work on this model can be found in Kelejian and Prucha (2005). Also, Franzese and Hayes (2004) have examined relatively close models but for alternative topics. The traditional spatial autoregressive model presumes that there is only one form of dependence and this form is presented by the spatial term kwi′ y i ,t in model (12). However, in many cases there may be several possible networks or forms of dependence which can be included in the spatial model. For example, it is possible to generalize the spatial autoregressive model (12) by using two distinct vectors wi′1 and wi′2 of spatial weights and in this case the model becomes: y i ,t = xi ,t β + k1 wi′1 yi ,t + k 2 wi′2 y i ,t + ε i ,t

(13)

where k1 and k2 are the relative spatial parameters needed to be estimated. The expanded spatial autoregressive model (13) is estimated as the standard spatial autoregressive model, provided that the two matrices are sufficiently different and that do not contain entirely overlapping information. Lacombe (2004) uses a model like this to estimate parameters distinguishing within-state unit and between-state unit effects of welfare programs on female labor force participation. Moreover, the expanded autoregressive spatial model (13) can be further expanded, as suggested by Zucker et al. (1998), by using the two distinct vectors of spatial effects wi′1 and wi′2 on exogenous variables in the following way: y i ,t = xi ,t β + k1 wi′1 y i ,t + k 2 wi′2 y i ,t + ρ1 wi′1 wi′2 xis,t + ρ 2 wi′1 wi′2 xiv,t + ε i ,t

(14)

where the full vector of exogenous variables is defined as X = xi + xis + xiv , meaning that in this case the explanatory variables are divided into three groups with xi denoting the exogenous variables of general interest (i.e., prices), xis the exogenous

10

variables related to social criteria (i.e., number of lines per country) and xiv the exogenous variables related to economic criteria (i.e., similar rates of GDP). The categorization of exogenous variables follows the criteria used for the definition of spatial weight matrices.

3.2 Spatial Statistics

Several diagnostic tests have been developed in the literature to determine the presence of spatial autocorrelation, i.e., correlation between the same attribute at two locations. In the context of regression analysis the most often used test for spatial error dependence is an extension of Moran’s I test, first discussed in Moran (1950), defined as: I=

e′We e′e

(15)

where e is the (n x 1) vector of OLS residuals, W is the (n x n) weight matrix and n is the number of observations.

Inference on this test statistic is based on normal

distribution. However, Monte Carlo simulation experiments by Anselin and Bera (1998) indicate that the use of the LM-ERR and the LM-LAG test statistics provide the best guidance for determining the functional form of the spatial dependence. The LM-ERR statistic is used to test for spatial error dependence and it is defined as follows: LM − ERR = where s 2 = e′e

n

(e ′We / s 2 ) T

(16)

and T = tr (W ′W − W 2 ) , with tr denoting the matrix trace operator.

The LM-LAG statistic, on the other hand, introduced by Anselin (1988), is used to test

11

for the presence of spatial lagged dependence and it is computed in the following way: (e′Wy / s 2 ) 2 LM − LAG = RJ ρ −α

where y is the dependent variable,

RJ ρ −α = [T + (WZa) ' M (WZa) / s 2 ]

(17) and

M = I − Z ( Z ′Z ) −1 Z ′ is the projection matrix. The LM-ERR and the LM-LAG test statistics follow a χ2 distribution with one degree of freedom and when both tests have high values, indicating significant spatial dependence in the data, the one with the highest value (lowest probability) will indicate the proper model specification.

3.3 Spatial Weights

An important decision in model estimation is the choice of the spatial weights. Explanatory data analysis typically provides a possible way of getting information about the structure of spatial dependence in the data. However, a method that is often used in practice and suggested by the existence literature is to apply some weight matrices in regression analysis and test for the presence of spatial dependence with each of the matrices. 2 In spatial econometrics the structure of dependence between observations is assumed to be known by the researcher and not to be estimated. Indeed, this structure is given by what is known as the “connectivity matrix”, which specifies the degree of connectivity (weights) between any two observations. However, the assumption that these weights are known a priori is strong, although it is crucial for the method of

2

For alternative specifications of weight matrices see Anselin , 2002.

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spatial econometrics to work. Of course, it is no stronger than the typical implicit assumption that all weights are zero, that is, all observations are spatially independent. Let the connectivity matrix denoted by W, where a typical element wij has a value greater than 0, if the observations i and j are connected. By convention, units are not considered to be connected to themselves, so any diagonal entry wii = 0. Also, we are assuming that we are dealing with situations where no observation is an isolate without any ties to other observations, meaning that we are ruling out

∑i=1 wi = 0 j

for

any observation i. The connectivity matrix is standardized so that each row vector wi sums to unity. As a consequence, it is not critical to worry about the units to measure connectivity, since W is invariant to affine transformations. Given some specification of connectivity or dependence we can define the “spatial lag operator”, which is the average value of y in a state i′s connected entities, as: y iw = wi′ y

(18)

Row-standardization ensures that the spatial lag y iw will have the same metric as the original y. In a geographic context, the elements of the connectivity matrix, that is the notion of observations being “nearby” one another, are determined purely by physical distance. 3 In our study we use three connectivity measures: i) a binary measure of contiguity or perhaps a binary measure of being closer than a certain specified threshold, ii) a continuous measure of inverse distance between all units and iii) a binary measure of multiple contiguities (i.e., k-neighbors contiguity, with k being a specific number of neighbors).

3

Although “nearby” is usually taken to mean geographical closeness, there is no reason why we cannot use any notion of nearness that makes theoretical sense, so long as this is specified by the analyst and so long as it does not violate any of the assumptions about the connectivity matrix stated above.

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In a non-geographic context, the notion of “distance” is determined by the trade volume and by the number of tourists. We consider as neighbors countries with similar volume of trade flows and a country is connected to all other countries if it has some trade with them.

The trade connectivity matrix differs from the previous

distance matrix in two notable ways. First, the trade matrix consists of weights where the importance of another state j to state i is given by the volume of the dyadic trade flow between i and j as a proportion of country’s i total trade, whereas the distance matrix assigns equal weights to any geographical neighbor.

Second, the trade

connectivity matrix weights large trading partners much more heavily than smaller trading partners, whereas in the distance matrix, any neighbor of i must always have j as a non-trivial neighbor. One interesting feature of the trade matrix is that some more-open developed countries have the bulk of their trade with large, wealthy, countries, which more often tends to demonstrate significant demand for outgoing calls.

As a result, these

countries that have greater openness and trade will tend to have a higher “spatial lag” on average demand for telecommunications among their trading partners. Moreover, the volume of tourists per country may generate an alternative contiguity matrix, which captures the significant human flows among different countries that affect the demand for telecommunications. Thus, trade and number of tourists may identify a very different set of pull factors than geographical proximity.

4. Data

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

14

structurally similar to the regional spatial interaction models. However, the selected explanatory variables are significantly different involving trade, tourism and financial commonalities. The demand for international telecommunications is strongly affected by a large number of several factors, although only a small number of them is typically included in an empirical study. This is due to the fact that some of these factors either may end up not having a significant effect on the demand during the period of study or their values may not be observed. These factors are presented in Table 1, as variables, and the data for them is obtained from Eurostat statistics, a European Union publication, for the years 1999 to 2002 for 25 member countries of the Union. 4

Table 1 Description of variables Variables m price trade tourists gdp rd lines

Description Minutes of outgoing traffic per line from country i in year t Real price from country i in year t Volume of trade (imports - exports) between from country i and other countries j in year t Number of tourists in country i in year t Real per capita Gross Domestic Product of country i in year t Research and development expenditures for telecommunications of country i in year t Number of telephone lines at country i in year t

Source: Eurostat, 2005

Hence, m, which stands for the outgoing minutes of conversations, is the dependent variable of our analysis and all other are the independent variables. The 4

The member countries are Austria, Belgium, Czech Republic, Denmark, Germany, Estonia, France, Finland, Greece, Great Britain, Spain, Sweden, Ireland, Italy, Cyprus, Latvia, Lithuania, Luxembourg, Hungary, Malta, Netherlands, Poland, Portugal, Slovenia and Slovakia.

15

price variable is the real average price per minute (including taxes) faced by customers of daytime and nighttime rate schedule, whereas the gdp variable is the real per capita GDP of each country. Deflation of the nominal prices and per capita GDP is based on the consumer price index (CPI) for the corresponding years of our analysis. The variable trade shows the volume of trade as an aggregate amount between European countries. It captures any economic transactions among different countries and represents significant economic activities. The variable tourists refers to the number of tourists of European residents visited the European countries, whereas the variable rd stands for research and development grants for telecommunications, which are the funds for investments used in telecommunication sector per country.

Lastly, the variable lines, which is the actual number of

telecommunications lines per country, provides a picture about country i’s infrastructure.

5. Estimation results

Although spatial concentration of economic activities in European countries has been documented by Bottazzi and Peri (2003), few studies take into account spatial interdependence between them.

The truth is that spatial effects and particularly

spatial autocorrelation cannot be ignored from any analysis as long as the data supports such evidence. In the case of estimating demand elasticities for international telecommunications for countries in E.U. several factors, such as labor mobility, trade between regions, knowledge diffusion and more generally regional spillovers, may lead to spatially interdependent countries and should be included in the analysis.

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Thus, the objective of this study is to determine demand elasticities for telecommunications taking into consideration spatial effects. Having identified the presence of spatial effects into our analysis the next step is to determine the type of these effects which will assist us to determine the proper model specification. For this purpose model (10) is estimated and the LM-ERR and LM-LAG test statistics are computed. Since the values of the LM-LAG test statistic are higher (lower p-value) than the LM-ERR test statistic, we conclude that the spatial lag formation is the proper formulation for our model. Thus, we estimate not only model (12) – hereafter Specification 1 – but also models (13) and (14) – hereafter Specifications 2 and 3 respectively – using three different distance weight matrices defined as: a) a binary distance measure of contiguity, b) an inverse distance measure of contiguity and c) a k-neighbors measure of contiguity for k = 6. In addition, we consider two weight matrices: an economic weight matrix using the volume of trade and a social weight matrix using the flow of tourist. The description of how these weights are calculated is presented analytically in each of the following subsection. For all specifications Lagrange Multiplier (LM) tests indicate that there is a small, but statistically significant, amount of serial correlation of the errors. This is not uncommon given the large sample sizes for TSCS data. These results suggest that the magnitude of the spatial error association appears relatively modest, once we take into account different definitions of weights for the lagged dependent variable. The latter is verified by the fact that LM-LAG test statistic is higher (lower p-value) than the LM-ERR test statistic, for the models under study.

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5.1 A binary distance measure of contiguity

Diffusion between countries may be likely to occur between nearby countries in a geographical sense.

Hence, the first connectivity criterion is based on the

geographical distance between European countries. We use the minimum distance data to define countries as connected if they are within 500 km of one another.5 This yields a binary connectivity matrix where each entry wij is 1, if states i and j are within 500 km distance from each other and 0 otherwise. Each neighboring country is given equal weight in the row for country i. The connectivity matrix is normalized so that each row vector wi sums to unity. Weights for trade and tourism are discussed in section 3.3. Table 2 reports the estimation results obtained by using Specifications 1, 2 and 3. In particular, Specification 1 has a spatial lag of dependent variable with a distance weight scheme (k), whereas Specification 2 has besides the distance weight scheme (k1) and a spatial lag with a trade (or tourism) weight scheme (k2).

Finally,

Specification 3 uses, in addition to the spatial lags of Specification 2, both alternative weight schemes (trade and tourism) in respect to specific explanatory variables. Hence, an interaction weight component is estimated for gdp per capita (ρ1) and lines (ρ2) respectively.

The interaction weight components capture the effects from

countries with similar distance, trade and tourism characteristics simultaneously. An F-test shows that the spatial lags per country are statistically significant in most estimated equations (Mátyás, 1998).

5

As suggest by the software of SpaceStat ®

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Table 2 Estimation results under predefined distance proximity

Variables

price trade tourists rd gdp line Spatial Components k

Specification

Specification

Specification

Specification

Specification

Specification

1

2

3

1

2

3

Space and trade criterion -0.82*** (22.1) 0.14*** (16.75) 0.05*** (4.11) 0.55 (1.01) 0.09** (7.71) 0.91 (0.88)

-0.63*** (16.2) 0.11*** (11.89) 0.07*** (4.96) 0.42 (1.62) 0.14** (4.53) 0.43 (1.51)

-0.55*** (11.6) 0.12*** (8.68) 0.06*** (4.23) 0.31 (1.68)

0.12*** (7.72)

k1 k2

Space and tourism criterion -0.96*** (10.91) 0.11*** (7.72) 0.03*** (3.88) 1.34 (0.42) 0.11*** (8.93) 0.16* (2.01)

-0.71*** (5.37) 0.08*** (9.17) 0.02** (2.81) 0.21* (2.12) 0.18** (5.55) 0.22* (2.55)

-0.39*** (3.71) 0.06*** (4.18) 0.09** (2.23) 0.41* (2.89)

0.06*** (4.11) 0.02 (1.12)

0.04*** (4.93) 0.02* (3.18)

0.05*** (3.23) 0.15*** (8.91) 0.11*** (6.73)

0.09*** (7.55) 0.07*** (5.22)

0.62

0.64

0.02 (0.72) 0.01 (0.11) 0.71

Interaction Components ρ1

R2adjusted

0.68

0.69

0.01 (0.44) 0.05 (0.31) 0.69

F test

9.17

9.64

10.01

9.36

9.75

10.85

Chi square test

64.27

65.16

68.11

65.52

68.79

66.75

ρ2

Note: Numbers in parentheses are t statistics where *, **, *** are 10%, 5% and 1% respectively.

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In turns out first of all that the estimates of the interaction components, i.e., estimates of coefficients ρ1 and ρ2, are all insignificant no matter the criterion. This result indicates that Specification 3 is not appropriate to use for this data set and with these criteria, meaning that the simultaneous use of weight specifications does not have any significant impact on the amount of outgoing calls. On the other hand, estimates of the spatial components, i.e., estimates of coefficients k, k1 and k2, are significant and do not differ substantially among alternative specifications. In fact their values vary from 0.02 (tourism criterion) to 0.15 (trade criterion), indicating that the presence of spatial effects on both criteria can only been seen on Specifications 1 and 2, which are suitable for this data set. The level of outgoing calls is affected significantly by the price and by the volume of trade among the countries of our data set regardless of the model specification. Under any type of weight schemes, geographic, economic or social, the coefficients of price and trade have a negative and positive impact on the number of calls respectively. The latter conclusion follows the lines of the existed literature such as Garin-Munoz and Pérez-Amaral (1998), in which it can be stated that international trade determines the economic transactions of each country. It is interesting to note that in all Specifications that absolute value of the coefficient of price is less than one indicating an elasticity of demand for international calls that it is inelastic The estimates of the coefficients of the remaining explanatory variables, number of tourists, rd, gdp, and number of lines, have all the expected sign, i.e., positive sign, but different impact on the amount of outgoing calls. Their level of significance varies though according the Specification and the criterion.

The

inclusion of gdp and number of lines in a spatially lagged formulation, i.e., Specification 3, tends to examine the impact of “neighboring” countries not only from

20

an economic perspective (gdp through the coefficient of ρ1) but also from an infrastructure perspective (number of lines through the coefficient of ρ2), although the estimates of the coefficients were not significant.

5.2 Inverse distance measure of contiguity

Our second specification of weight matrices uses the inverse distance criterion to account for the geographical distance between European countries.

The inverse

distance-based approach places less importance to all countries j that are far away from country i. In particular, the elements wij, of the inverse distance-based weight matrix are computed as: wij = (dij)−2, where d denotes distance between countries i and j, and are defined as a decaying function in space. The estimation results using this weight specification are reported on Table 3 and as it can be seen they are very similar to those results obtained in the previous weight specification.

First, spatial effects can be found basically only using

Specifications 1 and 2 since the estimates of the interaction components are not significant. Only the estimate of the interaction component which refers to gdp (coefficient ρ1) in the case of tourism is significant, indicating that the inverse distance weight matrix emphasizes the existence of regional economic clusters, since GDP of neighboring locations for any two countries affect the demand for calls. In contrast, no evidence is found for the relationship among outgoing calls of country i and neighboring infrastructure from countries j (coefficient ρ2). The latter result is robust under any type of weight criteria.

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Table 3 Estimation results under inverse distance proximity

Variables

Specification

Specification

Specification

Specification

Specification

Specification

1

2

3

1

2

3

Space and trade criterion

price

-0.71*** (19.23)

trade

0.12*** (14.57) 0.04*** (3.58) 0.48 (0.88) 0.08** (6.71) 0.79 (0.77)

tourists rd gdp line Spatial Components k

-0.55*** (14.09) 0.10*** (10.34) 0.06*** (4.32) 0.37 (1.67) 0.12** (3.94) 0.49 (1.31)

-0.48*** (10.09) 0.09*** (7.55) 0.05*** (3.68) 0.27 (1.64)

0.1*** (10.2)

k1 k2

Space and tourism criterion -0.96*** (10.91) 0.11*** (7.72) 0.02*** (3.14) 1.17 (0.37) 0.1*** (7.77) 0.14* (1.75)

-0.62*** (4.67) 0.07*** (7.98) 0.02 (0.71) 0.18 (1.84) 0.16*** (4.83) 0.19** (2.22)

-0.34*** (3.23) 0.05*** (3.64) 0.08 (1.07) 0.36** (2.51)

0.05*** (3.58) 0.02 (0.97)

0.03*** (4.29) 0.02** (2.77)

0.04** (2.81) 0.12*** (7.75) 0.07*** (5.86)

0.08*** (6.57) 0.06*** (4.54)

0.55

0.56

0.02** (2.63) 0.01 (0.1) 0.59

Interaction Components ρ1

R2adjusted

0.58

0.59

0.01 (0.38) 0.04 (0.27) 0.61

F test

8.11

8.92

9.11

8.74

8.36

9.77

Chi square test

75.08

73.72

70.92

71.11

70.96

73.41

ρ2

Note: Numbers in parentheses are t statistics where *, **, *** are 10%, 5% and 1% respectively.

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The remaining variables follow a similar pattern with respect to the results of Table 2.

Their magnitude and their significance do not present any serious

alterations, indicating that the robustness of these results is not affected either by the definition of economic or social weight specifications or by the nature of geographic weights. In fact even the absolute magnitude of the elasticities of demand did not change.

5.3 K-neighbors measure of contiguity (k = 6)

The k-neighbors criterion is based on a predetermined number of countries that are geographically close to country i. The choice of the exact number k is based on the number of geographical observations and their locational characteristics. Although we use k = 6, Specifications 1, 2 and 3 have also been estimated under alternative definitions of k, i.e., k = 4 and 8, but the results did not present any significant changes. Thus, Table 4 reports the estimation results under the assumption that k = 6. The most interesting result in this case is that a predetermined number of k neighbors can change the presence of spatial effects. As it can be seen from Table 4, Specification 3 has now significant estimates of the interaction components under both trade and tourism criteria ranging their values from 0.03 (tourism criterion) to 0.07 (trade criterion). This result shows that neighboring countries may have a unique effect on the outgoing calls. An example refers to southern Mediterranean countries where the volume of outgoing calls is affected by the group of countries which are located in that area. The geographic cluster coincides with the economic and social cluster and indeed this result verifies that countries with significant amount of tourists do affect the demand for outgoing calls.

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Table 4 Estimation results under k-neighbors proximity

Variables

price trade tourists rd gdp line Spatial Components k

Specification

Specification

Specification

Specification

Specification

Specification

1

2

3

1

2

3

Space and trade criterion -1.07*** (28.95) 0.18*** (21.94) 0.07*** (5.34) 0.72 (1.32) 0.12*** (10.1) 1.19 (1.15)

-0.83*** (21.22) 0.14*** (15.58) 0.09*** (6.51) 0.55** (2.52) 0.18*** (5.93) 0.56* (1.98)

-0.72*** (15.19) 0.16*** (11.37) 0.08*** (5.54) 0.41** (2.46)

0.13*** (13.36)

k1 k2

Space and tourism criterion -1.26*** (14.29) 0.14*** (10.11) 0.03*** (4.11) 1.53 (0.48) 0.14*** (10.18) 0.18** (2.29)

-0.81*** (6.12) 0.09*** (10.45) 0.03 (1.65) 0.24** (2.41) 0.21*** (6.33) 0.25** (2.91)

-0.45*** (4.23) 0.07*** (4.77) 0.1 (1.4) 0.47*** (3.29)

0.07*** (4.69) 0.03 (1.27)

0.04*** (5.62) 0.03*** (3.63)

0.16*** (15.35) 0.21*** (11.67) 0.14*** (8.82)

0.12*** (9.89) 0.09*** (6.84)

0.61

0.63

0.05*** (4.78) 0.03** (2.89) 0.65

Interaction Components ρ1

R2adjusted

0.57

0.56

0.04*** (3.58) 0.07*** (3.17) 0.56

F test

8.86

9.17

9.89

8.42

9.59

9.22

Chi square test

88.62

93.64

94.77

86.23

90.12

93.68

ρ2

Note: Numbers in parentheses are t statistics where *, **, *** are 10%, 5% and 1% respectively.

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Furthermore, estimates of the coefficients reported on Table 4 are very similar to those estimates previously obtained under different definitions of the weight matrices. The main difference is that in this case the magnitude of the elasticity of demand for international telecommunication has slightly changed and it has become elastic, i.e., greater than one in absolute terms, only though for Specification 1, whereas for all other Specifications do remain inelastic.

The estimates of the

coefficients of the remaining explanatory variables, number of tourists, rd, gdp, and number of lines, have all the expected sign and their magnitude does not differ significantly from the previously obtained results. In general, the results in Table 4, where the spatial weights involve the six adjacent countries per country, are more difficult to interpret. The positive and highly significant coefficients of the interaction terms point out the complex and synergistic effect of language commonality, which was also obtained with the previously defined weight matrices but it there were not significant. These results suggest that having clusters of countries with similar language in proximity encourages the generation of telephone conversation. Finally, we can conclude that there are spatial structure effects in international telecommunications, of both competitive and agglomerative nature.

6. Concluding Remarks

In

this

study

we

tried

to

estimate

demand

models

for

international

telecommunications for European countries in the context of spatial econometrics, a technique that has been lately used very frequently by many researchers in a variety of

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fields. In fact, because of the geographic heritage of these models, their primary application is to incorporate physical notions of space (distance) into the estimation procedure and to argue that geographically nearby units are linked together. The most important aspect in spatial econometrics is the definition of the weight matrix. We defined the distance weight matrices in three different ways: i.e., a) a binary distance measure of contiguity, b) an inverse distance measure of contiguity and c) a k-neighbors measure of contiguity for k = 6, and we also considered two additional weight matrices: an economic weight matrix using the volume of trade and a social weight matrix using the flow of tourist to incorporate the economic and social effects. This study finds evidence of spatial effects in all cases and the results are very robust in the sense that the estimates of the coefficients of all parameters in the models have not been affected by the definition of the weights matrices. Our results indicate the importance of trade and tourism in determining demand elasticities and of course the role of geography in the context of measuring distance and spatially dependent variables.

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