- Email: [email protected]
On price elasticities of international telecommunication demand
INFORMATION ECONOMICS AND POLICY
ELSEVIER
Information Economics and Policy 7 (1995) 27-36
On price elasticities of international telecommunication demand Peter Hackl a'*, A n d e r s H. Westlund b ~Department of Statistics, University of Economics and Business Administration, Augasse 2, A-I090 Vienna, Austria ~Department of Economic Statistics, Stockholm School of Economics, Stockholm, Sweden Received 30 March 1993; accepted 28 June 1994
Abstract
In this empirical study, the price elasticity of the demand for telecommunication between Sweden and six destination countries, Germany ( F R G ) , United Kingdom, USA, and the three Scandinavian countries Denmark, Finland, and Norway, is investigated. A linear regression model in logarithmic transforms of all variables is specified. To allow for time-varying regression coefficients the moving local regression technique is used to estimate the trajectory of the coefficients. The results of our study can be summarized as follows. For all countries except the USA, the (absolute) price elasticity increases over the observation period 1976-1990. The US price elasticity is close to zero, whereas the demand is relatively price elastic for the European countries. Our analysis shows that a model with constant price elasticities would be misleading when observations over a longer time period are analyzed. An appropriate method of analysis is suggested.
Key words: Telecommunication demand; Time-varying price elasticity; Moving local regression J E L Classification: C22; C49; L96
* Corresponding author, e-maih [email protected]. The authors are grateful to Swedish Telecom for providing the telecommunication traffic and price data, as well as for financial support. They would also like to thank Dr. Werner Miiller for his assistance with the numerical results. Moreover, they acknowledge the constructive comments of the referees which helped to improve the manuscript.
0167-6245/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0167-6245(94)00023-9
28
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
1. Introduction
International telecommunication is an essential component in the rapid development of an international economy that is characterized by multinationally acting enterprises and growing business flows. As a consequence, the demand for international telecommunication has increased significantly. A similar impact comes from the continuously increasing processes of international tourism and migration, as well as from the steady growth of the international network of political, social, and cultural organizations. Furthermore, the last ten or fifteen years have seen revolutionary technological changes in telecommunication. Examples are the transition from analog to digital switches, the introduction of fiber-optic cables, satellite transmission, automated telephone services, fax machines and cellular telephones. Many of these new features open ways to often radically new options in telecommunication, and all of them make existing services more efficient, reliable and cheaper. In the same period, the telecommunication market has been deregulated, leading to increased competition, and innovative price policies and arrangements. One consequence of this scenario is a great interest in price elasticity of international telecommunication demand. A good understanding of the price elasticity of the demand and its mutual interrelations with the economic environment is necessary for designing a rational price policy of the supplier. An excellent survey of theoretical and empirical studies on the demand for telecommunication services is given by Taylor (1980). In a recent volume, Mitchell and Vogelsang (1991) survey recent advances in the economic theory of tariffs and analyze from that perspective the various types of rate structure found in the US telecommunication market. Acton and Vogelsang (1992) investigate the demand for international telecommunication between the USA and 17 European countries and discuss the impact of various price scenarios. However, little is known, especially empirically, about the effects of alternative pricing policies on the demand for telecommunication services. This is probably due to (i) the complexity of the pricing systems, and (ii) the monopoly-like ownership of telecommunication systems. An important aspect of the relationship between price and demand for telecommunication services is its dynamic nature that is reflected by the evolution of the price elasticity over time. We think that our analysis and its resulting findings are useful for deepening the understanding of the interrelation between the pricing system and the demand for international telecommunication services. In an earlier paper (Hackl and Westlund, 1992) we have discussed in detail the specification and the analysis of a demand function for interna-
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
29
tional telecommunication. Based on this study, we specify in the present paper demand functions for international telecommunications from Sweden to a number of its most important business and trading partners: Germany (FRG), United Kingdom, United States, and Sweden's three Scandinavian neighbors Denmark, Finland and Norway. The demand functions are global in the sense that demand includes both private and business communication. We consider the aggregate demand for communication combining the various media such as telephone, fax, etc. Data for demand are the aggregated count units for the use of telephone lines to the various destination countries. As shown by Hackl and Westlund (1992), these demand functions are characterized by the time-varying nature of price elasticity. In the present paper, we analyze the evolution of price elasticity for the different countries. Section 2 gives a description of the model and the statistical technique that forms the basis for the analysis of the timevarying price elasticities. Section 3 exhibits and discusses the trajectories of the price elasticity for the various countries.
2. The model
The specification of the demand function that forms the basis for the analysis of price elasticities is documented in an earlier research report (Hackl and Westlund, 1992). The telephone network connecting Sweden with other countries in question is not used to its full capacity. Thus, the actual use coincides with the demand. The total demand for telecommunication consists of business and residential demand. International telecommunication from Sweden, particularly to non-Scandinavian countries mentioned, is dominated by business traffic. Estimates from surveys by Swedish Telecom indicate that business telecommunication comprises approximately 75% of the total volume. This, together with the fact that no good separate data are available for business and residential telecommunication, leads us to model the demand by means of a single equation. The dependent variable (USE) is the telephone traffic (in 1000 minutes of calling) from Sweden to each of the destination countries. At the specification stage, the predictive potential of a great number of variables was investigated; the explanatory variables under consideration describe the economic conditions in Sweden and the respective destination countries, the economic interaction between the countries, expectations with respect to future economic conditions, access to telecommunication technology, prices for access and use of telecommunication services, prices for access and use of substitutes for telecommunication services, and reciprocal
30
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
telecommunication effects. Given the availability of data, the relevant explanatory variables turned out to be • the deflated price per time unit of communication (PMM) • the deflated Swedish trade volume (exports + imports) with destination country (TRA) • the Swedish industrial production index (IPS) • the industrial production index of the destination country (IP) Our analysis covers the monthly data for the time period 1976:1-1990:12. Each time series contains 180 observations. Deflation is based on the consumer price index, as published by Statistics Sweden. The series TRA, IPS, and IP are taken from publications of Statistics Sweden. Swedish Telecom uses two prices for telecommunication with the USA; cheaper prices apply for calls during nights and weekends. We used the higher price as an explanatory variable, as a high percentage of calls to the USA are business calls. Fig. 1 shows a typical pattern of the trajectory of PMM for telecommunication with the United Kingdom. The explanatory variables that were included in our analysis are consistent with the prior literature. Discussions of determinants of the demand for international telecommunication are given by Lago (1970) and Yatrakis (1972). Yatrakis tried some twenty explanatory variables, and about half of them were found to be statistically significant. Pousette (1976a, b) restricts the explanatory variables to price and access to technology (number of telephones). Appelbe et al. (1988) include the so-called reciprocal calling effect as one of the important determinants for international telecommunication demand. Expectations concerning future economic conditions are considered in, e.g., Bartels et al. (1988). The demand function was formulated as a linear regression model in logarithmic transforms of both the dependent and explanatory variables. This double logarithmic functional relation, which is the most convenient for the interpretation of elasticities, turned out to be close to the optimal among all Box-Cox transforms. We also experimented with various dynamic specifications; lagging the endogenous variable by one period helped to model adequately the dependence structure of the demand over time. Lagged observations for IPS and IP, with lags up to six months, turned out to be important. The lag structure varied somewhat for the various destination countries. Seasonal dummies for July and August represent the effects of the Swedish summer vacation. Some characteristics of the demand functions that resulted from fitting models with nonvarying coefficients are given in Table 1. These functions were used to assess the relevance of the explanatory variables, including the lagged variable USE_~. The regressions resulted in high values of/~e: above
31
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
¥ 4~
"x ~a t~
C~
I
i9 76
I
I
I
I
I
I
I
I
1981
I
I
1
1986
I
I
I
I
I
199I
time (months)
Fig. l. Trajectory(time sequence plot) of the real price (in SEK/minute)for telecommunication services between Sweden and the United Kingdom. 0.95 for all functions and above 0.977 for non-Scandinavian countries. Table 1 shows short-term and long-term price elasticities. In view of the length of the observation period (180 months), it is reasonable to allow the model parameters to vary over time; this is especially true for price elasticities. There are several theoretical reasons for assuming nonconstant elasticities, such as the technological development within the telecommunication sector, changes in price policies and changing business cycle conditions. It is well-known from empirical results (see Taylor, 1980) that price elasticities increase with increasing distances. Although this statement assumes that economic conditions are the same, a fact that must be questioned when comparing models for different countries, this observation is another reason why different patterns of the coefficient trajectories for the various destination countries must be expected. The results reported in the next section are obtained by applying the moving local regression technique to the estimation of the regression
32
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 2 7 - 3 6
Table 1 Characteristics of the demand function for telecommunication services between Sweden and six destination countries Germany (D), UK, USA (US), Denmark (DK), Norway (N), and Finland (SF) Const.
USE 1
PMM
/~2
PEL
D
1.72
-0.369
0.44
0.977
-0.978
US
1.81
0.994
-0.961
DK
2.68
0.955
-0.975
N
1.70
0.971
- 1.178
SF
3.58
-0.258 (3.94) -0.492 (5.44) -0.122 (2.62) -0.392 (4.76) -0.509 (4.01) -0.302 (4.15)
0.978
UK
0.300 (5.32) 0.497 (8.10) 0.873 (26.73) 0.598 (9.27) 0.568 (9.99) 0.618 (13.36)
0.961
-0.627
Short-term price elasticities are given in column PMM with It[-values in parentheses; column PEL shows the corresponding long-term price elasticities. The functions are fitted in log-log form. coefficients. This estimation approach consists of fitting a regression model with constant p a r a m e t e r s to a window of data that shifts over the observation period. It generalizes the moving average approach by using nonconstant weights. It is discussed in a recent p a p e r by Cleveland et al. (1988). Similar versions of locally weighted curve fitting were suggested by Macaulay (1931), Pelto et al. (1968), and Cleveland (1979). An adaptation to time series due to Fedorov et al. (1992) shows how to adapt this approach to time series data. Applying of the moving local regression approach to the linear regression , . . ^ (o . m o d e l E { y , } = x , [3 results m esUmates [3 of the coefficients [3. The model is locally fitted using data around the time period t. The weighted least squares m e t h o d is used as the estimation approach /3 ( ' ) = ( X ' F t X ) - ~ X ' F t Y ;
(1)
where the diagonal matrix F, = diag(~-~ ') . . . .
, r~")
contains the weights (importance) ~.~0 that are given to observations (x i, Yi), i = 1 . . . . , T. Estimates of the standard deviation of/3 (0 are taken from the covariance matrix V a r { [ 3 ( ° } = ( X ' F t X ) - I & 2, where ~.2 is the estimated
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
33
disturbance variance and based on the residuals between observations and the locally fitted model. To guarantee properties such as unbiasedness, smoothness of the estimated response function, and robustness towards influential data points, the weights have to satisfy certain criteria. A comprehensive discussion of several useful weight functions is given by Mfiller (1991). In moving local regression, the time-varying parameters are estimated with little bias as the used data base for the estimate is restricted to the neighborhood of the time point of interest. Consequently, the estimates reflect changes in the coefficient structure. This approach takes smooth changes of the model structure into account. In this study we used the tricube weight function
_
u)
"Yi
•
1-
ifO<~]t-il<<-A
(2)
otherwise that has been suggested by Cleveland (1979). The "window width" 2A + 1 is a crucial parameter of the fitting procedure. The reported results use A = 26 months, which implies a window of 53 months (or approximately 4.5 years).
3. Trajectories of the price elasticity Fig. 2 shows the trajectories of the price elasticity of the demand that result from the moving local regression approach together with 2o- bounds. The curves for the six destination countries are rather smooth, corresponding to the relatively large value of the window width of 53 time periods. A smaller window width implies a smaller bias but an increased standard deviation. The variability in the estimated price elasticities increases if the window width is reduced, but our results show that the general time pattern is unchanged. The range of the estimated price elasticities goes from values close to zero (inelastic) to being greater than one (elastic). The trajectories for all countries (except the USA) show a continuous increase in the (absolute) price elasticity over time. Very similar patterns are observed for the Scandinavian countries and Germany. A considerable change towards more elastic demand happened during the eighties; the trajectory of the (absolute) price elasticity before that change can be characterized as slightly increasing, followed by a period of constancy. During the most recent years the Scandinavian countries exhibit a slight decrease in the (absolute) price elasticity, but in all cases the demand is price elastic or close to price elastic. For the United Kingdom, we observe a similar pattern that, however, starts from a somewhat higher (absolute) value than the other European countries;
.
'1976
.
.
.
.
.
.
81
.
.
_
DENMARK
•_
86
,
,
,
~
-
91
_
\
'1976
7
,
,
,
,
,
,
81
\
,
NORW4y
,
\ ~ ,
\\
,
"L
'1
,
~
Z
u~
,
1
.
.
.
.
.
86
\
\k \ ~
XX \
.
.
/
91
/,
z
\
/ /
'1976
i
7
Z
o
,--
_
/
81
\
\
FINLAND
\
86
/I
Fig. 2. Trajectories (time sequence plots, solid lines) of the price elasticity of the demand for telecommunication services between Sweden and six destination countries: Germany, UK, USA, Denmark, Norway, and Finland. The dashed lines indicate 2o" bounds.
4.1
I--~ ~
GCR~AN~
I
"--I
"-4
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
35
a slight increase in the (absolute) price elasticity is observed over the whole studied time period, and, at the end of the period under study, the demand is price elastic. An entirely different picture is found for the USA. Starting from a price elastic situation, the (absolute) price elasticity decreases in the mid-eighties to a value close to zero. Our results make it clear that an assumption of constant price elasticity is not adequate in our situation where observations over a rather long time period are used to fit the demand function. Using a moving local regression approach is recommended in this situation as the finite window width gives the flexibility of fitting the model locally without assuming a special structure for the time-variation of the model coefficients. We are cautious in our interpretation as we primarily are concerned with the methodological aspects. Moreover, the limitations of the used data may imply a misspecification of the model. In particular, important variables such as the number of telephones were not available; business and residential calls are not separated; the model describes only communication originating in Sweden and does not take into account the asymmetry of demand in reaction to the respective pricing systems in the source and destination country; the specification of the model might change over time. The large temporal range in the estimated price elasticities might surprise. However, the close similarity in the patterns for the European countries increases the credibility of our findings. One possible argument for the increasing (absolute) price elasticity in European countries is the growing consumer awareness of their strength. A growing proportion of non-business calls may further contribute to that pattern. Two features of the trajectories need to be explained more:
• At the beginning of the observation period, positive price elasticities are found for Germany, Norway, and Finland: as the 2ty bounds include 0, the null-hypothesis of "zero price elasticity" cannot be rejected in all three cases. • The pattern for the USA is different from all other tra/ectories; the small estimates for the mid to late eighties contradict the theory that the price elasticity should increase (absolutely) with increasing distances: the substantial decrease in the (absolute) price elasticity within a very short period of less than two years might reflect changes in behavior that resulted from the US deregulation of long distance telecommunication. However, a detailed analysis of the relevance of this or other possible causes is beyond the scope of our study. The fact that the price elasticity for the last few years is close to zero requires further investigation.
36
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
References Acton, J.P. and I. Vogelsang, 1992, Telephone demand over the Atlantic: evidence from country-pair data, Journal of Industrial Economics 40, 305-323. Appelbe, T.W., N.A. Snihur, C. Dineen, D. Farnes and R. Giordano, 1988, Point-to-point modelling, Information Economics and Policy 3, 283-309. Bartels, R., J. Murray and A.A. Weiss, 1988, The role of consumer and business sentiment in forecasting telecommunications traffic, Journal of Economic Psychology 9, 215-232. Cleveland, W.S., 1979, Robust locally-weighted regression and smoothing scatterplots, Journal of the American Statistical Association 74, 829-836. Cleveland, W.S., S.J. Devlin and E. Grosse, 1988, Regression by Local Fitting, Journal of Econometrics 37, 87-114. Fedorov, V.V., P. Hackl and W. MOiler, 1992, Moving local regression, Journal of Nonparametric Statistics 3, 355-368. Hackl, P. and A.H. Westlund, 1992, Demand for international telecommunication: time-varying price elasticity, Paper presented at the CRDE/Journal of Econometrics Conference on Recent Developments in the Econometrics of Structural Change, Montreal. Lago, A.M., 1970, Demand forecasting models of international telecommunications and their policy implications, Journal of Industrial Economics 19, 6-21. Macaulay, F.R., 1931, The smoothing of time series (National Bureau of Economic Research, New York). Mitchell, B.M. and I. Vogelsang, 1991, Telecommunications pricing: theory and practice (Cambridge University Press, Cambridge). MOiler, W.G., 1991, On moving local regression, with special reference to experimental design in economics, Technical Report, Department of Statistics and Informatics, University of Vienna. Pelto, C.R., T.A. Elkins and H.A. Boyd, 1968, Automatic contouring of irregularly spaced data, Geophysics 33, 424-430. Pousette, T., 1976a, Efterfr~igan p~ telefontj~inster och telefoner (Industriens Utredningsinstitut). Pousette, T., 1976b, The demand for telephones and telephone services in Sweden, Manuscript presented at the European Meeting of the Econometric Society, Helsinki. Taylor, L.D., 1980, Telecommunications demand: A survey and critique (Ballinger Publishing Co., Cambridge, MA). Yatrakis, P.G., 1972, Determinants of the demand for international telecommunications, Telecommunication Journal 39, 732-746.
ELSEVIER
Information Economics and Policy 7 (1995) 27-36
On price elasticities of international telecommunication demand Peter Hackl a'*, A n d e r s H. Westlund b ~Department of Statistics, University of Economics and Business Administration, Augasse 2, A-I090 Vienna, Austria ~Department of Economic Statistics, Stockholm School of Economics, Stockholm, Sweden Received 30 March 1993; accepted 28 June 1994
Abstract
In this empirical study, the price elasticity of the demand for telecommunication between Sweden and six destination countries, Germany ( F R G ) , United Kingdom, USA, and the three Scandinavian countries Denmark, Finland, and Norway, is investigated. A linear regression model in logarithmic transforms of all variables is specified. To allow for time-varying regression coefficients the moving local regression technique is used to estimate the trajectory of the coefficients. The results of our study can be summarized as follows. For all countries except the USA, the (absolute) price elasticity increases over the observation period 1976-1990. The US price elasticity is close to zero, whereas the demand is relatively price elastic for the European countries. Our analysis shows that a model with constant price elasticities would be misleading when observations over a longer time period are analyzed. An appropriate method of analysis is suggested.
Key words: Telecommunication demand; Time-varying price elasticity; Moving local regression J E L Classification: C22; C49; L96
* Corresponding author, e-maih [email protected]. The authors are grateful to Swedish Telecom for providing the telecommunication traffic and price data, as well as for financial support. They would also like to thank Dr. Werner Miiller for his assistance with the numerical results. Moreover, they acknowledge the constructive comments of the referees which helped to improve the manuscript.
0167-6245/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0167-6245(94)00023-9
28
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
1. Introduction
International telecommunication is an essential component in the rapid development of an international economy that is characterized by multinationally acting enterprises and growing business flows. As a consequence, the demand for international telecommunication has increased significantly. A similar impact comes from the continuously increasing processes of international tourism and migration, as well as from the steady growth of the international network of political, social, and cultural organizations. Furthermore, the last ten or fifteen years have seen revolutionary technological changes in telecommunication. Examples are the transition from analog to digital switches, the introduction of fiber-optic cables, satellite transmission, automated telephone services, fax machines and cellular telephones. Many of these new features open ways to often radically new options in telecommunication, and all of them make existing services more efficient, reliable and cheaper. In the same period, the telecommunication market has been deregulated, leading to increased competition, and innovative price policies and arrangements. One consequence of this scenario is a great interest in price elasticity of international telecommunication demand. A good understanding of the price elasticity of the demand and its mutual interrelations with the economic environment is necessary for designing a rational price policy of the supplier. An excellent survey of theoretical and empirical studies on the demand for telecommunication services is given by Taylor (1980). In a recent volume, Mitchell and Vogelsang (1991) survey recent advances in the economic theory of tariffs and analyze from that perspective the various types of rate structure found in the US telecommunication market. Acton and Vogelsang (1992) investigate the demand for international telecommunication between the USA and 17 European countries and discuss the impact of various price scenarios. However, little is known, especially empirically, about the effects of alternative pricing policies on the demand for telecommunication services. This is probably due to (i) the complexity of the pricing systems, and (ii) the monopoly-like ownership of telecommunication systems. An important aspect of the relationship between price and demand for telecommunication services is its dynamic nature that is reflected by the evolution of the price elasticity over time. We think that our analysis and its resulting findings are useful for deepening the understanding of the interrelation between the pricing system and the demand for international telecommunication services. In an earlier paper (Hackl and Westlund, 1992) we have discussed in detail the specification and the analysis of a demand function for interna-
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
29
tional telecommunication. Based on this study, we specify in the present paper demand functions for international telecommunications from Sweden to a number of its most important business and trading partners: Germany (FRG), United Kingdom, United States, and Sweden's three Scandinavian neighbors Denmark, Finland and Norway. The demand functions are global in the sense that demand includes both private and business communication. We consider the aggregate demand for communication combining the various media such as telephone, fax, etc. Data for demand are the aggregated count units for the use of telephone lines to the various destination countries. As shown by Hackl and Westlund (1992), these demand functions are characterized by the time-varying nature of price elasticity. In the present paper, we analyze the evolution of price elasticity for the different countries. Section 2 gives a description of the model and the statistical technique that forms the basis for the analysis of the timevarying price elasticities. Section 3 exhibits and discusses the trajectories of the price elasticity for the various countries.
2. The model
The specification of the demand function that forms the basis for the analysis of price elasticities is documented in an earlier research report (Hackl and Westlund, 1992). The telephone network connecting Sweden with other countries in question is not used to its full capacity. Thus, the actual use coincides with the demand. The total demand for telecommunication consists of business and residential demand. International telecommunication from Sweden, particularly to non-Scandinavian countries mentioned, is dominated by business traffic. Estimates from surveys by Swedish Telecom indicate that business telecommunication comprises approximately 75% of the total volume. This, together with the fact that no good separate data are available for business and residential telecommunication, leads us to model the demand by means of a single equation. The dependent variable (USE) is the telephone traffic (in 1000 minutes of calling) from Sweden to each of the destination countries. At the specification stage, the predictive potential of a great number of variables was investigated; the explanatory variables under consideration describe the economic conditions in Sweden and the respective destination countries, the economic interaction between the countries, expectations with respect to future economic conditions, access to telecommunication technology, prices for access and use of telecommunication services, prices for access and use of substitutes for telecommunication services, and reciprocal
30
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
telecommunication effects. Given the availability of data, the relevant explanatory variables turned out to be • the deflated price per time unit of communication (PMM) • the deflated Swedish trade volume (exports + imports) with destination country (TRA) • the Swedish industrial production index (IPS) • the industrial production index of the destination country (IP) Our analysis covers the monthly data for the time period 1976:1-1990:12. Each time series contains 180 observations. Deflation is based on the consumer price index, as published by Statistics Sweden. The series TRA, IPS, and IP are taken from publications of Statistics Sweden. Swedish Telecom uses two prices for telecommunication with the USA; cheaper prices apply for calls during nights and weekends. We used the higher price as an explanatory variable, as a high percentage of calls to the USA are business calls. Fig. 1 shows a typical pattern of the trajectory of PMM for telecommunication with the United Kingdom. The explanatory variables that were included in our analysis are consistent with the prior literature. Discussions of determinants of the demand for international telecommunication are given by Lago (1970) and Yatrakis (1972). Yatrakis tried some twenty explanatory variables, and about half of them were found to be statistically significant. Pousette (1976a, b) restricts the explanatory variables to price and access to technology (number of telephones). Appelbe et al. (1988) include the so-called reciprocal calling effect as one of the important determinants for international telecommunication demand. Expectations concerning future economic conditions are considered in, e.g., Bartels et al. (1988). The demand function was formulated as a linear regression model in logarithmic transforms of both the dependent and explanatory variables. This double logarithmic functional relation, which is the most convenient for the interpretation of elasticities, turned out to be close to the optimal among all Box-Cox transforms. We also experimented with various dynamic specifications; lagging the endogenous variable by one period helped to model adequately the dependence structure of the demand over time. Lagged observations for IPS and IP, with lags up to six months, turned out to be important. The lag structure varied somewhat for the various destination countries. Seasonal dummies for July and August represent the effects of the Swedish summer vacation. Some characteristics of the demand functions that resulted from fitting models with nonvarying coefficients are given in Table 1. These functions were used to assess the relevance of the explanatory variables, including the lagged variable USE_~. The regressions resulted in high values of/~e: above
31
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
¥ 4~
"x ~a t~
C~
I
i9 76
I
I
I
I
I
I
I
I
1981
I
I
1
1986
I
I
I
I
I
199I
time (months)
Fig. l. Trajectory(time sequence plot) of the real price (in SEK/minute)for telecommunication services between Sweden and the United Kingdom. 0.95 for all functions and above 0.977 for non-Scandinavian countries. Table 1 shows short-term and long-term price elasticities. In view of the length of the observation period (180 months), it is reasonable to allow the model parameters to vary over time; this is especially true for price elasticities. There are several theoretical reasons for assuming nonconstant elasticities, such as the technological development within the telecommunication sector, changes in price policies and changing business cycle conditions. It is well-known from empirical results (see Taylor, 1980) that price elasticities increase with increasing distances. Although this statement assumes that economic conditions are the same, a fact that must be questioned when comparing models for different countries, this observation is another reason why different patterns of the coefficient trajectories for the various destination countries must be expected. The results reported in the next section are obtained by applying the moving local regression technique to the estimation of the regression
32
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 2 7 - 3 6
Table 1 Characteristics of the demand function for telecommunication services between Sweden and six destination countries Germany (D), UK, USA (US), Denmark (DK), Norway (N), and Finland (SF) Const.
USE 1
PMM
/~2
PEL
D
1.72
-0.369
0.44
0.977
-0.978
US
1.81
0.994
-0.961
DK
2.68
0.955
-0.975
N
1.70
0.971
- 1.178
SF
3.58
-0.258 (3.94) -0.492 (5.44) -0.122 (2.62) -0.392 (4.76) -0.509 (4.01) -0.302 (4.15)
0.978
UK
0.300 (5.32) 0.497 (8.10) 0.873 (26.73) 0.598 (9.27) 0.568 (9.99) 0.618 (13.36)
0.961
-0.627
Short-term price elasticities are given in column PMM with It[-values in parentheses; column PEL shows the corresponding long-term price elasticities. The functions are fitted in log-log form. coefficients. This estimation approach consists of fitting a regression model with constant p a r a m e t e r s to a window of data that shifts over the observation period. It generalizes the moving average approach by using nonconstant weights. It is discussed in a recent p a p e r by Cleveland et al. (1988). Similar versions of locally weighted curve fitting were suggested by Macaulay (1931), Pelto et al. (1968), and Cleveland (1979). An adaptation to time series due to Fedorov et al. (1992) shows how to adapt this approach to time series data. Applying of the moving local regression approach to the linear regression , . . ^ (o . m o d e l E { y , } = x , [3 results m esUmates [3 of the coefficients [3. The model is locally fitted using data around the time period t. The weighted least squares m e t h o d is used as the estimation approach /3 ( ' ) = ( X ' F t X ) - ~ X ' F t Y ;
(1)
where the diagonal matrix F, = diag(~-~ ') . . . .
, r~")
contains the weights (importance) ~.~0 that are given to observations (x i, Yi), i = 1 . . . . , T. Estimates of the standard deviation of/3 (0 are taken from the covariance matrix V a r { [ 3 ( ° } = ( X ' F t X ) - I & 2, where ~.2 is the estimated
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
33
disturbance variance and based on the residuals between observations and the locally fitted model. To guarantee properties such as unbiasedness, smoothness of the estimated response function, and robustness towards influential data points, the weights have to satisfy certain criteria. A comprehensive discussion of several useful weight functions is given by Mfiller (1991). In moving local regression, the time-varying parameters are estimated with little bias as the used data base for the estimate is restricted to the neighborhood of the time point of interest. Consequently, the estimates reflect changes in the coefficient structure. This approach takes smooth changes of the model structure into account. In this study we used the tricube weight function
_
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otherwise that has been suggested by Cleveland (1979). The "window width" 2A + 1 is a crucial parameter of the fitting procedure. The reported results use A = 26 months, which implies a window of 53 months (or approximately 4.5 years).
3. Trajectories of the price elasticity Fig. 2 shows the trajectories of the price elasticity of the demand that result from the moving local regression approach together with 2o- bounds. The curves for the six destination countries are rather smooth, corresponding to the relatively large value of the window width of 53 time periods. A smaller window width implies a smaller bias but an increased standard deviation. The variability in the estimated price elasticities increases if the window width is reduced, but our results show that the general time pattern is unchanged. The range of the estimated price elasticities goes from values close to zero (inelastic) to being greater than one (elastic). The trajectories for all countries (except the USA) show a continuous increase in the (absolute) price elasticity over time. Very similar patterns are observed for the Scandinavian countries and Germany. A considerable change towards more elastic demand happened during the eighties; the trajectory of the (absolute) price elasticity before that change can be characterized as slightly increasing, followed by a period of constancy. During the most recent years the Scandinavian countries exhibit a slight decrease in the (absolute) price elasticity, but in all cases the demand is price elastic or close to price elastic. For the United Kingdom, we observe a similar pattern that, however, starts from a somewhat higher (absolute) value than the other European countries;
.
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Fig. 2. Trajectories (time sequence plots, solid lines) of the price elasticity of the demand for telecommunication services between Sweden and six destination countries: Germany, UK, USA, Denmark, Norway, and Finland. The dashed lines indicate 2o" bounds.
4.1
I--~ ~
GCR~AN~
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P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
35
a slight increase in the (absolute) price elasticity is observed over the whole studied time period, and, at the end of the period under study, the demand is price elastic. An entirely different picture is found for the USA. Starting from a price elastic situation, the (absolute) price elasticity decreases in the mid-eighties to a value close to zero. Our results make it clear that an assumption of constant price elasticity is not adequate in our situation where observations over a rather long time period are used to fit the demand function. Using a moving local regression approach is recommended in this situation as the finite window width gives the flexibility of fitting the model locally without assuming a special structure for the time-variation of the model coefficients. We are cautious in our interpretation as we primarily are concerned with the methodological aspects. Moreover, the limitations of the used data may imply a misspecification of the model. In particular, important variables such as the number of telephones were not available; business and residential calls are not separated; the model describes only communication originating in Sweden and does not take into account the asymmetry of demand in reaction to the respective pricing systems in the source and destination country; the specification of the model might change over time. The large temporal range in the estimated price elasticities might surprise. However, the close similarity in the patterns for the European countries increases the credibility of our findings. One possible argument for the increasing (absolute) price elasticity in European countries is the growing consumer awareness of their strength. A growing proportion of non-business calls may further contribute to that pattern. Two features of the trajectories need to be explained more:
• At the beginning of the observation period, positive price elasticities are found for Germany, Norway, and Finland: as the 2ty bounds include 0, the null-hypothesis of "zero price elasticity" cannot be rejected in all three cases. • The pattern for the USA is different from all other tra/ectories; the small estimates for the mid to late eighties contradict the theory that the price elasticity should increase (absolutely) with increasing distances: the substantial decrease in the (absolute) price elasticity within a very short period of less than two years might reflect changes in behavior that resulted from the US deregulation of long distance telecommunication. However, a detailed analysis of the relevance of this or other possible causes is beyond the scope of our study. The fact that the price elasticity for the last few years is close to zero requires further investigation.
36
P. Hackl, A.H. Westlund / Information Economics and Policy 7 (1995) 27-36
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