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Intrastate interLATA telecommunications demand modeling.

Intrastate InterLATA Telecommunications Demand Modeling

Introduction

In recent years, there has been considerable interest in econometric models specified in a panel data context. That is, models which use time series data collected over cross-sections such as individuals, firms, industries, or states. These panel data models, whether specified in a fixed coefficient or random coefficient framework, contain theoretical, empirical, and practical advantages over similar models specified using single-equation approaches. In fact, at AT&T, demand analysts have often found panel data models useful for solving the analytical needs of their business.

AT&T has developed a panel data model of interstate switched access demand, which has been used to support AT&T intervention filings with the FCC. Using this model, AT&T contested the accuracy of the demand forecasts, and hence the reasonableness of the switched access rates filed by the National Exchange Carrier Association (NECA) and the Local Exchange Carriers (LECs). The model uses a fixed coefficient cross-sectional time-series pooling approach in a dynamic demand framework. The monthly access minutes of use data for each of the 94 Tier 1 LECs are summed to the level of the 48 contiguous states and Washington, D.C., which are used as cross-sections. The dynamics are estimated using polynomial distributed lags (PDL).

As a result of the divestiture of the Bell System on January 1, 1984, AT&T has been in the business of providing MTS service within a state between areas known as Local Access Transport Areas or LATAs. This service has been termed I/I MTS. To suit its business needs, AT&T has developed and estimated MTS demand models for each of the states in which it has I/I certification. These I/I MTS demand models have been used to forecast for financial and network planning, to support tariff filings with state Public Utility Commissions (PUCs), and to evaluate alternative pricing strategies. Mainly because of their role in regulatory jurisdictions, most of the state-level models have utilized single-equation Generalized Least Squares (GLS) techniques. Some of the models have been segmented along call characteristics, such as customer class or type of call. These models have served AT&T's business needs well and will continue to do so in the future.

Due to the proprietary nature to AT&T of the release of up-to-date demand elasticity data and model results, all of the available I/I MTS demand data have not been used. However, to keep in line with scholarly disclosure, we will provide the results of our study using only data prior to 1983. The limitation on the amount of data utilized also serves other purposes. By using only 15 quarterly demand observations, we are better able to assess the relative efficiency of the RCR method compared to a single-equation fixed coefficient GLS approach in the face of a short estimation interval and correspondingly greater multicollinearity problems. Further, limiting the estimation interval to the period prior to 1983 allows us to abstract from the complexities introduced by the advent of competition from Other Common Carriers (OCC), such as MCI and U.S. Sprint, and the marketing of new I/I telecommunications services by AT&T which are highly cross-elastic with I/I MTS. The preliminary results presented indicate that the RCR panel data methodology may provide a better framework than comparable single-equation approaches for the estimation of disaggregate demand models, especially in situations where the informational requirements of the models are outweighed by the lack of sufficient time series data or hampered by the presence of multicollinearity among price and income series.

I/I MTS Disaggregate Demand Modeling

The objective of the study is to assess the feasibility of developing models, which can quantify the changes in the demand for I/I MTS messages that result from changes in the prices of those messages or the prices of related goods at a highly disaggregated level. The goal of our model is to estimate own and cross-price elasticities of demand for various I/I MTS market segments at the aggregate or national level, as well as for the individual state jurisdictions. This information is necessary for tariff filings with state Public Utility Commissions (PUCs), financial and network planning and evaluation of alternative pricing strategies.

However, there are data, resource, and methodological issues which present potentially significant barriers to the success of such a disaggregate modeling effort. It is often the case that state-specific equations, estimated with a time series of only 15 quarterly demand observations, suffer from high degrees of multicollinearity among the explanatory variables. As a consequence, the estimated price elasticities of demand based on single-equation fixed coefficient methods, such as GLS or SUR, are not reliable, i.e., the variances of the estimated coefficients are very large.

These methodological concerns suggest that the pooling of the time series demand data for all of the states in a panel data framework may be appropriate, especially if the level of disaggregation desired for the I/I MTS marketplace is to be maintained. Theoretical and empirical studies have shown that the panel data approach can lead to substantial gains in estimation efficiency relative to single-equation analysis of the time-series of individual cross-sections. However, the standard fixed coefficient panel data pooling methodology places undue restrictions on the coefficients by taking them to be exactly the same for each cross-section. Although the fixed coefficient panel data model yields reasonably precise estimates of the average or national relationships among variables, it does not enable the estimation of the micro-parameters for each of the component cross-sections. In light of the emphasis on the estimation of individual state-specific I/I MTS elasticities of demand at a disaggregate level, the fixed coefficient pooling procedure does not seem appropriate for the estimation of our model.

Previous results suggest that the random coefficient regression approach is a more efficient procedure for the pooling of time series and cross-sectional data. The RCR panel data framework allows for parameter heterogeneity across the states, while also taking advantage of the similarity of the coefficients and the efficiency gains of pooling. Therefore, the RCR pooling methodology appears to be a viable alternative for disaggregate modeling, given the informational requirements and methodological issues.

Essentially, our RCR panel data demand model hypothesizes that for any I/I MTS market segment the demand elasticities for each state are similar in that they are drawn from the same distribution and share a common mean and variance, i.e., the expected values of the demand elasticities are the same. In addition, the model also postulates that the coefficients for each state are different, and vary about the mean by a random component that may be different for each state. Thus, the RCR demand model under study can be seen as a compromise between demand models based on applying single-equation estimation techniques for each state in which the elasticities are treated as fixed, but vary across the states, and those utilizing the fixed coefficient panel data methodology in which they are treated as fixed and exactly the same over the states. Given the objectives of our I/I MTS disaggregate demand modeling study, this compromise seems warranted. Given the assumptions of the model, theoretical and empirical studies have shown that RCR estimators and predictors are efficient relative to corresponding fixed coefficient panel data or single time-series methods. Owing to its intuitive appeal, applicability in the I/I MTS market place for disaggregate modeling and forecasting, efficient estimation and prediction properties, as well as relative ease of implementation, the RCR panel data pooling approach was selected as the basis for the development of the econometric models of I/I MTS demand under study.

Model Specification and Methodology

Assuming a utility maximization framework and a budget restriction, the demand by a consumer can be expressed in terms of the prices of the available goods, and the consumer's income. It can also be shown that this demand is homogeneous of degree zero in prices and income. This means that if all prices and income change by the same percentage, holding all else constant, the quantity demanded by the consumer will remain unchanged. The implication of the homogeneity of degree zero restriction is that consumers will only alter their demand quantities if real, not nominal, prices or income change. Further, if the good is a non-Giffen good, the sign of the elasticity of demand with respect to the own-price is negative.

Consistent with this standard microeconomic theory of the consumer, we specify the following system of telecommunications demand functions for residential consumers of those services:

(1) [Q.sub.ik] = F([P.sub.i]/P, [P.sub.j]/P, [Y.sub.k]/P)

where [Q.sub.ik] is the demand for telecommunications service i by the kth cross-sectional unit; [P.sub.i] is the price of that service; [P.sub.j] is a price vector of other "closely related" services; P is a price index that represents all goods that are not accounted for by [P.sub.i] and [P.sub.j]; and [Y.sub.k] is an income measure corresponding to the kth cross-sections. There are i, j = 1, 2, ..., N services and k = 1, 2, ..., K cross-sections.

Telecommunications services are not only demanded by consumers, but also by firms. In a cost minimization framework subject to an output restriction, the demand for goods and services by a firm is a derived demand. Assuming such a framework, and that MTS services are used by firms as factors of production, it is not difficult to show that the derived demand for an MTS service is a function of its price, other factor prices, and a given output level. Again, it can be shown that such a derived demand function is homogeneous of degree zero in factor prices.

Consistent with the derived demand framework, we assume the following system of telecommunications demand functions for MTS services used by business customers:

(2) [M.sub.ik] = G([R.sub.i]/R, [R.sub.j]/R, [E.sub.k])

where [M.sub.ik] is the demand for MTS service i by the kth firm; [R.sub.i] is the cost of that service; [R.sub.j] is a price vector corresponding to "closely related" factors; R is a general price index of all goods and services not accounted for by i and j; and [E.sub.k] is a measure of output corresponding to the kth cross-section.

Now that the analytical framework of our model has been specified, we will describe the I/I MTS market segmentation used in the study. The market disaggregations are based on the structure of the AT&T I/I MTS tariff schedules, which vary by state. Within the rate structures, the relevant breakdowns are for type of call (way of placing call), rate period (time of day), and length of haul (mileage band). Additionally, although rates do not vary by customer class, the theoretical considerations described above suggest that business and residential customers may behave differently.

One potential market segmentation for the I/I MTS marketplace which accounts for the issues described above is:

* Customer class (3): business, residence, coin

* Type of call (4): direct-dial, calling card, operator-assisted, person-to-person

* Rate period (3): day, evening, night and weekend

* Length of haul (3): 0-30 miles, 31-124 miles, greater than 125 miles. (1)

However, to disaggregate to this level for each state-specific I/I MTS tariff would yield many market segments.

In addition, a problem of feasibility would arise because the message data available are derived from a 0.1 percent sample of the universe of all I/I MTS messages, and some of the theoretically defined sub-markets would contain few, if any, demand observations. This would make precise estimation of a demand model for many of the markets virtually impossible. Therefore, as a compromise between the large sampling variability inherent in the I/I MTS message data for many of the market segments and the desirability to preserve some level of disaggregation implicit in the tariff structures, we have chosen to disaggregate the I/I MTS marketplace, for each state, as follows:

* Business direct-dial (6): 2 rate periods, 3 mileage bands

* Business operator/calling card (3): 3 mileage bands

* Business person-to-person (3): 3 mileage bands

* Residence direct-dial (9): 3 rate periods, 3 mileage bands

* Residence operator/calling card (3): 3 mileage bands

* Residence person-to person (3): mileage bands

* Coin (all types and rates) (3): 3 mileage bands. (2)

This disaggregation yields 30 I/I MTS sub-markets for each of the 48 contiguous states, and hence 1,440 distinct I/I MTS demand equations to be estimated in our study.

The I/I MTS message demand relationships are specified using a log-linear functional form for each of the market segments. This form was chosen for several reasons. First, our basic interest is in estimating disaggregate price elasticities of demand, which are unit-independent parameters that indicate the responsiveness of demand to changes in relevant prices. The coefficients of a log-linear demand equation are elasticities, and so their estimates have direct interpretation as such. Second, our RCR panel data approach assumes that the regression coefficients for each state have the same expected value. This may be a plausible assumption concerning the state elasticities, but it would be unlikely for the individual regression coefficients (partial derivatives) in a linear model, since they are scale dependent. (3)

The I/I MTS message equations are specified in a dynamic framework, reflecting the notion that changes in message demand caused by changes in prices and income do not occur instantaneously, but over time, as consumers and firms gradually adjust consumption patterns. For each of the demand equations, a polynomial distributed lag (PDL) model is specified, with a second degree polynominal fit over three lagged quarters and the contemporaneous quarter. This specification is suggested by theory, convention, and the results of numerous statistical studies. We have attempted to be parsimonious in imposing restrictions on the lag structures for each market. However, in cases where the estimated lag distribution does not fit a priori expectations or relevant statistical criteria, end-point restrictions have been imposed. (4)

Implicitly, we consider the demand for I/I messages for each state and market segment to be an aggregation over the individual units (consumers or firms), which constitute that demand. Consistent with this, we specify the demand for I/I MTS messages in each state for each of the 15 residential market segments of our model to be a function of the own-price of the message in the state, a cross-price index reflecting changes in the prices of alternative ways to place the call in the state, and the level of disposable per capita income in the state. The cross-price indices reflect changes in the tariff schedules for other types of call and/or different rate periods. Both the own-price and cross-price indices for each market segment and state have been adjusted to reflect the Federal Excise Tax levied on interLATA calls. Further, the nominal price and income variables are deflated by a state-specific Consumer Price Index (CPI) to be consistent with the homogeneity restriction of demand theory. Additionally, the dependent variable is formed as the ratio of messages to the number of residential telephones in the state. In this case, the telephone series serves as a proxy for market size and also accounts for the access/usage conditional nature of I/I MTS demand, which involves the necessity of having access to a telephone in order to purchase a message.

Further, the three coin equations are specified in an analogous manner, except that the cross-price terms are omitted since we have aggregated over the type of call and rate period alternatives. Similarly, we deflate total coin messages for each length of haul by the number of coin telephones in each state.

For the 12 I/I MTS business market segments, we specify the demand for I/I MTS business messages in each state to be a function of the own-price of the call in the state, a cross-price index reflecting changes in the prices of messages for other types of call and/or rate periods in the state, and the level of employment per business telephone in the state. The state specific employment per business telephone variable serves as a proxy for the amount of labor input demanded and hence the level of output of firms within the state. This variable also helps to capture the complementarities between factors of production, such as MTS goods and labor services in the production process. Analogous to the residence and coin equations, the state-level business message series have been deflated by the number of business telephones in the state. All nominal price variables in the business equations are deflated by the implicit GNP price deflator, which is an overall measure of the price of all goods and services in the nation.

For each of the I/I MTS sub-markets, we specify the following state equations:

(3) log ([MSG.sub.jit]/[TEL.sub.it])= [BO.sub.ji] + [[Sigma].sub.q] [Bl.sub.q,ji]* log([OP.sub.ji,t-q]/[POTH.sub.i,t-q]) [[Sigma].sub.q] [B2.sub.q,ji]* log([CP.sub.ji,t-q]/[POTH.sub.i,t-q]) + [[Sigma].sub.q] [B3.sub.q,ji]* log([ECO.sub.i,t-q]) + [W.sub.jit]

where j = 1, 2, ..., 30 submarkets; i = 1, 2, ..., 48 state indicators; t = 1, 2, ..., 15 quarters; and q = 0, 1, 2, 3 lag indicators. The table on page 27 provides a description of the variables and their sources. The model errors (W) for each segment are assumed to be first-order autocorrelated with a state and heteroschedastic across the states. We do not assume contemporaneous correlation across the states.

The equations for each of the 48 contiguous states corresponding to each of the 30 I/I MTS market segments (a total of 1,440) are estimated using the random coefficient regression panel data methodology. As discussed above the estimation interval has been shortened to include only the I/I MTS message data for the 15 quarters starting with the second quarter of 1979 and ending with the fourth quarter of 1982. The source of the quarterly message demand quantities is a 0.1 percent sub-sample derived from the Centralized Message Data System (CMDS). (5)

The RCR panel data methodology utilized in this study assumes that for each state, the demand elasticities in each market segment possess the following properties:

(4) [D.sub.i]= D + [U.sub.i] where E [[U.Sub.i]] = 0 (5) E[[U.sub.i] [U.sub.i]'] = V; E[[U.sub.i][U.sub.j]'] = 0 for i not equal to j

where [D.sub.i] is the zxl vector of demand elasticities for state i; D is the corresponding zxl mean vector; and [U.sub.i] is the zxl vector of random components specific to state i. These assumptions imply E([D.sub.i]) = D for all i, i.e., the expected value of the vector of demand elasticities for each state is equal to the mean vector of elasticities. Also, since the random components, [U.sub.i], corresponding to each state have zero mean and are uncorrelated across the states, D can be interpreted as a vector of national averages of state elasticities. The reason for this is that the elements of [([D.sub.i] + ... + [D.sub.n])/N - D] converage in probability to zero as N approaches infinity.

Our specifications in (4) imply that some state elasticities will be above, and some below, the corresponding mean elasticity values. Our assumption in (5) that the variance-covariance matrix of [U.sub.i] is homoschedastic implies that the discrepancy between the state elasticities and their corresponding mean values are not expected a priori to be either large or small for certain states. In a sense, these assumptions allow for both a homogeneous and a heterogeneous nature of individual state elasticities. In contrast, in a fixed coefficient panel data pooling approach, one would necessarily assume that [D.sub.i] D for all i. Clearly, the RCR panel data specification is less restrictive.

The formulas for the best linear unbiased estimators (BLUE) of the mean coefficients, D, and the best linear unbiased predictors (BLUP) of the individual cross-sectional coefficient, [D.sub.i], of an RCR panel data model with a single random component are generally known but since some readers may not be familiar with such estimators and predictors, we outline some of their essential properties.

Since the RCR panel data model is a pooling model, the estimator for the mean vector of elasticities is comparable to the standard fixed coefficient pooling estimator, except that the variance-covariance matrix involved is more complicated, as it involves not only the model errors (W) but also the random components (U) and the independent variable data. However, the mean coefficients can also be estimated without ever having to form the "pooled" problem, i.e., without having to stack the data from each of the states together in a single matrix. It can be shown that the BLUE of the mean coefficient vector in a RCR panel data model is a weighted average of the single-equation GLS estimates of the cross-sections, with the weights involving the variance-covariance of the random components (V). Intuitively, more weight is given to estimates of state elasticities which have greater precision (lower variance); therefore, the mean coefficients are estimated using the most reliable sample information. This is one reason these estimators are efficient.

The BLUPs of the individual state coefficients in our single component RCR panel data model can also be expressed as a weighted average. They are a weighted average of the single-equation GLS estimates of the cross-sectional parameters, [D.sub.i], and the BLUE of the mean coefficient vector, D. Hence, the predictor for each cross-sectional coefficient uses the information, not only for that cross-section but also for other cross-sections. This additional information is particularly useful in empirical applications where significant multicollinearity between explanatory variables exists or there are few degrees of freedom available to estimate the state coefficients individually. The weight matrix is such that the predictors for any cross-section will be weighted more toward the mean coefficients the larger variances of the estimates of the cross-sectional coefficient or the smaller the variances of the individual coefficients, [D.sub.i], around the mean vector, D.

This is a remarkable degree of simplification in terms of strategies for estimating the mean and the individual state coefficients, and helps to reduce the computer resource requirements of estimating RCR panel data models. These results suggest an iterative estimation process. A major issue involves the appropriate feasible estimator to be used to estimate V, the variance-covariance matrix of the random components. For the results presented here, a linearized maximum likelihood estimator has been utilized.

Model Results

Considering the vast number of estimated elasticities at the disaggregate equation level (there are 18,720), we will provide only the long-run mean own-price, cross-price and economic variable elasticities for each of the 30 I/O MTS market segments. In addition, we will only show details for the long-run "net-price" and economic variable elasticities for each of the 48 states aggregated over the 30 markets. The long-run demand elasticities are the sum of the short-run or marginal demand coefficients, and reflect the effect on demand once all intermediate adjustments have been made. "Net-price" elasticities are the sum of the own-price and cross-price estimates and measure the impact on demand of a uniform change in all I/I MTS rates, i.e., all prices are adjusted by the same percentage. (6) In order to protect the proprietary nature to AT&T of the disaggregate demand elasticity information, we will not delineate the market segments or states, but only enumerate them in random order.

In addition to the estimation and prediction of the national and state demand elasticities using the RCR methodology, the individual state elasticities for each of the 30 market segments have been estimated by applying a standard single-equation GLS technique. By way of an overall summary, we provide a comparison of the net-price and economic variable elasticities estimated by both of these approaches at the aggregate state level, i.e., aggregating the results across all 30 market segments for each state.

Despite the use of only 15 quarterly demand observations for I/I MTS messages, the RCA panel data methodology provides estimates of the 87 long-run mean demand elasticities, which are generally statistically significant and consistent with the theoretical expectations. For 23 of the 30 I/I MTS market segments, the net-price elasticity is negative, as expected. The seven segments in which a positive net-price elasticity was estimated each represent less than one percent of the total I/I MTS marketplace, so precise estimation in those segments is hampered by the statistical sampling used to derive the message data. Also, the estimated net-price elasticities in 23 of the 30 segments are statistically significant at the five percent level, with only two of those being positive. The estimated economic variable elasticities are positive in 28 of the 30 market segments, with the two estimated negative economic elasticities being statistically insignificant. Furthermore, 23 of the 30 own-price elasticities are of the anticipated (negative) sign. Finally 60 percent of the estimated cross-price elasticitives are positive indicating some degree of substitutability among I/I MTS services.

A comparison can be made of results based on RCA panel data and single-equation fixed coefficient GLS techniques. The results relate to the aggregate long-run net-price and economic variable demand elasticities for each of the 48 states under study. The aggregate state elasticities are derived by taking a weighted average of the estimated state-specific demand elasticities for each of the 30 I/I MTS markets, with the weights being the state message proportions for each of the 30 markets. The two methodologies provide similar estimates of the national I/I MTS price and economic demand elasticities. However, there are significant differences in the estimated results at the state level.

The 47 state-specific aggregate I/I MTS price elasticities of demand predicted by the RCR panel data methodology all possess the anticipated (negative) sign and are all in the inelastic range. (7) They range in value from -0.159 to -0.949. In contrast, the state aggregate price elasticities based on the single-equation GLS technique are much more widely dispersed. In fact, 11 of these 47 estimated price elasticities are positive. Further, nine of the 36 state price elasticities which are negative are in the elastic region of the demand curve. The values range from 3.442 to -4.505. With respect to the state aggregate I/I MTS economic variable elasticities, 43 of the 47 predicted by the RCA panel data approach are of the anticipated (positive) sign, while only 33 of the 47 estimated by the single-equation GLS procedure are positive. Similar to the price elasticity results, the state aggregate economic elasticities predicted by the RCA panel data method are much more homogeneous. They range in value from -0.033 to 1.714, while those estimated with the single-equation technique range from -8.827 to 13.235.

In summary, it should be clear that the single-equation fixed coefficient GLS methodology provides a markedly wider dispersion of the individual state-specific I/I MTS demand elasticities. It also yields estimates that are more often counter to theoretical expectations. The results are even more dramatic for the individual state-level elasticities at the 30 market segment level of detail. From a statistical point of view, the empirical distribution of the single-equation estimates based on the fixed coefficient model is due much more to the sample variances of the individual estimates than the actual heterogeneity of the true elasticities. This would lead us to expect that the relatively homogeneous predictions of the RCR panel data approach are more indicative of the actual dispersion of the true state-level I/I MTS demand elasticities.

It may also be of interest to note that both approaches imply very similar long-run I/I MTS price and economic variable demand elasticities. The aggregate mean estimates from the RCR panel data framework are -0.431 and 0.523 for price and income, respectively, while those estimated via the single-equation GLS methodology are -0.491 and 0.592. These price elasticity estimates indicate that the overall I/I MTS marketplace is inelastic with respect to changes in price, at least over the interval in which they were estimated. This result is consistent with other empirical studies as well as other internal AT&T models. As a final note, it appears that the I/I MTS marketplace is somewhat more inelastic than the interstate MTS market.

Future Research

The preliminary results for the I/I MTS marketplace presented in this pilot study, as well as those based on applying the RCR panel data methodology over the entire available historical interval, are quite promising. Compared to standard single-equation fixed coefficient OLS or GLS approaches, the results would indicate that there are potentially significant gains in estimation efficiency when RCR panel data models are utilized to estimate disaggregate demand systems.

In its current form, our model of I/I MTS demand does not explicitly account for the Slutsky symmetry condition of demand theory. Generalizing the model in this direction should be of interest. In a similar vein, one suspects that telecommunications goods, such as I/I MTS, are weakly separable from other goods in the economy. If so, a development of the model assuming weak separability should also be of interest. Also, our model of I/I MTS does not account for the possible cross-elastic effects than AT&T Wide Area Telecommunications Service (WATS) demand or Other Common Carrier (OCC) demand may have on AT&T I/I MTS demand. Extending the model to estimate these cross-price elasticities is also important.

Further, another direction for future research concerns the specifications of the RCR panel data approach itself. In our model, only one stochastic or random component was specified, that relating to the individual cross-sectional units. Clearly, the possibility that demand elasticities have additional random components that relate to other call characteristics should be considered, i.e., mileage band or customer class, Therefore, perhaps a multiple component RCR panel data model should be considered. In addition, once two or more stochastic components are specified, the possibility for interactions of those components should also be considered.

Footnotes

1. The three length of haul breakdowns represent a workable compromise among individual state tariff schedules, which characterize geographically distinct entities. They are also directly analogous to mileage breakpoints which have proven to be practicable for modeling interstate MTS toll demand.

2. For the business direct-dial sub-markets, there is an aggregation over the evening and nigh and weekend rate periods. This market segmentation is again based on interstate MTS toll demand modeling experience.

3. Elasticities are chosen as the relevant parameters because they readily accommodate the statistical design, while lending themselves to economic interpretation. For instance, strategic economic information is obtained by observing the absolute value of the own-price elasticity of demand. If its absolute value is greater (less) than 1.0 then demand is elastic (inelastic) and, since demand curves are downward sloping, revenues in a market segment can be increased (decreased) by lowering price.

4. With respect to the end-point restrictions imposed, the relevant criterion include, but are not limited to, correct signs on all the marginal elasticities and a unimodal shape implied by the specified lag distribution.

5. Some of the states have zero observations in some of the 30 defined sub-markets. For example, the state of Connecticut has virtually zero records of I/I MTS messages in the sample. In sub-markets where a state has few or no observations, it is not included in the panel data pooling procedure.

6. The concept of a "net-price" elasticity is relevant when considering the various types of aggregate MTS goods that can be defined from disaggregate MTS demand equations. The net-price elasticity for any state in sub-market j can be expressed as the sum of the own and cross-price elasticities for that state in segment j. Further, the aggregate state ("own") price elasticity can be derived as a weighted average of the individual sub-market net-price elasticities for that state. The weights are the proportion of total I/I MTS toll messages for that state in each of the sub-markets, and are such that they sum to one.

7. Because Connecticut has virtually no sampled I/I MTS messages in the available database, it was not included in the panel data pooling procedure for any of the 30 sub-markets.

Joseph P. Gatto and Scott W. Stephan are Economists in the Market Analysis and Forecasting organization at AT&T in Bedminster, New Jersey. Harry H. Kelejian is a Professor of Economics at the University of Maryland in College Park, Maryland

Editor's Note: Due to space limitations, the bibliography is not included, the references were shortened, and some of the tables were omitted. A complete copy of the paper is available upon request. If interested, please contact the Review of Business.
COPYRIGHT 1989 St. John's University, College of Business Administration
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1989 Gale, Cengage Learning. All rights reserved.

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Author:Gatto, Joseph P.; Kelejian, Harry H.; Stephan, Scott W.
Publication:Review of Business
Date:Sep 22, 1989
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