and slightly elastic, respectively, (2) business demand is relatively more price- elastic than residential ..... WATS messages, the called party (800-numbers exclusively in our sample) pays ... process, particularly if their numbers were small.
Jean-Michel Guklmann
Modeling Residential and Business Telecommunication Flows: A Regional Point-to-Point Approach
Regional telecommunicationj o w s , measured in terms of numbers of messages and conversation minutes, are analyzed with a systematic random sample of toll calls characterized by their timing, duration, cost, and origin-destination ( 0 - D ) locations. Point-to-point models are econometrically estimated, with such independent variables as destination market size, 0 - D distance, and average and time-of-day (TOD) prices, for the residential and business sectors separately. The results indicate that (1)the demandsfor calls and conversation minutes are price-inelastic and slightly elastic, respectively, (2) business demand is relatively more priceelastic than residential demand, ( 3 ) distance is a strong determinant of telephone demand, and (4) most TOD demand substitutions resulting from TOD price changes would take place between the daily and evening rate periods. Several areas for further research are outlined. 1. INTRODUCTION
Telecommunication interactions, like transportation interactions, take place over space. However, in contrast to the huge literature devoted to the analysis of point-to-point transportation demand (for example, commuting, shopping, and recreation trips), relatively little research is available (at least in the public domain) on point-to-point telecommunication demand. One important reason for this dearth of research is that, in contrast to the usual public availability of transportation data, similar telecommunication data are often viewed as proprietary by the private (at least in the United States) companies that provide telecommunicaA preliminary version of this paper was presented at the 30th European Congress of the Regional Science Association, August 28-31, 1990, Istanbul, Turkey. Financial support from the Urban Affairs and Urban Assistance Program, Ohio Board of Regents, is gratefully acknowledged. The views ex ressed in this pa er are not necessarily endorsed by the Ohio Board of Regents or by the &phone company t i a t provided the data used in this study. For proprietary reasons, the identity of this company may not be revealed. However, the author wishes to e x ress his gratitude to its officials for agreeing to supply the data without which this research woulfnot have been feasible, and for helping him clarify many issues that arose during the research process. Thanks are also due to an anonymous reviewer for helpful comments on an earlier draft.
Jean-Michel Guldmunn is professor of city and regional planning at The Ohio State University. Geographical Analysis, Vol. 24, No. 2 (April 1992) 0 1992 Ohio State University Press Submitted 10/90. Revised version accepted 12/90.
122 I
Geographical Analysis
tion services. However, a better understanding of the geographical and economic determinants of telecommunication flows is likely to become more and more important in the quickly evolving environment in which the telecommunication industry operates in the United States and other countries (for example, Great Britain). For instance, with increasing competition not only in the long-distance markets but also in the local ones, a better assessment of route-specific price elasticities may be essential to formulate efficient pricing rules for local exchange companies to reduce the threat of uneconomic bypass of their networks by large telecommunication users. In addition to this traditional industrial organization issue, the knowledge of the spatial structure of telecommunications interactions may also provide a better understanding of regional social and economic linkages, which are mirrored, at least in part, by telecommunication linkages, and help clarify such issues as the complementarity and substitution effects between transportation and telecommunication (Wigan 1985)and the role of telecommunication and related information technologies on patterns of urban and regional development (Gillespie and Williams 1988). A strong case for compiling a new set of industry statistics based on Mi'lT-minutes of telecommunications t r & c t o serve as a new economic indicator to track the business cycle is also presented by Staple and Mullins (1989). The purpose of this paper is to contribute to the above debate through an econometric analysis of regional point-to-point telecommunication flows, making use of a new and very rich data base on toll calls. The estimated models extend those available up to now on several counts. First, telephone flows are explicitly characterized by both number of calls and conversation duration, and both measures are analyzed extensively. Second, both distance and price variables are successfully introduced into the models, thus allowing for discrimination between distance (that is, spatial separation) and price effects. Third, a hierarchical modeling framework, similar to one often used in energy demand analysis, is introduced to model both aggregate and time-of-day telecommunication demands on a point-to-point basis, thus providing both own- and cross-price elasticities information. Finally, all the analyses are carried out separately for the residential and business sectors, thus accounting for differences in telecommunication usage, in contrast to most past studies where both traffic flows were merged. The remainder of the paper is organized as follows. Section I1 consists in a review of the relevant telecommunication demand literature. The methodology underlying the econometric analysis is presented in section 111. The results of the empirical analysis are reviewed in section IV, and their elasticity implications are discussed in section V. Conclusions and areas for further research are outlined in section VI. 2. LITERATURE REVIEW
Telephone flows have been analyzed by both geographers and economists. However, both streams of studies have essentially ignored each other, with geographers emphasizing the effects of distance and place sizekentrality, and economists focusing on price and income effects. In the geographical stream, the earliest study of intercity telephone flows appears to be that of Hammer and Ik16 (1957), who regressed the total number of telephone calls, in both directions, between pairs of cities with the airline distance and their respective numbers of subscribers, using a log-linear functional specification. A similar gravity model was estimated by Leinbach (1973), using telephone flow data for West Malaysia, and regressing, in logarithmic form, the number of intercity messages with distance and city modernization scores, as obtained from
Jean-Michel Guldrnunn I
123
a principal component analysis of various socioeconomic data. However, in addition, Leinbach estimated similar models for sixteen originating exchanges separately, and then demonstrated a significant relationship between the estimated distance coefficient and the distance of the exchange from a modernization core located close to the capital, Kuala Lumpur. Thus, convincing evidence was provided with regard to the influence of location on the effect of distance upon the pattern of telecommunication. Finally, Hirst (1975), using telephone calls data for Tanzania, showed that combining the distance variable with dummy variables that discriminate between dyads that do and do not include the dominating 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. In the economic stream, most studies have focused on interstate toll calls, including Larsen and McCleary (1970), Deschamps (1974), Pacey (1983), and, most recently, Appelbe et al. (1988). Both Deschamps and Pacey developed regression relationships relating the number of calls between two cities to the numbers of subscribers in both cities, the average income at the origin city, toll rate measures, and, in the case of Deschamps, the distance between the cities expressed through the use of dummy variables. Pacey was not able to separate distance and price effects. Both obtained price elasticities around -0.24. In Deschamps’ model, the coefficients of the distance dummy variables turned out to be negative, increasing with distance, and highly significant. In addition, Pacey developed a model for the average call duration, with a price elasticity of around - 0.30, and with distance as a positive determinant. Both modeling efforts dealt with total traffic, that is, merged business and residential traffic. In contrast, Larsen and McCleary did relate separately the interstate number of residential and business toll calls to income and price variables, and to the interstate mail volume, which turned out to be the most significant predictor. They obtained a unit-price elasticity, but also a negative and significant income elasticity. These results are suspect, and the model may well have been misspecified, as it is by no means clear that mail volume explains call volume, and it is likely that both variables are simply collinear. Appelbe et al. have regrouped interprovincial and Canada-U.S. routes by mileage bands, and, for each group, have estimated pointto-point models at a rather highly aggregate level. Their dependent variables are the deflated revenues for intra-Canada flows, and billed minutes for Canada-U. S . flows. Their major contribution is the introduction in this interstate model of the reverse traffic as an explanatory variable, as well as the separate analysis of fullrate and discount-rate flows. They have obtained unidirectional price elasticities ranging from - 0.21 to - 0.53, and bidirectional elasticities ranging from - 0.36 to -0.75. No distinction was made between residential and business calls. The idea of using reverse traffic (from j to i) as a determinant of the traffic from i to j was first proposed by Larson, Lehman, and Weisman (1990) in their analysis of high density toll routes consisting each of a large metropolitan area (A) and a relatively small suburb or town (B).All traffic volumes (in minutes) are from A to B, and are aggregated over all rate periods. No information is provided as to the geographical location of these routes, nor to their length. Traffic flow from A to B is taken as a function of rates, income, population, and tr&c from B to A, with route-specific intercept terms (that is, dummy variables), but route length does not appear as an explanatory variable. The estimated price elasticities were around - 0.75. In addition to these point-to-point models, we should mention the large number of studies of intrastate toll demand performed “in-house” by the Bell Operating Companies (BOCs), at the aggregate level (that is, flows are not specified geographically), as reported in detail by Taylor (1980). These models are variations of the distributed-lag model where the total number of messages in year
124
/
Geographical Analysis
t is a function of that lagged number, the state per capita income, price variables, and the number of telephone stations in the state, with generally no distinction between residential and business calls. Their price elasticity estimates vary, in the long run, from - 0.22 to - 1.04. Similar aggregate models have been estimated for the interstate toll market, with elasticities as high as -1.20 (Taylor 1980, p. 115). In concluding this review, it is important to place the above, rather disparate, literature on telecommunication flow modeling within the broader and wellestablished framework of gravity and spatial interaction modeling in geography and regional science (see, for instance, Fotheringham and O’Kelley 1989). Such models have been abundantly and successfully used to analyze locational choices, transportation patterns (commuting, shopping, recreation, airlines, etc.), and migration flows. This literature has developed a large body of estimation techniques, and has also identified important and still unresolved issues, particularly the influence of spatial structure on spatial interaction behavior, and therefore may provide important leads toward improving telecommunication flow models, as discussed in the concluding section of this paper. 3. METHODOLOGY
The modeling approach builds upon the point-to-point models reviewed in section 2, and extends them by considering both aggregate and time-of-day (TOD) demand equations, borrowing from methodologies used in energy demand analysis, for example, the modeling of aggregate energy consumption and fuel choice (Baughman and Joskow 1976), and the modeling of electricity usage under TOD pricing (Kohler and Mitchell 1983). The telephone user decision-making process is conceptualized as a two-stage process. First, the user (residential or business) decides on the level of total telecommunication services to be consumed during a given period (for example, a day or a month), based on an average measure of prices for these services, the need for telecommunication interactions, and the opportunities for such interactions (that is, the universe of potential callees). Next, this user makes a decision as to when to purchase these services, accounting for the fact that rates vary over the day. Consider an aggregation of similar telephone users at location i (wire center). These users can place toll calls to a set of target locations j (1-N) at varying distances D,. Let Vi and Vj be vectors of variables characterizing the users at i and the potential callees a t j , and P, a measure of the price for calling from i t o j . Let F, be a measure of the aggregate demand for telecommunication services from i to j, with
F,
= f(Vi,Vj,D,,P,).
We assume that the above demand function decreases with both P , and D,. A negative price relationship is of course implied by consumer behavior theory. With regard to distance, it is reasonable to assume that, everything else remaining constant, the farther the potential callees are located, the less likely they are to be called because the less likely it is that they belong to the set of people/ businesses with whom the callers interact. In contrast, ifV. includes such variables as population and number of businessedemployees at j , t i e demand for calls to j will vary positively with these variables, which measure the number of calling opportunities at j . The vector Vi must of course include the number of users at i,
Jean-Michel Guldmann I 125 but also some of their characteristics, the most commonly used being average income. Both of these variables are to be positively related to F,. Once users have determined their aggregate demand F,, they must split this demand among different rate periods t( = 1+T), each characterized by a different toll rate structure PVt. Let SH,, be the share of the total demand to be consumed during period t . We assume that
SH,,
=
g(Vi,Vj,D,,P,,, . . . , P,,, . . . , PYT)
(2)
T
with, of course, SH,, = 1. Thus, it is necessary to estimate only (T - 1) share equations. One approach is to estimate a set of multinomial logit functions (Baughman and Joskow 1976). Another approach, used in this study, is to estimate directly the share equations (Kohler and Mitchell 1983). The demand F,, for telecommunication services during period t is then obtained by combining equations (1) and (2):
F Ilt ..
=
SH,,
* F, .
(3)
4. EMPIRICAL ANALYSIS
4 . 1 Data The data pertain to a 5 percent systematic sample, with a random starting point, of all the toll calls that took place within a certain Local Access and Toll Area (LATA) somewhere in the United States during the month of December 1987. This sample was drawn daily from a billing/accounting data base. Because of the proprietary nature of the information, the name of the company that provided these data may not be revealed, and any parameter that might be used to identify it is given on an interval basis only. Toll messages are classified according to four service categories: (1) MTS (Message Toll Service) messages originating at residential and business stations (69 percent of all calls); ( 2 ) MTS messages originating at coin-telephones (3 percent of all calls); (3) Out-WATS (Wide Area Toll Service) measured-time messages originating at a WATS measured time number (20 percent of all calls); and (4)In-WATS messages terminating at an In-WATS number (8 percent of all calls). This study is limited to the analysis of non-coin MTS residential and business messages for several reasons. First, while all non-coin MTS users face the same toll rate structure, tolls for coin messages are higher, and thus combining both types of messages is inappropriate. In addition, the behavioral underpinnings of coin toll demand are likely to be different from those of regular station toll demand. Second, the rate structure for Out-WATS messages is fundamentally different from MTS, with users paying an access charge and a usage charge proportional to call volume, irrespective of destination location within the LATA. This service is primarily used by businesses, which will choose WATS over MTS if the anticipated volume at the WATS rates is cheaper than paying MTS rates. Large business users do often subscribe to both services. Out-WATS calls do include local calls, in contrast to MTS. Because of these differences, it would be clearly inappropriate to aggregate MTS and Out-WATS calls. However, there is no doubt that MTS and Out-WATS services are substitutable, and one approach to assess this substitutability is to include WATS prices in MTS demand functions. While this was done by Pacey (1983) in her analysis of interstate call durations with varying WATS
126 I Geographical Analysis rates, this is clearly unfeasible (from a statistical viewpoint) in this study because of nonvarying WATS rates. Such effects would be best captured with time-series data over a period with varying MTS and WATS rates. Finally, in the case of InWATS messages, the called party (800-numbers exclusively in our sample) pays for the service. The caller does not pay any charge for placing such a call, and obviously the behavioral determinants of such traffic are quite different from those of MTS and Out-WATS traffic. A separate analysis of this tr&c is very much warranted, but could not be performed within the framework of this study. The total number of sampled non-coin MTS messages lies within the interval [300,00&500,000]. Each message is characterized by a large number of variables, including the message date (day of month, time of day), the message duration, the message charge, the coordinates of the two wire centers where the message originates and terminates, and the Standard Industrial Classification (SIC) code of the caller. The latter code was used to classify messages as residential or business. Next, message characteristics (numbers, durations, charges) were aggregated by rate periods and origin-destination (0-D) wire centers. There are three rate periods (day, evening, nighdweekend), each characterized by a different toll structure. There are N (~[100-200])wire centers in the LATA, and thus at most N*(N - 1) 0 - D linkages. This is an upper bound for two reasons: first, it may be that no call was placed from wire center i t o j during December 1987, and, second, even if such calls were placed, it is possible that none were selected in the sampling process, particularly if their numbers were small. Total values for numbers of calls, durations, and charges were estimated by multiplying the sample values by the inflation factor of 20, thus unavoidably creating some measurement errors. In order to mitigate the severity of this problem, we have restricted the analysis of point-to-point flows to the twelve largest origin wire centers in terms of the traffic they generate, representing about 50 percent of all non-coin MTS traffic. The size (attraction) of wire center j receiving messages from any wire center i is measured by two variables: N V T j = total number of calls received b y j from all origins, and M T T j = total duration (in minutes) of calls received by j from all origins. Alternative measures of the size of the destination nodes might involve population, employment, and numbers of subscribers (access lines), as used in some of the studies reviewed in section 2. Such data were not available within the framework of this study, but may be considered in further research. In addition to the variables N V T j and M T T j , each observation in the final data set, corresponding to a given link i-j and a given sector (residentialhusiness), includes the following: total number of calls between i andj, total number of calls between i and j during rate period t, total duration (in minutes) of calls between i andj, total duration (in minutes) of calls between i a n d j during rate period t, total charge (in dollars) of calls between i andj, total charge (in dollars) of calls between i a n d j during rate period t , distance between i a n d j (in miles). Obviously, we have 3
c NV,,
t=l
3
=
NV,,
c MT,,
t=l
3
=
MT,,
MC,, t=l
=
MC,
.
(4)
Jean-Michel Guldmann I 127 Average prices are then derived by dividing call charges by call duration:
PA,
P,,
MC,/MT,
= =
(5)
;
(t
MC,,/MT,,
=
1 + 3).
(6)
The final data set includes 1,538 observations (that is, links) for the residential sector, and 1,320 observations for the business one. The twelve originating wire centers are identified as A, B, C, D, E, F, G, H, I, J, K, and L. Their shares of observations are presented in Table 1, and basic descriptive statistics for the whole data set are provided in Table 2. The average 0 - D distance is about fifty-three miles for the residential sector and forty-nine miles for the business sector. The maximum distance lies in the interval [loo-2001 miles. Most of the traffic (92.7 percent of residential calls and 92.8 percent of business calls), however, is characterized by a haul of less than fifty miles. Several features emerge from a review of the information in Table 2. First, while the total numbers of calls from both sectors are comparable, business calls have shorter durations. This is true for all mileage bands and rate periods, but particularly so in the evening and at night (with ratios close to 2:l). Second, the distribution of calls and conversation-minutes over the three periods is highly different among the two sectors: while residential callers use the network primarily in the evening (43.6 percent of total minutes), and
TABLE 1 Numbers of Origin-Destination Linkages by Originating Wire Center and Sector Orieinatine Wire Center Sector
A
B
C
D
E
F
G
H
1
1
K
L
Total
Residential Business
136 130
131 107
130 98
122 98
117 101
130 120
137 134
126 97
138 133
131 119
117 85
123 98
1,538 1,320
TABLE 2 Residential Sector
Business Sector (N = 1.320)
(N = 1.5%)
Variable
Number of Calls Total Day Evening Night/Weekend
1,316 585 439 292
20 0 0
Conversation Duration (minutes) Total Day Evening Night/Weekend
0
110,680 57,220 32,660 22,743
1,215 964 143 108
20 0 0 0
102,980 85,340 10,560 7,520
691.6 238.5 301.7 151.4
2 0 0 0
50,014 21,106 19,464 10,269
388.1 304.5 49.5 34.1
2 0 0 0
33,772 28,710 3,198 2,526
21.1 32.2 19.2 12.6
8.1 14.7 9.2 6.3
200 200 66 181
28.5 31.8 20.2 13.8
7.7 15.9 10.4 5.9
209 209 66 181
Average Prices - (@/minute)
Total Day Evening NightIWeekend
128 /
Geographical Analysis
secondarily during the day (34.5 percent), business callers use the network primarily during day time (78.5 percent). This difference obviously reflects the daytime pattern of activity of business users, and the broader options of residential callers. Finally, the average prices per rate period clearly reflect the increasing discounts offered when shifting from day to evening to night periods, and are very similar among the two sectors. However, the overall average price for the business sector (28.5eIminute) is larger than the corresponding residential price ( 2 1 . 1 ~ ) because of its much higher daytime traffic loading. 4.2 Functional Specijications Consider a given origin i, and all the destinations j for which positive flows (NV,, MT,) have been observed. The general aggregate models for numbers of messages and conversation minutes, as discussed in section 3, are specified as follows: NV, = Fi(NVTj,D,,PA,)
;
(7)
We consider logarithmic specifications of both the first and second orders, and estimate these models separately for each of the twelve origin wire centers (A-L). The twelve subsamples are then pooled, and the above models are estimated over the whole sample, but while introducing dummy variables ( I A - I K ) to account for the varying size of the twelve centers in terms of tr&c flow generation. For instance, the first-order model for the number of messages becomes
where IA = 1if i = A and 0 otherwise (etc.). Time-sharing models need to be estimated for two periods (say, day and evening), the third-period model being then derived from the estimated coefficients. Consider the case of conversation minutes. The traffic share of period t is defined as
The models considered are
SH,,
=
bo + bllnMTT'
SH,
=
co
+ b2lnDV+ b31n(P,1/P,3) + b4ln(PV2/P,,) ;
+ cllnMTTj + c21nD, + ~,ln(P,,/l',~) + C ~ ~ ( P , ~ / P. , ~ )
(11) (12)
The share model for period 3 (nighdweekend) is obtained as
Similar models are considered for the time sharing of the number of messages. In addition to being estimated for each of the twelve origins separately, the above
Jean-Michel Guldmunn
I 129
equations are also estimated for the whole sample while again using dummy variables.
4.3 Aggregate Telecommunication Flow Models Equations (7) and (8) were estimated by using ordinary least squares (OLS). However, we tested for cross-equation correlations of the error terms by also estimating these two equations as a system, using Zellner's (1962) seemingly unrelated regression (SUR) estimation method. In all cases, the results from SUR were essentially the same as those obtained with OLS. Equations (7) and (8)were initially estimated as first-order linear forms for each origin and for each sector (residential and business). In all cases, the coefficients of the destination size variables (lnNVT,lnMTT)were positive, as expected, highly significant, and overall close to one, suggesting proportional effects. Also as expected, the coefficients of the distance and price variables (lnD,lnPA) were generally negative. The distance coefficients were in most cases highly significant. However, the price coefficients were often insignificant in the message models, but significant to highly significant in the minutes models. Overall, these results did suggest that the demand for calls is inelastic, and the demand for minutes elastic. The next step was to estimate second-order models by adding quadratic terms. A strong improvement was obtained in all the models by adding (lnD)', the effects of the other squared variables as well as cross-products being generally insignificant or very marginal. We thus report in Tables 3 and 4 the estimation of the message and minutes models with the only addition of (1nD)2.A comparison with the first-order models shows an increase in the R2 in all cases, particularly strong
TABLE 3 Second-Order Models for the Aggregate Number of Messages by Origin Variables
Origin Intercept
I
InNVT
B C D E F c, H
I
J
K L A B C
D E F G H I J K L
I
InD
14.06 12.68 18.94 13.66 20.66 19.67 11.25 14.09 13.84 12.62 20.99 12.39
(6.58)* (7.18) (7.63) (6.99) (7.24) (6.11) (6.85) (7.56) (6.30) (6.16) (6.98) (6.79)
1.02 1.05 0.96 0.95 0.96 0.94 1.13 0.98 1.02 0.97 0.93 0.89
(18.13) (18.08) (15.25) (14.63) (13.07) (15.05) (28.05) (18.03) (19.05) (13.55) (12.01) (14.89)
Residential Sector - 9.13 (7.76) - 8.55 (9.49) - 11.21 (8.32) - 8.88 (9.14) -11.75 (7.10) - 12.19 (6.46) - 7.98 (9.70) - 9.14 (9.25) - 8.51 (7.82) - 7.90 (7.25) -12.54 (7.06) - 7.69 (8.55)
12.12 10.42 13.32 14.56 23.56 19.38 2.82 18.98 11.16 9.02 18.39 7.94
(5.30) (4.43) (3.70) (6.42) (7.96) (5.44) (1.29) (6.86) (4.35) (4.58) (4.89) (3.29)
0.99 0.84 0.98 0.83 1.04 0.96 1.03 0.73 1.00 0.98 0.96 0.99
(16.60) (12.72) (13.39) (12.28) (14.26) (12.83) (20.32) (10.55) (18.68) (16.00) (10.39) (13.74)
Business 7.03 6.04 7.97 - 8.24 - 13.41 - 11.89 - 1.63 - 10.38 - 6.25 - 5.15 -11.19 - 5.50
~
A
I
*The t-statistics are in parentheses.
-
Sector (5.41) (4.86) (4.07) (6.98) (8.01) (5.59) (1.42) (7.01) (4.75) (4.96) (5.00) (4.43)
(lnD)2
I
[
InPA
R*
1.10 1.02 1.33 1.06 1.34 1.58 1.00 1.08 0.99 0.89 1.52 0.88
(7.03) (8.64) (7.45) (8.18) (6.15) (5.97) (9.61) (8.42) (7.33) (5.99) (6.24) (7.63)
0.47 -0.10 0.05 -0.07 -0.02 -0.45 -0.33 -0.01 0.06 0.05 0.09 0.19
1.32) l0.50) (0.22) (0.33) (0.08) (1.40) 1.22) 10.07) (0.21) (0.19) (0.36) (0.84)
0.836 0.867 0.838 0.853 0.764 0.733 0.922 0.851 0.838 0.833 0.778 0.847
0.79 0.64 0.87 0.94 1.56 1.49 0.29 1.22 0.66 0.49 1.34 0.58
(4.57) (3.90) (3.30) (5.97) (7.15) (4.99) (1.99) (6.24) (4.07) (3.45) (4.24) (3.58)
-0.58 0.07 0.06 -0.26 - 0.19 0.46 -3.44 0.05 -0.50 -0.11 0.09 0.00
(1.69) (0.29) (0.21) (0.90) (0.85) (1.05) (9.41) (0.18) (1.68) (0.47) (0.26) (0.01)
0.818 0.797 0.803 0.849 0.773 0.668 0.820 0.735 0.848 0.878 0.727 0.817
130 I Geographical Analysis TABLE 4 Second-Order Models for the Aggregate Number of Conversation Minutes by Origin Origin
Variables Intercept
I
lnMTT
I
InD
I
hD)Z
I
lnPA
I
€I2
Residential Sector A
B C D E F G H I J K L
11.96 9.65 14.91 9.67 15.32 13.38 6.08 10.33 8.81 7.82 11.99 9.84
(5.17)* (3.78) (4.78) (3.39) (4.81) (3.31) (2.77) (3.60) (2.83) (2.84) (3.21) (3.39)
9.47 9.20 10.82 10.85 19.53 15.61 0.64 17.06 2.78 4.69 13.72 3.58
(3.89) (2.83) (2.64) (3.50) (5.04) (3.77) (0.30) (4.5ij (0.89) (1.87) (2.88) (1.16)
1.03 1.21 1.06 1.15 1.00 1.10 1.22 1.11 1.09 1.10 1.03 1.10
(16.47) (14.40) (12.89) (12.20) (11.41) (13.51) (22.45) (13.04) (14.20) (11.46) (10.15) (11.68)
- 8.09 (6.55) - 8.33 (6.77) - 9.86 (5.97) - 8.20 (6.23) - 9.06 (4.79) - 9.76 (4.16) - 6.19 5.88) - 8.17 15.55) - 6.38 (4.28) - 6.23 (4.52) - 7.94 (3.62) - 7.91 (5.93)
1.05 0.95 1.11 0.96 1.15 1.05 1.12 0.85 1.13 1.07 0.95 1.05
(17.02) (10.71) (13.70) (10.85) (12.04) (12.32) (24.09) ‘(9.06j (18.00) (14.39) (8.12) (12.15)
-
Business Sector 5.91 (4.35) 5.69 (3.45) - 7.26 (3.32) - 6.63 (4.26) - 11.83 (5.38) - 10.17 (4.12) - 1.04 (0.98) - 9.40 (4.82j - 2.29 (1.47) - 3.11 (2.46) - 8.01 (2.81) - 3.12 (2.04)
1.00 1.06 1.25 1.04 1.03 1.31 0.83 1.02 0.76 0.75 0.93 0.96
(6.08) (6.59) (5.70) (5.90) (4.17) (3.99) (6.22) (5.30) (4.10) (4.01) (3.10) (5.61)
-0.18 -1.37 -1.56 -1.25 -0.94 -1.88 -1.37 -0.97 -0.94 -1.42 -1.25 -0.47
(0.49) (4.85) (5.08) (4.26) (3.34) (4.68) (3.93) (3.67) (2.43) (4.09) (3.72) (1.40)
0.806 0.804 0.783 0.786 0.711 0.682 0.871 0.752 0.698 0.759 0.737 0.734
0.70 0.67 0.85 0.81 1.39 1.29 0.22 1.15 0.22 0.26 0.98 0.30
(3.86) (3.06) (2.88) (3.91) (4.87) (3.73) (1.67) (4.47) (1.18) (1.50) (2.42) (1.51)
-1.43 (4.00 -1.32 (3.661 -1.47 (4.31) -1.98 (5.09) -1.20 (3.96) -0.52 (1.02) -3.87 (11.45) -1.23 ‘(2.84) -2.36 (6.73) -1.24 (4.20) -1.68 (3.84) -1.36 (3.59)
0.813 0.720 0.805 0.797 0.695 0.645 0.864 0.652 0.828 0.846 0.642 0.786
~
~
A
B C D E F G H I J K L
~
*The t-statistics are in parentheses.
in the residential sector (6 percent to 10 percent). The coefficients of the destination size variables (lnNVT,lnMTT)now vary in a much more narrow range, very much clustered around one for the message models, and slightly above for the minutes models. The coefficients of 1nD and (1nD)2are, in most cases, both very significant, with negative and positive signs respectively in all cases, thus suggesting partly U-shaped demand curves with regard to distance. The coefficients of the price variable are insignificant in most of the message models, suggesting a low to zero price elasticity of message demand. In this respect, the second-order models are consistent with the results obtained with the first-order specifications. With regard to the demand for conversation minutes, the price coefficients are significant to very significant, as in the case of the first-order models, but their magnitudes are generally lower, averaging - 1.13for the residential models, and - 1.64 for the business models. Despite unavoidable variations in the estimated coefficients across the twelve origins, most likely due to sampling effects, the previous results display an overall striking homogeneity with regard to both signs and magnitudes, thus warranting pooling the twelve subsamples to estimate both message and minutes models with dummy variables. These results are presented in Tables 5 and 6. Four models have been estimated in each case: Model 1is the first-order model; model 2 extends model 1 with the addition of (lnD)2;model 3 extends model 2 with the addition of (lnNVT)2or (1nMTq2; finally, model 4 extends model 3 with the addition of (lnPA)2.The results confirm the patterns observed with the originspecific models: the largest improvements in both the R2 and adjusted R2 are obtained when adding (1nD)2to the first-order models, with concomitant decrease
Jean-Michel Guldmann I 131 TABLE 5 Aggregate Message Models with Dummy Variables Residential Sector
Variable
Intercept ZA
1, 1,: ZLJ
ZE
1,. ZG
zn I,
4 1,
InNVT
0.430 (1.36)* 0.793 (8.00) 0.425 (4.28) 0.360 (3.62) - 0.078 (0.77) -0.013 (0.13) 0.246 (2.46) 1.452 (14.72) -0.067 (0.67) 1.129 (11.49) 0.291 (2.93) - 0.114 (1.12) 0.899 (43.61)
14.114 (22.92) 0.899 (10.70) 0.449 (5.34) 0.423 (5.03) - 0.076 (0.89) 0.023 (0.27) 0.420 (4.94) 1.524 (18.27) - 0.024 (0.28) 1.173 (14.11) 0.265 (3.16) -0.027 (0.31) 0.965 (54.71)
- 1.019 (21.34)
-0.312 (3.67)
-9.OOO (27.59) 1.066 (24.61) - 0.030 (0.42)
19.818 (18.45) 0.873 (10.52) 0.444 (5.35) 0.419 (5.04) -0.076 (0.90) 0.027 (0.32) 0.395 (4.71) 1.501 (18.21) - 0.028 (0.34) 1.165 (14.20) 0.272 (3.27) -0.032 (0.38) - 0.298 (1.51) 0.063 (6.44) - 8.660 (26.54) 1.019 (23.51) -0.063 (0.87)
0.768 0.766
0.834 0.833
0.839 0.837
(1nNVT)' 1nD (1nD)2 lnPA (InPA)'
R2 Adj. R2
Business Sector
20.944 (19.28) 0.842 (10.20) 0.448 (5.45) 0.413 (5.01) -0.068 (0.81) 0.041 (0.49) 0.376 (4.52) 1.472 (17.97) -0.023 (0.28) 1.148 (14.10) 0.262 (3.19) -0.030 (0.36) -0.361 (1.85) 0.065 (6.70) - 9.151 (27.18) 1.071 (24.29) 0.942 (4.62) - 0.533 (5.26) 0.842 0.840
1.341 (4.43) 0.912 (6.04) 0.096 (0.82) 0.312 (2.59) -0.111 (0.92) 0.253 (2.11) 0.569 (4.94) 2.349 (20.81) - 0.277 (2.29) 1.184 (10.51) 0.826 (7.17) -0.261 (2.08) 0.896 (41.18)
12.360 (16.10) 0.967 (9.27) 0.105 (0.97) 0.373 (3.37) - 0.135 (1.22) 0.268 (2.43) 0.675 (6.35) 2.402 (23.12) - 0.232 (2.09) 1.202 (11.60) 0.800 (7.55) - 0.179 (1.55) 0.918 (45.77)
- 1.121 (20.69)
-0.545 (5.58)
-7.456 (17.99) 0.847 (15.40) - 0.239 (2.60)
18.500 (15.80) 0.932 (9.07) 0.098 (0.92) 0.360 (3.31) - 0.151 (1.39) 0.254 (2.35) 0.643 (6.16) 2.358 (23.04) - 0.250 (2.29) 1.173 (11.50) 0.782 (7.50) - 0.187 (1.65) - 0.469 (2.31) 0.073 (6.86) -7.262 (17.79) 0.821 (15.14) -0.260 (2.87)
0.764 0.761
0.800 0.798
0.807 0.804
19.465 (16.80) 0.896 (8.87) 0.084 (0.80) 0.366 (3.41) - 0.160 (1.50) 0.283 (2.66) 0.620 (6.04) 2.308 (22.91) -0.250 (2.33) 1.133 (11.30) 0.783 (7.65) - 0.167 (1.49) -0.561 (2.81) 0.077 (7.32) - 7.890 (19.20) 0.900 (16.54) 1.378 (5.50) -0.774 (7.00) 0.814 0.811
*The t-statistics are in parentheses.
in price elasticity and increase in the coefficient of the destination size variable in all cases. Models 3 and 4 point to a partly U-shaped demand curve with regard to destination size in all cases, as well as to -a -a -a -a
very low (close to zero) price elasticity of residential message demand; low (around - 0.25) price elasticity of business message demand; slightly price-elastic demand of residential minutes (around - 1.20); moderately price-elastic demand of business minutes (around - 1.50).
In model 4,the coefficient of (InPA)' is negative and highly significant in all cases, pointing to an elasticity increasing with price. This variability will be analyzed in more detail in section 5. Finally, the magnitudes of the dummy variable coeffi-
132 I Geographical Analysis TABLE 6 Aggregate Minutes Models with Durnrnv Variables Residential Sector
Variable
Intercept IA
I, IC
ID
I, IF
1, IH
Ir
4 I, lnMTT
10.019 - 1.889 (3.98)* (12.33) 1.055 1.152 (10.80) (9.06) 0.558 0.536 (5.23) (4.59) 0.526 0.470 (4.92) (4.02) - 0.049 -0.052 (0.46) (0.43) 0.275 0.242 (2.01) (2.50) 0.514 0.358 (4.77) (3.04) 1.727 1.661 (16.30) (14.33) 0.112 0.073 (1.04) (0.62) 1.355 1.315 (12.83) (11.39) 0.446 0.469 (4.18) (4.02) - 0.122 -0.043 (0.40) (1.02) 1.082 1.018 (45.68) (39.76)
- 1.434 (14.35)
(18.54) 0.953 (17.34) - 1.176 (12.71)
19.845 (7.35) 1.132 (10.65) 0.552 (5.20) 0.524 (4.92) -0.050 (0.47) 0.275 (2.52) 0.495 (4.60) 1.708 (16.17) 0.107 (1.00) 1.347 (12.82) 0.449 (4.22) - 0.049 (0.45) -0.390 (1.01) 0.052 (3.82) - 7.418 (17.72) 0.916 (16.49) - 1.211 (13.08)
0.727 0.725
0.772 0.770
0.774 0.772
(InMTT)' -0.552 (9.84)
1nD (lnD)' lnPA
- 7.684
(1nPA)'
R2 Adj. R2
Business Sector
21.817 (8.07) 1.092 (10.33) 0.557 (5.28) 0.516 (4.88) -0.041 (0.38) 0.292 (2.70) 0.471 (4.41) 1.670 (15.91) 0.113 (1.06) 1.324 (12.69) 0.437 (4.15) - 0.047 (0.43) -0.518 (1.35) 0.056 (4.10) - 8.027 (18.60) 0.981 (17.35) 0.048 (0.18) -0.670 (5.16) 0.778 0.776
-0.041 (0.10) 1.062 (8.36) 0.072 (0.55) 0.333 (2.47) - 0.106 (0.78) 0.357 (2.66) 0.584 (4.53) 2.228 (17.63) - 0.249 (1.84) 1.265 (10.02) 0.873 (6.77) - 0.167 (1.19) 1.OOO (41.33)
8.736 (9.50) 1.105 (9.06) 0.078 (0.62) 0.382 (2.94) - 0.126 (0.97) 0.369 (2.86) 0.668 (5.38) 2.270 (18.69) -0.214 (1.65) 1.279 (10.56) 0.851 (6.87) - 0.102 (0.76) 1.016 (43.64)
-0.700 (11.57)
(16.35)
-5.767 (11.91) 0.678 (10.54) - 1.541 (14.33)
18.463 (8.28) 1.076 (8.89) 0.077 (0.61) 0.373 (2.90) - 0.135 (1.05) 0.361 (2.83) 0.641 (5.20) 2.232 (18.49) -0.223 (1.73) 1.255 (10.44) 0.840 (6.84) - 0.108 (0.80) -0.533 (1.64) 0.060 (4.78) - 5.633 (11.71) 0.659 (10.32) - 1.565 (14.66)
0.750 0.748
0.770 0.767
0.774 0.771
- 1.787
19.766 (9.01) 1.034 (8.70) 0.061 (0.49) 0.380 (3.01) - 0.144 (1.15) 0.397 (3.17) 0.613 (5.07) 2.173 (18.31) -0.221 (1.75) 1.209 (10.23) 0.843 (7.00) -0.082 (0.63) -0.625 (1.96) 0.062 (5.08) - 6.409 (13.25) 0.758 (11.82) 0.428 (1.46) - 0.942 (7.25) 0.783 0.780
*The t-statistics are in parentheses.
cients closely reflect, as expected, the sizes of the twelve traffic generating wire centers. The results reported in Tables 5 and 6 can also be used to derive some information with respect to average call duration, which is defined, for the 0 - D wire centers i and j, as
AVD,
=
MT,/NV,.
Consider first model 1 in both tables. The price elasticities suggest that call durations are slightly elastic in the residential sector ( - 1.434 0.312 = - 1.122)
+
Jean-Michel Guldmann I
133
+
as well as in the business sector (-1.787 0.545 = -1.242). Second, the coefficients of InD clearly indicate that duration increases with distance, and confirm the telephone industry adage that “the longer the haul the longer the call.” This feature was also empirically confirmed by Pacey (1983) in the case of interstate calls. We have directly estimated log-linear duration models reflecting the variables used in model 2. The dummy variables turned out to be insignificant, and were dropped from these models. The results are as follows: Residential
+
lnAVD = -3.05 0.8761nMTT - 0.7721nNVT (4.89) (9.35) (8.71)
+ 1.3481nD (5.53)
- 0.117(lnD)’ - 1.1721nPA.
(3.65)
(21.20)
R2
=
0.297
(15)
Business lnAVD = -1.987 (3.52)
+
0.5921nMTT - 0.4981nNVT (6.89) (5.74)
+ 1.6211nD (6.43)
- 0. 160(lnD)2- 1.3031nPA .
(4.77)
(23.35)
R2
=
0.335
(16)
The threshold distances at which the average call duration starts decreasing with distance are 317 and 158 miles for the residential and business sectors, respectively, thus beyond or at the boundaries of the sampled data set. 4.4 Time-of-Day Telecommunications Flow Models The share equations (11)and (12) have been estimated for conversation minutes and for the day and evening periods, for each of the twelve origins separately. The distance variable turned out to be insignificant and was dropped from the models. The results are presented in Tables 7 and 8. The most striking feature of the results is the correct sign, in all cases, of the coefficients of the price ratios, and also their generally very high significance. It is also important to note that the derived coefficients of the price ratios in the night share models, SH,, have, in most cases, also the correct signs (that is, positive). In the few negative sign cases, the coefficients are very close to zero, thus suggesting that little substitution may take place. The destination size variable, InMTT, is generally insignificant for the residential sector, but significant to highly so in the business sector, with uniformly positive effects during daytime and negative ones in the evening. This result suggests that the larger the called market, the larger the number of business telephone contacts that must be placed during daytime. In view of the overall homogeneity of the origin-specific models, the twelve subsamples were pooled, and the same equations estimated. Dummy variables
Day Share Minutes Flow Models by Origin Origin
A B C D E F G H I
J
K L
Variables Intercept
0.303 0.981 -0.029 0.504 0.297 0.170 0.461 0.299 0.242 0.218 0.299 0.391
I
(1.68)* (3.71) (0.11) (1.54) (1.30) (0.85) (2.23) (0.92) (1.31) (0.85) (1.05) (1.22)
I
InMTT
0.0141 -0.0191 0.0346 0.0065 0.0130 0.0287 0.0004 0.0173 0.0257 0.0218 0.0299 0.0194
I
In(PdPd
Residential Sector (1.15) -0.335 (1.08) -0.558 (2.18) -0.347 (0.30) -0.528 (0.86) -0.331 (2.19) -0.444 (0.03) -0.328 (0.77) - 0.459 (1.97) -0.572 (1.25) -0.465 (1.50) -0.581 (0.88) -0.664
(4.38) (5.96) (3.70) (5.75) (5.85) (7.02) (5.65) (3.96) (6.60) (6.18) (5.23) (6.15)
In(PdPd
0.250 0.238 0.345 0.496 0.178 0.294 0.321 0.436 0.504 0.492 0.293 0.614
(3.09) (2.19) (4.31) (3.64) (2.52) (5.37) (3.16) (3.69) (5.19) (6.34) (2.92) (5.66)
0.215 0.353 0.062 0.470 0.302 0.251 0.338 0.797 0.536 0.132 0.406 0.343
(2.26) (3.22) (0.67) (2.73) (2.12) (2.64) (3.93) (4.33) (4.13j (1.25) (4.80) (2.38)
I
RZ
0.166 0.315 0.265 0.338 0.361 0.407 0.217 0.198 0.292 0.380 0.283 0.398
Businf :ss Sector ~~~~.~
~
~
~
A
I J K L
0.413 -0.005 0.336 0.318 0.746 0.259 - 0.512 - 0.030 0.285 -0.296 0.055 -0.534 ~~~
~
(2.49) (0.02) (0.97) (0.98) (2.55) (1.20) (2.93) io.09) (1.38j (1.13) (0.27) (1.52)
0.0339 0.0701 0.0341 0.0579 0.0462 0.0619 0.1206 0.0814 0.0555 0.0707 0.0862 0.1019
-0.246 - 0.424 -0.094 -0.665 -0.909 -0.556 -0.620 -0.826 -0.606 -0.030 -0.805 -0.381
(2.73) (3.67) (1.57) (2.76) (2.19) (3.96) (9.15) (3.37) (3.76j (3.47) (4.94) (4.02)
~
(2.73) (3.42) (0.56) (3.06) (6.41) (4.84) (6.16) (4.76) (4.73) (0.26) (5.93) (3.38)
0.205 0.522 0.089 0.450 0.576 0.425 0.530 0.570 0.402 0.251 0.626 0.477
*The t-statistics are in parentheses.
Intercept
A
B C D E F G H I J K L A
B C D E F G H I J K L
0.476 -0.262 0.927 0.741 0.380 0.550 0.538 0.189 0.280 0.244 0.697 0.293 0.203 0.527 0.543 0.324 0.094 0.400 0.392 0.792 0.316 0.760 0.777 1.116
lnMTT
(2.00)* (0.85) (2.95) (2.17) (1.27) (2.23) (2.30) (0.61) (1.37) (0.85) (2.38) (0.78)
-0.0039 0.0515 -0.0269 -0.0253 0.0006
(1.32) (2.60) (2.39) (0.98) (0.60) (2.23) (3.91) (2.64) (2.10) (3.43) (3.50) (3.68)
-0.0105 -0.0393 -0.0305 -0.0287 -0.0060 -0.0273 -0.0291 -0.0683 -0.0233 -0.0406 -0.0686 -0.0755
*The t-statistics are in parentheses.
0.0006
-0.0039 0.0120 0.0079 O.oo00 -0.0281 0.0089
I
WdPd
Residential Sector (0.24) 0.292 (2.51) 0.308 (1.35) 0.196 (1.11) 0.414 (0.03) 0.278 (0.03) 0.088 (0.25) 0.211 (0.56) 0.446 (0.55) 0.328 (0.00) 0.531 (1.37) 0.345 (0.34) 0.368 Business Sector (0.92) 0.267 (2.74) 0.413 (2.13) 0.070 (1.33) 0.505 (0.53) 0.417 (2.10) 0.302 (3.85) 0.308 (3.03) 0.736 0.446 (2.17) (2.35) 0.119 (3.61) 0.596 0.365 (3.46)
I
WdPd
I
R2
(2.89) (2.83) (1.67) (4.33) (3.77) (i.14j (3.21) (4.03) (3.43) (6.31) (3.02) (2.91)
-0.570 -0.740 -0.554 -0.723 -0.319 -0.406 -0.505 -0.808 -0.579 -0.656 -0.382 -0.796
(5.33) (5.86) (5.55) (5.10) (3.46) (6.02j (4.39) (7.18) (5.41) (7.55) (3.70) (6.25)
0.224 0.337 0,340 0.316 0.208 0.294 0,154 0.426 0.223 0.428 0.175 0.393
(3.20) (4.43) (0.64) (2.27) (5.48) (3.18) (5.33) (4.54) (4.80) (1.24) (4.03) (3.76)
-0.307 -0.440 -0.104 -0.505 -0.492 -0.312 -0.247 -0.752 -0.530 -0.285 -0.414 -0.437
(3.48) (5.36) (1.68) (2.86) (6.45) (3.96) (5.00) (4.37) (5.61) (3.19) (4.50) (3.52)
0.180 0.632 0.181 0.326 0.627 0.288 0.278 0.534 0.398 0.254 0.520 0.481
Jean-Michel Guldmann
/
135
were initially considered, but turned out to be insignificant, and were dropped. The results are as follows: Residential Sector
SH,
=
0.3286 (4.82)
+ 0.01521nMTT - 0.43381n(P1/P3)+ 0.36251n(P2/P3) (3.29)
(18.85)
(14.58)
R2 SH2
=
0.3875 (4.95)
=
0.264
(17)
+ 0.00141nMTT + 0.30391n(P1/P3)- 0.54391n(P2/P3). (0.27)
(11.50)
(19.05)
R2
=
0.255
(18)
Business Sector SH1 = -0.0379 (0.53)
+ 0.07291nMTT (13.79)
-
0.40821n(P1/P3)+0.28111n(P2/P3). (11.30) (8.48) R2
S H , = 0.4523 - 0.03051nMTT (8.70) (7.97)
+ 0.30441n(P1/P3)
-
(11.63)
=
0.351
(49)
0.31541n(P2/P3). (13.13) R2 = 0.293
(20)
The share equations for the nightlweekend period are then Residential SH,
=
0.2839 - 0.01661nMTT
+ o.12991n(P1/P3)+ 0.18141n(P2/P3)
(21)
=
0.5856 - 0.04241nMTT
+ 0.10381n(Pl/P3) + 0.03431n(P2/P3)
(22)
Business
SH3
The coefficients of the price ratios are correct in all cases, and highly significant. Also, the coefficients of lnMTT are very significant for the business sector, as well as for the daytime residential share equation. However, this variable has clearly no effect on the evening residential share. The share models can be used to estimate/forecast minutes of telephone traffic by rate period, once an aggregate estimate/forecast has been obtained with the aggregate model discussed in the previous section. In addition, these models can be used to estimate own- and cross-price elasticities over the three periods, as discussed in detail in section 5. Finally, it should be noted that similar sharing models were considered for the numbers of messages. However, the results were considerably less satisfactory, both in terms of explanatory power (R'), wrong signs, and significance, and are not reported here. However, this is an area where further research would be desirable.
136 I
Geographical Analysis
5. TELECOMMUNICATION DEMAND ELASTICITY ANALYSIS
The models developed in section 4 can be used to analyze the sensitivity of telephone demand to variations in its determinants. In the following, we assess the impacts of destination size, distance, and prices on the demands for messages and conversation minutes, through an analysis of the corresponding elasticities. 5.1 Destination Size The aggregate message and minutes demand elasticities with respect to destination sizes are defined as =
dlnNV/dlnNVT;
(23)
EMTT =
dlnMTldlnMTT.
(24)
ENVT
They measure the percentage change in demand resulting from a 1 percent increase in the size variables. The effect is elastic if I E I > 1. These elasticities are simply the coefficients of lnNVT and hMTT in models 1 and 2, as reported in Tables 5 and 6. Their values are slightly below 1 for the message models, and slightly above 1for the minutes models. They can be viewed as average elasticities across all sample values of lnNVT and InMTT. However, models 3 and 4 clearly show that a second-order approximation is justified, and that in fact these elasticities always increase with destination size. As an illustration, consider model 3. The elasticities are then expressed as Messages
= -0.469
+ 0.1261nNVT : residential. + 0.1461nNVT : business.
eMm = -0.390
+ 0.104lnMTT : residential.
(27)
+ 0.120lnMTT : business.
(28)
cNVT= -0.298 ENVT
(25) (26)
Minutes
EMTT =
-0.533
The unit-elasticity values of NVT and MTT can be obtained by solving the equations E N ~ T= 1and cMm = 1, with -29,780 and 23,427 calls for the residential and business sectors, respectively; -637,548 and 353,274 minutes for the residential and business sectors, respectively. The above values are close to the mean sample values of NVT, but significantly below in the case of MTT, suggesting that an increasing destination size has a particularly strong “accelerating” effect on conversation minutes. In the case of the share models [equations (17)-(22)] rewritten in simplified form as SH,
= a,
+ PJnMTT + ytllnP, + ytzlnP, + y&P,
,
(29)
Jean-Michel Guldmann
Period 1
Sector I
Residential Business
Period 3
Period 2
Share
Total
0.054 0.097
1.162 1.169
II
I 137
Share
Total
0.003 -0.214
1.111 0.858
II
Share
Total
- 0.069
1.039 1.474
0.402
we see that the share elasticity can be formulated as
c&
= (dSHt/dMTT)/(SHt/MTT)= PJSH,
.
(30)
SHt
The estimates of eMTTat the sample mean values of SH, have been computed for both sectors and for the three periods, and are presented in Table 9. To compute the elasticity of the telephone flow (in minutes) MT, during period t, we must combine the effect of destination size MTT on traf€ic share with its effect on the total tr&c MT. As MT,
=
SH,. MT
(31)
it follows that E::!
=
(dMT,/dMTT)/(MTJMTT) = (aSHJdMTT) * (MTTIMTJ * MT SH, * (aMT1dMTT) . (MTTIMT,)
+
(32)
or MT, SHt EMTT = EMTT
+
EMTT
(33)
The values of EMTT were estimated at the sample mean, using equations (27) and (28), with 1.108 for the residential sector, and 1.072 for the business one. The MTt resulting values for the elasticities EMTT are also reported in Table 9 under the “total” heading. The destination size variable has clearly increasing returns to scale effects in all cases (E > 1)but for the business sector in the evening (0.858) as a result of the negative coefficient of lnMTT in equation (20). 5.2 Distance The results for model 1in Tables 5 and 6 indicate that, on average, the demands for messages and minutes decrease with distance in slightly elastic and inelastic fashions, respectively. However, the very high precision of the estimates of (1nD) and (1nD)’ obtained with models 2c4 clearly shows that these elasticities vary with distance. In the case of model 3, they are expressed as Messages =
-8.660
=
-7.262
+ 2.0381nD : residential. + 1.6421nD : business.
(34) (35)
138 I
Geographical Analysis
Minutes eD = -7.418
eD = -5.633
+ 1.8321nD : residential. + 1.3181nD : business.
(36) (37)
Starting with strongly negative values for small distances, the elasticities eD increase with distance. The effect becomes inelastic when eD = -1, and both messages and minutes start increasing with distance when eD = 0. Using equations (34)-(37), we have computed the unit-elasticity (eD = - l)and zero-elasticity (eD = 0) distances. They are reported in Table 10. Very few calls take place at distances beyond the zero-elasticity values. The demand for messages is mostly elastic (eD< - I), but around 30 percent of the demand for conversation minutes falls within the inelastic range.
5.3 Prices Price elasticities must be analyzed both at the aggregate level and for each of the three time periods. Considering first the aggregate level, we neglect the case of model 1 because it is most likely that the coefficient of lnPA reflects in part distance effects. Models 2 and 3 provide overall very similar results: inelastic demand for messages, elastic demand for minutes. In addition, in each case business demand is more elastic than residential demand. The demand for residential messages is very inelastic, and it is impossible to reject the null hypothesis of zero elasticity at the 5 percent level of significance. The elasticity of business messages is around 0.25, but the estimates are significant. The demand for residential minutes is close to unit-elastic [1.18-1.21], and that for business minutes is clearly elastic, around 1.55. These results are not inconsistent with the actual experience of the company. Indeed, recent decreases in toll rates did not lead to an increase in revenues, a clear sign that demand is inelastic. As all MTS calls are priced with a fixed charge for the first minute, and another, lower charge for each additional minute, it is clear that the overall effect on revenues of a change in the toll rate level will depend upon the share of oneminute calls. As extreme cases, consider the residential sector, and assume (a) that all calls last up to a minute, and (b) that all calls are longer than a minute. Also, assume that the demand for calls is zero-elastic, and thus that the number of calls does not change with a decrease in rate. In case (a), the consequence will obviously be a decline in revenues, and in case (b) a very slight increase in revenues at the most. In the sample, the number of one-minute (as billed) calls is close to 40 percent of all calls, which appears consistent with an overall inelastic revenue effect.
TABLE 10 Messages
Minutes
Jean-Michel Guldmann I 139 The results with model 4 in Tables 5 and 6 point to an elasticity that increases with price, with the coefficients of (1nPA)' always very significant. We obtain the following price elasticity functions: Messages epA = 0.942 - 1.0661nPA : residential.
(38)
epA = 1.378 - 1.5481nPA : business.
(39)
Minutes
epA = 0.048 - 1.3401nPA : residential.
(40)
epA = 0.428 - 1.8841nPA : business.
(41)
Using equations (38)-(41), we have computed the values of the price PA corresponding to zero-elasticity (epA = 0) and unit-elasticity (epA= - I), as reported in Table 11. Referring to the sample price statistics in Table 2, we see that the price elasticity function for minutes demand is well behaved over most of the sample (that is, epA< O), and that this demand is mostly in the elastic range. However, in the case of message demand the threshold values for epA= 0 are close to the mean prices, pointing to a large number of cases with positive elasticities. For prices above these threshold values, the demand for messages is mostly inelastic, as was the case for models 2 and 3. Because of this result, models 2 and 3 are clearly preferable over model 4 in the case of message demand. In order to estimate time-of-day (TOD) demand elasticities, we must combine share price elasticities and aggregate demand elasticities, in a way similar to the procedure used for the elasticity of destination size by time of day (section 5.1). Using equation (29), we obtain the elasticity of the share SH, in period t with respect to price Pi as
If epAis the aggregate demand elasticity, it can be shown that the elasticity ey for minutes demand in period t with respect to price Pj is Etj
= eti SHt
+ epA- (Pj
*
SHj)/PA.
(43)
TABLE 11 M.%ages
Minutes
140 I Geographical Analysis TABLE 12
Day Evening Night
Evening
Day
Period
- 1.46 0.67 0.49
- 1.92 0.21 0.03
1.22 - 1.21
0.69
Night
0.68 - 1.75 0.15
0.24 0.54 - 1.18
0.03 0.33 - 1.39
The quantity (P.* SHj)lPA simply represents period j share of the total charge. Using the coedcient estimates of model 3 and the sample mean values of the three periods’ prices and other relevant variables (for example, MTT), we have computed the TOD share and quantity elasticities for the residential sector, as reported in Table 12. The results show that the TOD demands for minutes are elastic with respect to their own-prices, but inelastic with respect to cross-prices. The own-price elasticities decline from the day to the night periods. The strongest (though inelastic) cross-effects are related to the impact of the evening price on the day demand, of the day price on the evening demand, and of the night price on the evening demand. Overall, there is little substitution between the day and night demands. 6. CONCLUSIONS AND AREAS FOR FURTHER RESEARCH
We have reported the results of an empirical analysis of point-to-point IntraLATA MTS telephone flows for both the residential and business sectors. The major results are that (1)the demand for calls is price inelastic, but the demand for conversation minutes is slightly elastic, (2) business demand is relatively more price elastic than residential demand, (3)distance is an important determinant of telephone flows, but its effect decreases with distance, and (4) most time-of-day substitutions take place between the day and evening rate periods. Several extensions of this research are desirable. First, disaggregating the business sector into subsectors (for example, manufacturing, trade, services, etc.) might provide a much better understanding of the telecommunication demands of the business sector, and point to differential elasticities. Second, following Larson et al. (1990), it might be useful to test the relevance of the reverse tr&c as an explanatory variable. From a data viewpoint, this would require the SIC identification of the callees, which was not possible within the framework of this study. Third, the spatial interaction modeling literature suggests that improved models might be obtained by accounting for the effects of spatial structure on spatial flow behavior. Promising variations of the traditional approach, such as the competing destinations model developed by Fotheringham (Fotheringham and O’Kelly, 1989, chapter 4), and the competing central places and intervening models developed by Fik and Mulligan (1990), should be considered in future research.
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