Are Telephone Monopolies Unnatural?
Subadditivity in the Production of Local Telephone Services
Wesley W. Wilson,
Department of Economics, University of Oregon and
Yimin Zhou, Department of Management & Economics, Aomori Public College
Summary
Introduction
In early 1996, Congress passed the Telecommunications Act of 1996. An important objective of
this legislation is to establish a pro-competitive and deregulatory national policy framework in the
telecommunications industry. Specifically, this legislation opens local telecommunications
monopolies to competition by removing legal and regulatory barriers and reducing economic
impediments to entry. Prospective entrants, e.g., inter-exchange carriers (IXCs), competitive
access providers (CAPs), and cable TV companies, welcome the new legislation. Incumbent local
exchange carriers (LECs), however, have worked to block its implementation and have had
moderate success in that the U.S. Court of Appeals for the 8th Circuit suspended "pricing and
contract rules that would have forced the Baby Bells to extend discounts and other advantages to
new rivals entering their local phone markets."
An important premise for introducing competition into local telephone markets is that these
markets are not (or no longer) natural monopolies. However, empirical evidence pertaining to the
natural monopoly issue is far from conclusive. Evans and Heckman (1983 and 1984), for
instance, found evidence that the pre-divestiture AT&T did not have subadditive costs. Shin and
Ying (1992) using an unbalanced panel of data pertaining to LECs also found that the costs of the
major LECs are not subadditive. These studies suggest that the telecommunications industry is an
"unnatural monopoly." However, Charnes, Cooper and Sueyoshi (1988), using the same data set
as Evans and Heckman, used different techniques and found opposite results. Röller (1990a, and
1990b) using a generalized CES cost function also found pre-divestiture Bell data are also
consistent with a natural monopoly. In a recent study, we used an unbalanced panel of LECs and
found that estimates of scale economies are dramatically affected by the treatment of unobserved
firm heterogeneity (Wilson and Zhou (1997)). When we control for unobserved heterogeneity,
scale effects are substantial. However, without such controls, constant or near constant returns
result. Given the mixed empirical evidence and the sensitivity to different specifications, we
reexamine the subadditivity issue in this paper and evaluate the effects of different market
structures on costs.
There are compelling reasons for controlling unobserved heterogeneity. While the modeling of
unobserved heterogeneity is not common in estimation of costs in telephone markets, there are
now a number of studies that use such controls in the railroad markets (e.g. Caves et. al (1985),
Vellturo et. al (1992), and Berndt et. al (1993). In addition to network effects identified in those studies which likely also apply in telecommunication markets, Gabel and Kennet (1994)
recently identified a number of plausible and additional sources of heterogeneity unobserved by
the econometrician in telephone markets. These include the omission of vertical services,
interexchange services, the use of proxy variables for customer density which may bias results on
key parameters, and the measurement of capital stock. These variable omissions and
measurement difficulties which are each potential sources of specification error vary
systematically across firms and should be reduced or removed by modeling them as sources of
unobserved heterogeneity. In addition, production in these markets occurs with a network
technology. The effects of different network configurations may be in the error as has been
conjectured in railroad studies. Also, LECs operate in different geographical areas and are subject
to differing regulatory environments As such, network effects, heterogeneous market conditions,
and diverse regulatory constraints may be another source of unobserved heterogeneity when
relevant data are not available.
We estimate a cost functions for LECs controlling and not controlling for unobserved
heterogeneity. We then simulate the costs of LECs and conduct subadditivity tests using both
specifications and compare the results. When we control for unobserved heterogeneity, costs are
subadditive. However, when we do not control for heterogeneity, costs are not subadditive, but,
in fact, are superadditive. We then examine the effects of the product mix of LECs (local and toll
costs) on the subadditivity results. In the model with heterogeneity controls, multifirm production
results in substantial cost increases, while in the model without heterogeneity controls, multifirm
production results in substantial cost decreases. In both cases, the mix of products produced by
firms has a tremendous effect on the magnitudes of cost changes from single firm to multifirm
production. These findings not only underscore the importance of controlling unobserved
heterogeneity but also suggest the existence of scope economies in joint production of local and
long-distance services.
Model
We estimate a translog cost function with and without controls for unobserved heterogeneity in
the error structure. The error term is taken as a linear function of time dummies and firm
dummies, denoted as Dm and Dn for time period m and firm n. Berndt et. al (1993) and Vellturo et. al
(1992), we allow firm dummies to interact with the factor prices in order to account for
heterogeneity in the errors of the share equations, and in the cost function allowing for slope
heterogeneity. The reason for this approach is that firm-specific network attributes and other
effects not known to the econometrician may determine factor employment decisions (Berndt et.
al (1993)). We also allow annual dummy variables to interact with all the linear terms on the
right hand side of the cost function. Application of Shephard's Lemma yields the cost shares
which are then estimated with the cost function with the imposition of symmetry and homogeneity
restrictions. We omit the material share equation from the system to avoid singularity.
Data
The primary source of data is the Statistics of Communications Common Carriers (SOCC)
published annually by the FCC. This source includes data on the major LECs assets, liabilities,
revenues, expenses, plant statistics, and output. The raw data set includes an unbalanced panel of
71 LECs over seven years from 1988 to 1995. We removed from the data, observations with
missing or suspect values resulting in extreme outliers. After removing these observations, we
have 399 valid observations from an unbalanced panel of 67 LECs for cost function estimation
and subadditivity tests. In total, these firms account for about 90 percent of the nation's local
telephone markets served, and the results of our estimation and subadditivity tests should be
representative of the markets served by more than 1300 local telephone companies. We use the
communications equipment implicit price deflator obtained from various years of The National
Income and Product Accounts for computing the real capital stock. The average yield of
domestic telephone bonds (used in computing the total capital expenses) is obtained from
Moody's Public Utility Manual.
We use total cost C as the dependent variable. The three exogenous factor price variables used
are labor, capital and materials. We include one output variable, i.e., access lines and one variable
for product mix (see below). We use the ratio of percentage of electronic switching equipment
assets to total central office switching assets to represent the effects of observed technological
change. For unobserved sources of technological change we include a set of annual dummy
variables. In the remainder of this section, we describe the construction of these variables and
rationalize their inclusion.
To compute total cost, we subtract depreciation and amortization expenses from the total
operating expenses, and then add it to capital expenses. Total operating expenses include plant
specific operation expenses, plant non-specific operations expenses, other operation related
expenses and employee compensation. We use the same methodology as Shin and Ying (1992) in
computing capital expenses. First, we obtain an implicit price deflator by averaging
communications equipment price indices over a 20 year period. We then compute the real capital
stock by dividing total communications plant by the implicit price deflator. Finally, we convert
the real capital stock to current dollars and compute the capital expenses.
Wage rate PL is computed by taking the ratio of total employment compensation to the total
number of employees. Capital price PK is obtained by dividing capital expenses with total number
of access lines. Price of materials PM is obtained as the residual expenses divided by total number
of access lines. We use total access lines YA as our output variable. Whether treatment of access
lines as a fixed input or as an output is largely a matter of interpretation. Following previous
research, we first specified our model with usage output terms as well -- the number of local and
long-distance calls. The results that emanate from this treatment and variations of this treatment
were consistent with earlier results and are disappointing. In some specifications, for example, we
observe small and statistically significant negative estimates on the linear term, suggesting that at
mean values, increases in the percentage of calls that are local, decreases costs. In other
specifications, we observe small positive but statistically insignificant estimates. On inspection,
we observed considerable multicollinearity in the data pertaining to output. Yet, usage and the
differences between firms producing a high proportion of local calls and those producing a high
proportion of toll calls is important. To explain these differences across firms in costs producing
different levels of local and long-distance outputs, we define a product mix variable. This variable
is the proportion of local calls to total calls . Our results, described later, suggest that such a
variable is useful in explaining differences in costs across firms, is of the sign that is consistent
with priors, and allows subadditivity to be described for different product mixes in a meaningful
manner.
We also include the number of central offices and average loop length to account for operating
characteristics. Ideally, we would also like to include variables that account for the intensity of
the traffic, and other operating characteristics of LECs. These ideal data, however, are
unavailable. These effects, therefore, are likely sources of unobserved heterogeneity and should
be reflected in the associated controls for unobserved heterogeneity.
Empirical Results
For both specifications, we estimate the system of equations using Zellner's iterative-seemingly-unrelated-regression technique, with the materials equation as the omitted equation. We first test
whether heterogeneity exists in the error structure, examine the source of the heterogeneity, and
finally, examine whether heterogeneity takes the form of fixed or random effects. Test results
provide strong evidence in favor of a specification, controlling for heterogeneity. Likelihood ratio
tests indicate that parameters for firm-specific dummy variables (Chi-Square (66)=912), for interaction
terms between firm dummies and factor prices (Chi-Square (132)=924) and for all terms related to firm
dummies (Chi-Square (198)=1293) are statistically significant.
In general, the heterogeneity model fits the data well with R2s over 0.9 for all three equations in
the system. With positive marginal costs for all observations and 69 percent of the observations
having costs concave in factor prices, the regularity conditions are generally satisfied. Most linear
terms have the expected signs and are statistically significant. For the factor prices, all of the first-order terms are positive. The estimated factor shares are 0.37, and 0.34 for labor and capital for
the base firm in 1988, and the average labor and capital shares are 0.27 and 0.38 for the entire
sample. Values for all firms are easily calculated with the appropriate interaction terms.
The parameter estimate of the first-order term for access lines is 0.79 in the model, controlling
for heterogeneity. This result suggests there are economies associated with increases in the
number of access lines -- a one percent increase in access lines leads to an estimated 0.79
percent increase in cost. Since scale economies at the sample means may not have relation to
scale economies away from the sample means, we use our parameter estimate and compute scale
economies at each level of access lines holding all other variables constant at their sample means
and the results suggest that scale economies exist for the majority of firms in the sample, and
smaller LECs tend to have greater scale economies to exploit.
The parameter estimate for product mix is positive and significant (0.13), which implies that the
costs of LECs depend significantly on the product mix. Specifically, a one percent increase in the
proportion of local usage results in 0.13 percent cost increases, while an increase in the
proportion of toll usage reduces production costs, ceteris paribus. The significant second-order
term for product mix suggests that production costs increase with the proportion of local calls at
an increasing rate. Alternatively, these parameter estimates suggest that there exist scope
economies in providing local and long-distance services.
The non-heterogeneity specification yields several parameter estimates both quantitatively and
qualitatively different from those of the heterogeneity model. Among all the disparities, the first
obvious difference is the estimated coefficient for access lines which is 0.96 (vs. 0.79 in the
heterogeneity model). This implies that there are only very modest scale economies associated
with access lines at mean values of the other variables. Another disparity is that, contrary to
conventional wisdom, the parameter estimate for average loop length is negative in the non-heterogeneity model. These results along with the results presented point to the extreme
sensitivity associated with the treatment of unobserved heterogeneity.
Subadditivity
Our parameter estimates based on the heterogeneity specification indicate that local telephone
companies exhibit scale economies and that costs depend in a nontrivial way on the mix of
products produced. The estimates based on the nonheterogeneity specification indicate that there
are no significant scale economies, but that costs do depend on the product mix. We now assess
whether the cost structure estimated with these LEC data are consistent with natural monopolies.
In so doing, we simulate costs and conduct a series of subadditivity tests similar to those of Evans
and Heckman (1983 and 1984), and Shin and Ying (1992). Conceptually, a firm is a natural
monopoly if and only if its cost function is globally subadditive. A typical subadditivity test
determines whether one firm can produce the same level of output as two (or more) firms can no
matter how the single firm output is split between the two firms.
We conduct subadditivity tests on both cost specifications -- the results with and without
heterogeneity controls. For both specifications, we have two sets of tests with different
treatments of the product mix variable. In our first set of tests, we hold product mix as it is and
use access lines as the only output variable Y1. This is equivalent to varying the hypothetical
outputs without changing the product mix. In the second set of tests, we allow the product mix
to vary. Since access lines are connected to and switched in central offices, we allow central
offices to vary as follows. We give hypothetical firms the same proportions of central offices to
their proportions of access lines. That is, if firm A is given 10 percent of the access lines, its
proportion of the central offices is also 10 percent. All remaining variables except those discussed
are held at their observed values.
We have altogether 399 valid observations. Depending on the treatment of product mix variable,
there are either 1995 or 16359 hypothetical paired output combinations. Specifically, when
product mix is held constant, we let the proportion of single firm output to be split between two
firms at intervals of .1, .2, 3, ..., .9. When product mix varies, there are 41 unique combinations.
Using parameter estimates from the non-heterogeneity model, we find LEC costs are
superadditive. Specifically, the simulated cost savings from replacing single-firm production with
two-firm production range from 1.31% to 5.18%, when product mix is held constant, and 18.87
to 86.82 when product mix varies. These results are qualitatively consistent with empirical
findings by Evans and Heckman (1983) and Shin and Ying (1992) although the magnitudes of
cost savings differ. For instance, across different specifications the percentage gains by multifirm
production simulated by Evans and Heckman (1983) range from -17% to 25%, but none of these
figures are statistically different from zero. Hence, they conclude that the cost function is locally
additive. The average percentage gains by multifirm production obtained by Shin and Ying range
from 0.94% to 3.8%, depending on whether positive marginal costs and the number of central
offices are controlled for in simulating the cost function.
When using parameter estimates from the heterogeneity model, we find very different results in
that LEC costs are subadditive. The hypothetical cost increases range from a low of 23.94% and
to a high of 73.40 when product mix is held constant, and from 21.12% to 52.84% when product
mix varies. These results are qualitatively consistent with findings by Charnes et al. (1988) and
Röller (1990a, and 1990b). According to Charnes et al., for instance, the hypothetical costs of
multifirm production are 15% to 34% higher than single firm production on average, and the
maximum cost increase due to multifirm production is 86%. Depending on the specifications used,
Röller (1990a) find that multifirm production costs 7% to 47% more than single firm production.
As competitive entry is a more likely policy option than breaking up incumbent local monopolies,
we follow Shin and Ying and conduct the same sets of subadditivity tests by allowing each
hypothetical firm to have the same number of central offices that the monopoly firm has. The
results of our subadditivity tests remain qualitatively unchanged.
These diametrically different results strongly suggest that subadditivity tests are sensitive to the
specifications of cost functions. Given the strong empirical evidence in favor of heterogeneity
controls and the results of our subadditivity tests, we contend that the U.S. local telephone
markets are consistent with natural monopolies. Future research, however, needs to be targeted
not only at identifying the sources of currently unobserved heterogeneity, but also at developing
data and measures of these sources.
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