Telecommunications deregulation and subadditive costs: Are local telephone monopolies unnatural?

International Journal of Industrial Organization19 (2001) 909–930

www.elsevier.com/ locate /econbase

Telecommunications deregulation and subadditive costs:Are local telephone monopolies unnatural?

a , b*Wesley W. Wilson , Yimin ZhouaDepartment of Economics, University of Oregon, Eugene, OR 97403, USA

bDepartment of Management and Economics, Aomori Public College, Goshizawa Yamazaki,Aomori City, Aomori 030-0196, Japan

Received 1 December 1998; received in revised form 1 June 1999; accepted 1 September 1999

Abstract

In early 1996, Congress passed the Telecommunications Law, providing the foundationfor the opening of regulated local telephone monopolies to competition. One importantpremise for introducing competition into local telephone markets is that these markets arenot (or are no longer) natural monopolies. This paper reexamines the natural monopolyissue using a cost function that controls for firm heterogeneity. Our subadditivity testssuggest that Local Exchange Carriers’ (LECs) costs are subadditive when there are controlsfor unobserved heterogeneity, suggesting that local telephone markets are natural monopolymarkets. 2001 Elsevier Science B.V. All rights reserved.

1. Introduction

In early 1996, Congress passed the Telecommunications Act of 1996. Thislegislation opens local telecommunications monopolies to competition by remov-ing legal and regulatory barriers and reducing economic impediments to entry.Prospective entrants, e.g., inter-exchange carriers (IXCs), competitive accessproviders (CAPs), and cable TV companies, welcomed the new legislation.Incumbent local exchange carriers (LECs), however, worked to block its im-

*Corresponding author. Tel.: 11-514-346-4690; fax: 11-541-346-1243.E-mail addresses: [email protected] (W.W. Wilson), [email protected] (Y. Zhou).

0167-7187/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PI I : S0167-7187( 99 )00054-5

910 W.W. Wilson, Y. Zhou / Int. J. Ind. Organ. 19 (2001) 909 –930

plementation with moderate success in that the U.S. Court of Appeals for the 8thCircuit suspended ‘pricing and contract rules that would have forced the BabyBells to extend discounts and other advantages to new rivals entering their local

1phone markets.’An important premise for the introduction of competition into local telephone

markets is that these markets are not (or no longer) natural monopolies. As aresult, entry can occur without loss of economic efficiency, or alternatively, mayeven increase economic efficiency. Our research suggests this premise of non-subadditive (or superadditive) costs may be seriously in question. Indeed, ourresults suggest that costs of local exchange carriers are subadditive, and there maybe significant reductions in efficiency by allowing entry into the industry.

There have been a number of studies examining the subadditivity of costs in thisindustry as well as other industries. Yet, despite the considerable number ofempirical studies of the issue, the evidence pertaining to subadditivity and thenatural monopoly issue is far from conclusive. Early studies used predivestitureAT&T data. Evans and Heckman (1983, 1984) found evidence suggesting that

¨costs were not subadditive. Charnes et al. (1988) and Roller (1990a,b) usingdifferent techniques or specifications found the pre-divestiture Bell data areconsistent with a natural monopoly. These findings, using pre-divestiture data,generally suggest sensitivity of the results to differing specifications. Shin andYing (1992) examined the issue using a balanced panel of data pertaining to localexchange carriers (LECs). Using these data, they found that the costs of the majorLECs are not subadditive. In our recent paper (Wilson and Zhou, 1997), we use aspecification and a data set comparable to Shin and Ying (1992). We found thatestimates of scale economies (as well as productivity) are dramatically affected bythe treatment of unobserved firm heterogeneity. When we control for unobservedheterogeneity, scale effects are substantial. However, without such controls,constant or nearly constant returns result. The conflicting empirical evidence inthis myriad of studies may, as Waverman (1989) pointed out, have resulted fromdifferences in the levels of data aggregation, functional forms, imposed con-straints, and assumed objective functions used in these studies. In our earlier work,we did not examine the subadditivity issue. Given its importance to current policyand the sensitivity of econometric models to cost, we examine this issue in thispaper along with an alternative method for dealing with multiple outputs.

There are a number of reasons for treating unobserved heterogeneity in theestimation of cost functions. Recent studies examining the structure of costs in therail industry rationalize the inclusion of controls for heterogeneity to capture‘network’ effects (e.g., Caves et al., 1985; Vellturo et al., 1992; and Berndt et al.,1993). We note that such effects may be present in the telecommunications

1 See ‘Baby Bells Win Possible Delay Of Competition,’ The Wall Street Journal, October 16, 1996.

W.W. Wilson, Y. Zhou / Int. J. Ind. Organ. 19 (2001) 909 –930 911

industry as well. In addition, however, a recent study by Gabel and Kennet (1994)identify a number of additional unobserved influences on costs which may bias theresults of a traditional specification of costs. These unobserved influences includethe omission of vertical services, interexchange services, the use of proxy variablesfor customer density which may bias results for key parameters, and the

2measurement of capital stock. In addition, LECs operate in different geographicalareas and are subject to differing regulatory environments. To the extent that theseeffects influence costs, they are another source of heterogeneity which, due to datalimitations, cannot readily be included.

Ideally, measures for omitted variables should be developed and included in theestimation. The development of measures for unobserved sources of error or bettermeasures for proxy variables, however, is quite difficult and, in our case, we havebeen unable to develop measures for these variables. Instead, we treat theseomissions as sources of heterogeneity in the error structure that are unobserved bythe econometrician. We estimate models with and without controls for unobservedheterogeneity. If the controls do not have a significant effect on the key parametersof interest, then the qualitative results of the analysis should be unchanged. Wefind, however, that the qualitative and quantitative results are distinctly different,and depend critically on the treatment of unobserved influences or heterogeneity.

In addition to the introduction of controls for heterogeneity, we also examinealternative measures of output, focusing on the treatment of multiple outputs. Theissue of subadditivity rests on the behavior of costs across multiple outputs. Recentstudies commonly exhibit negative marginal cost estimates as well as non-concavities in factor prices. Our approach in modeling is to estimate a modelmirroring the literature with and without controls for heterogeneity, accompaniedby an assessment of marginal costs and concavity. We then estimate models with adifferent treatment of outputs (the consolidation of local and long-distance into aproduct mix measure) with and without controls for heterogeneity. Such anapproach is comparable to studies in motor carrier markets. These studies use ameasure (the percentage of less-than-truckload traffic) to capture the differences inoutputs requiring distinctly different operations. In the results section, we presentall four estimation results and compare the specifications in terms of fit,parameters, regularity conditions, and, most important, subadditivity. The modelswith controls for unobserved heterogeneity yield qualitative and numericaldifferences in the subadditivity tests from those in the specification withoutcontrols. This is true regardless of the output treatment. In all cases, our statistical

2 Typically, the main line of business of LECs is to provide access lines to end users and transportcalls within their respective operating territories. In addition to access lines and local service, however,many LECs also provide interexchange services such as transporting intra-LATA and inter-LATA tollservices as well as vertical services such as private branch exchange, key system, caller ID, callwaiting, and a variety of other products which are ‘vertically’ related to their main line of business.


tests point to the inclusion of heterogeneity controls and the product mixspecification of output.

These findings have strong policy implications. Specifically, we find that costsexhibit a high degree of subadditivity: a single firm can produce an output vectorat a lower cost than a division of the output vector among two or more firms. Theresult suggests that LECs are natural monopolies. To the extent that entry occurswith the opening of local exchange markets, an important issue not examined inthis paper, multiple firms in the market may be short-lived. In the usual naturalmonopoly case, any sunk costs incurred from entry would be lost and the industrywould experience higher costs from an undue number of firms in the market.

2. Model

We estimate a cost function with and without controls for unobserved hetero-geneity in the error structure. In a general form, the cost function with additiveerrors is:

C 5 C(P, Y, T, t) 1 ´ (1)

where P is a vector of factor prices, Y is a vector of outputs, T represents a vectorof observed technology and operating characteristics, and t is a time trend that

3captures the unobserved technological change. The error term is taken as a linearfunction of firm dummies, denoted as D for firm n 5 1, 2, . . . , N. We approximaten

4the cost function with a translog function written quite generally as:

ln C 5 a 1 tt 1O a D 1O b ln P 1O g ln Y 1O d ln T0 n n i i j j k kn i j k

1 1] ]1 OO h ln P ln P 1 OO u ln Y ln Yik i k jl j l2 2i k j l

1]1 OO i ln T ln Tkl k l2 k l

1OO l ln P ln Y 1OO m ln P ln T 1OO j ln Y ln Tij i j ik i k jk j ki j i k j k

3 In the specifications with a ‘traditional’ treatment of output, there are three outputs, consisting ofaccess lines, local calls, and toll calls. In our alternative specifications of output, there are two elementsin the output vector, consisting of access lines and product mix.

4 We estimate Shin and Ying’s specification as a non-heterogeneity alternative to our heterogeneityspecification. In the non-heterogeneity specification, there is a BELL dummy, as in Shin and Ying(1992).


1O r t ln P 1OO f ln P Di i ni i nni i

1O c t ln Y 1O v t ln T 1 ´ (2)j j k kj k

5here ´ is the error term. We mirror the research by Berndt et al. (1993) andVellturo et al. (1992) by allowing firm dummies to interact with factor prices in

6the cost specification. This treatment allows heterogeneity to affect not only thecost function (in the intercept and in the factor price slopes) but also the factorshare equations. The result is a direct reflection of the fact that the unobservedinfluences may impact factor employment decisions (see Berndt et al., 1993). Wealso allow the time trend to interact with all the linear terms on the right-hand sideof the cost function. Application of Shephard’s Lemma yields the cost shares offactors as:

S 5 b 1O h ln P 1O l ln Y 1O m ln T 1 r t 1O f D 1 ´ , (3)i i ik k ij j ik k i ni n ink j k

where ´ is an error term for the ith share equation. Symmetry and homogeneity ofi

factor prices require the following restrictions:

h 5h ; i, k; q 5u ; j, l; i 5 i ; k, l;ik ki jl lj kl lk

O b 5 1, O h 5 0 ; k, O l 5 0 ; j, O m 5 0 ; k, O f 5 0 ; n,i ik ij ik nii i i i i

O r 5 0. (4)ii

The cost function and share equations are jointly estimated by iterated-seeming-ly-unrelated-regression techniques. We omit the material share equation from the

7system to avoid singularity. Finally, we follow common practice of normalizing

5 We also estimated an alternative specification with annual dummies in lieu of a time trend. Theresults of both procedures are very similar. We chose to use a trend variable and mirror Shin and Ying’s(1992) specification as closely as possible in order to demonstrate the impact of firm heterogeneity onthe estimation and simulation results.

6 With a limited number of observations, we are not able to allow firm dummies to interact with eachof the linear terms on the right-hand side of the cost function. Instead, we interacted the time trend onlywith each of the right-hand-side linear terms one at a time along with interactions between firmdummies and factor prices. An earlier reader suggested that we also examine the sensitivity of thegeneral result by interacting the firm dummies with all linear right-hand-side terms. We have done soand found that doing so does not alter our general conclusions. The specifications reported herein fit thedata better and have the added advantage of entering into the factor share equations. We therefore basethe remainder of discussion on the models with heterogeneity controls in factor prices.

7 The choice of omitted share is arbitrary, and our parameter estimates are invariant to the omittedfactor share equation.


all continuous variables by their respective sample means, allowing the linearterms to be directly evaluated with a mean value reference point.

3. Data sources and variable measurement

The primary source of data is the Statistics of Communications Common8Carriers (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 eight years, from

91988 to 1995. We removed from the data observations with missing or suspect10values. After removing these observations, we have 401 valid observations from

67 LECs for cost function estimation and subadditivity tests. All observationsemployed are summarized in Table 1. To compute capital stock, capital expenses,and capital rental price, we use the communications equipment implicit pricedeflator obtained from various years of The National Income and ProductAccounts and the average yield of domestic telephone bonds obtained from

11Moody’s Public Utility Manual.The firms in the sample are quite inclusive and representative of the industry,

accounting for about 90% of the nation’s local telephone markets. Although morethan a thousand smaller LECs that serve the remaining 10% of the local marketsare not included in the sample, we believe that the issue we are examining makesour sample representative and the results of our estimation and subadditivity testsvalid. Specifically, we want to determine whether large LECs are naturalmonopolies, and whether competition should be introduced into those largemonopolistic markets. In this specific context, it is a legitimate assertion that theresults of our estimation and subadditivity tests should be a valid approximation ofthe market conditions in general.

The LECs in the sample differ in output vectors, product mixes, and operating

8 Large telephone companies with more than $100 million in annual revenues are required to reporttheir operating statistics to the FCC. Smaller companies are not included in the SOCC.

9 The data and construction of the variables largely mirror Shin and Ying (1992). Our data, however,cover the years 1988–1995, while Shin and Ying (1992) cover the years 1976–1983. The two data setsare not quite comparable, owing to different regulatory environments and different reportingrequirements. The data are from the same sources and are measured in the same manner as in ourearlier work (Wilson and Zhou, 1997), but we have added one additional year, 1995, to the earlier dataset.

10 Our raw data set is an unbalanced panel of 420 observations from 71 LECs over eight years. It isunbalanced because some LECs either did not appear in SOCC for certain years or they did not haverelevant information we need in constructing variables. In addition, we removed from the data set thoseobservations that have negative material shares.

11 These measures are used by Shin and Ying (1992) and Wilson and Zhou (1997).


Table 1aLocal exchange carriers observed in the sample

Carrier code Carriers Years with valid data

1 Illinois Bell Telephone Co. YR88–YR952 Indiana Bell Telephone, Inc. YR88–YR953 Michigan Bell Telephone Co. YR88–YR954 The Ohio Bell Telephone Co. YR88–YR955 Wisconsin Bell, Inc. YR88–YR956 The Bell Telephone of Pennsylvania YR88–YR957 Chesapeake & Potomac Telephone Co. YR88–YR958 Chesapeake & Potomac Telephone of Maryland YR88–YR959 Chesapeake & Potomac Telephone of Virginia YR88–YR95

10 Chesapeake & Potomac Telephone of W.Virginia YR88–YR9511 The Diamond State Telephone Co. YR88–YR9512 New Jersey Telephone Co. YR88–YR9513 Bellsouth YR92–YR9514 New England Telephone Telegraph Co. YR88–YR9515 New York Telephone Co. YR88–YR9516 Nevada Bell YR90–YR9517 Pacific Bell YR88–YR9518 South Wester Bell Telephone Co. YR88–YR9519 US West YR91–YR9520 Cincinnati Telephone Co. YR88–YR9521 The Southern New England Telephone Co. YR88–YR9522 Citizens Utilities YR92–YR9323 Commonwealth YR91–YR9524 Contel of California YR88–YR9525 Contel of New York YR88–YR9326 Contel of The South YR93–YR9527 Contel of Texas, Inc. YR88–YR9428 Contel of Virginia YR88–YR9329 GTE California, Inc. YR88–YR9530 GTE Florida, Inc. YR88–YR9531 GTE Hawaiian Telephone, Inc. YR88–YR9532 GTE Midwest YR93–YR9533 GTE North, Inc. YR88–YR9534 GTE Northwest, Inc. YR88–YR9535 GTE South, Inc. YR88–YR9536 GTE Southwest, Inc. YR88–YR9537 Lincoln Telephone Telegraph Co. YR88–YR9538 Puerto Rico Communications YR9339 Puerto Rico Telephone Company YR90–YR9540 Rochester Telephone Corporation YR89–YR9541 Central Telephone Company YR93–YR9542 Central Telephone of Florida YR89–YR9543 Central Telephone of Illinois YR89–YR9544 Central Telephone of Virginia YR88–YR9545 Carolina Telephone Telegraph Co. YR88–YR9546 United Telephone Southeast YR92–YR9547 United Telephone of Florida YR89–YR95


Table 1. Continued

Carrier code Carriers Years with valid data

48 United Telephone of Indiana YR88–YR9549 United Telephone of Missouri YR90–YR9550 United Telephone New Jersey YR91–YR9551 United Telephone of Ohio YR88–YR9552 United Telephone of Pennsylvania YR88–YR9553 United Telephone of Texas YR92–YR9554 Central Telephone (Nevada & N. Carolina) YR90–YR9255 Contel of Illinois YR88–YR9256 Contel of Indiana YR91–YR9257 Contel of Missouri YR88–YR9258 Contel of West YR9259 South Central Bell Telephone Co. YR88–YR9160 Southern Bell Telephone Telegraph Co. YR88–YR9161 United Inter-mountain Telephone Co. YR88–YR9162 The Mountain State Telephone Telegraph Co. YR88–YR9063 Northwestern Bell Telephone Co. YR88–YR9064 Pacific Northwest Telephone Co. YR88–YR9065 Central Telephone (Nevada) YR8966 United Telephone Co. of Northwest YR95

a Included in the estimation are 67 LECs with 401 observations in total. Illinois Bell Telephone Co.is the base firm.

characteristics. The largest LEC has 1967 central offices whereas the smallest hasonly 23, with the sample mean being about 371 and the sample median 225 (seeTable 2 for details). Like the distribution of the LECs’ central offices, the

Table 2aDescriptive statistics

Variable Mean Std. dev. Minimum Maximum

Total cost 1,507,161.9309 2,149,516.7600 63,925.0547 11,902,100.0000Labor price 40.3672 6.7026 27.2570 66.8052Capital price 0.2209 0.0499 0.1295 0.6347Materials price 0.2038 0.0604 0.0620 0.4501Local calls 8,500,890.0000 13,784,500.0000 148,449.0000 90,294,300.0000Toll calls 1,476,850.0000 2,372,270.0000 36,037.0000 16,821,700.0000Product mix 0.8322 0.0760 0.4587 0.9665Access lines 2794.0401 4120.9806 76.2350 22,595.4000Technology proxy 0.9520 0.0683 0.6892 1.0000Number of central offices 370.6658 406.4280 23.0000 1967.0000Average loop length 0.0426 0.0321 0.0035 0.1701

a Total cost, labor price, capital price, materials price, local and toll calls, and access lines aremeasured in thousands. Average loop length is measured in miles.


distributions of all output variables and other operating characteristics are skewed12to the right, except the product mix measure and technology proxy. The LECs

also differ substantially in factor prices. In all cases, the descriptive statistics pointto two facts: (i) this is not a group of homogeneous firms; (ii) most LECs in thesample are not of very large size (in terms of central offices). Indeed, the thirdquartile has 445 central offices, a much smaller number than the largest LEC with1967.

3.1. Variable construction

We model total cost C and associated factor shares as a function of threeexogenous factor prices including labor, capital and materials. Three variables aretypically used in the traditional treatment of outputs. They are number of localcalls, number of toll calls (both intra-LATA and inter-LATA), and access

13 ,14lines. Due to the problem discussed in the Introduction (and footnote 14), aswell as our conjecture that usage and differences between firms’ product mix oflocal and toll calls are important, our alternative specifications replace local andtoll calls with a product mix variable defined as PM 5 LC /(LC 1 TC), where LCis the number of local calls, and TC is the number of intra-LATA and inter-LATA

15toll calls. We use the ratio of percentage of electronic switching equipment assetsto total central office switching assets to represent the effects of observed

12 The negatively skewed product mix measure and technology proxy suggest that majority of theLECs in the sample have relatively greater proportion of local services in their product mixes and usemore electronic switching equipment.

13 Whether treatment of access lines are viewed as a fixed input or as an output is largely a matter ofinterpretation. For more detailed discussions, see Duncan (1990) and Taylor (1993).

14 The results obtained from using these three outputs, with both heterogeneity and non-heterogeneityspecifications, are consistent with earlier results and are disappointing. For example, we observe astatistically significant negative estimate on the linear term for toll calls with the non-heterogeneityspecification (and an insignificant negative estimate with the heterogeneity specification). This suggeststhat at mean values, increases in the percentage of toll calls decrease costs. An earlier reader suggeststhat this finding may reflect the fact that in lower population density areas, costs are lower and thepercentage of toll calls is higher. We examined this potential by calculating the correlation betweenaverage loop length and the percentage of toll calls, finding a positive but modest correlation. Thisfinding is consistent with the notion that LECs with longer average loop lengths tend to have higherpercentages of toll calls and lower costs i.e., the higher percentage of toll calls may indeed besystematically related to lower population density and lower cost.

15 This approach amounts to forming a composite index representing these two important variables.Discussion of this approach can be found in Kennedy (1998). Results from using this approach suggestthat such a variable is useful in explaining differences in costs across firms, is of the sign that isconsistent with priors, and allows subadditivity to be described for different product mixes in ameaningful manner.


16technological change. For unobserved sources of technological change weinclude a time trend. In the remainder of this section, we describe the constructionof these variables and rationalize their inclusion.

To compute total cost, we first subtract depreciation and amortization expensesfrom the total operating expenses, and add the result to capital expenses. Totaloperating expenses include plant-specific operation expenses, plant non-specific-operations expenses, other operation-related expenses and employee compensation.To compute capital expenses, we follow the same methodology as Shin and Ying(1992) and Wilson and Zhou (1997). First, we obtain an implicit price deflator byaveraging communications equipment price indices over a 20 year period. We thencompute the real capital stock by dividing total communications plant by the

17implicit price deflator. Finally, we convert the real capital stock to current dollarsand compute the capital expenses as:

rK]]]C 5 1 rK (5)2rtK W1 2 e

where C is the capital expenses, K the capital stock, r the interest rate, t the lifeK

of capital which is assumed to be 20 years, and K the working capital obtainedW

by subtracting current liabilities from current assets. This formulation is based on18the assumption that the productivity of capital is constant over the 20-year life.

The wage rate P is computed by taking the ratio of total employmentL

compensation to the total number of employees. The capital price P is obtainedK

by dividing capital expenses by the total number of access lines. The price ofmaterials P is obtained as the residual expenses divided by the total number ofM

16 Alternatively, the ratio of electronic access lines to total access lines has been used in someprevious studies. These data, however, are not available for the sample period. Since electronic accesslines are connected to electronic switches the two measures are likely to be highly correlated and ourmeasure should yield results similar to those using the other measure. We also experimented with othermeasures, e.g., the percentage of deployed fiber-optic cables to total cables. The resulting estimate forunobserved technological change is not significant.

17 Our interest is in the effects of controlling for firm heterogeneity on subadditivity tests. Therefore,we follow Shin and Ying (1992) in constructing the capital stock variable (and all other variables). Therationale for doing so is that adopting other ways of constructing capital stock (and defining othervariables) might make it difficult to determine what causes our subadditivity results to differ from Shinand Ying. Thus, our intention is to introduce controls for heterogeneity into a common specificationwith no variable definition changes to insure that the results of the tests are due to heterogeneitycontrols. We have, however, experimented with perpetual inventory method and used an alternativemeasure of capital rental price similar to that used in Nadiri and Schankerman (1981) and in Oum andZhang (1995). Our results using this alternative measure of capital rental price yielded qualitativelyequivalent and numerically similar findings.

18 This formulation follows directly from Shin and Ying (1992).


access lines. Other variables include the number of central offices and average19loop length to account for operating characteristics. Descriptive statistics for all

the variables are presented in Table 2.

4. Empirical results

We estimate two sets of specifications (four altogether): one set with controls forunobserved heterogeneity and the other without. For each set, we estimate atraditional three-output model as well as a product-mix model. For all spe-cifications, we estimate a system of equations given by Eqs. (2)–(4), usingZellner’s iterative-seemingly-unrelated-regression technique, with the materialsequation omitted. In Table 3 we provide parameter estimates for all fourspecifications, excluding the estimates for the firm dummies used in the hetero-

20geneity models. Specification 1 is the non-heterogeneity specification with thetraditional three-output variable treatment. Specification 2 adds controls forunobserved heterogeneity. Specifications 3 and 4 are the specifications with accesslines and product mix, without and with controls for unobserved heterogeneity.

We test whether heterogeneity exists in the error structure, and examine thesource of the heterogeneity. The test results provide strong evidence in favor of aspecification controlling for heterogeneity. With the product-mix specification,likelihood ratio tests indicate that parameters for firm-specific dummy variables

2(x (66) 5 724), for interaction terms between firm dummies and factor prices2 2(x (132) 5 878), and for all terms related to firm dummies (x (198) 5 1211) are

statistically significant. With the three-output specification, likelihood ratio tests2 2 2yield very similar results (x (66) 5 767, x (132) 5 926, and x (198) 5 1253,

respectively). The results of these tests provide strong statistical evidence thatcontrols for unobserved heterogeneity should be used in analyzing costs.

In addition to the statistical support for the addition of heterogeneity controls,we also examine the concavity of costs in factor prices and the behavior of costswith respect to changes in output. At the mean values of factor shares, the costfunction is concave in factor prices with all four specifications. Specificationsusing three outputs suffer from the problem of negative marginal costs. Inparticular, when we estimate the heterogeneity specification with three outputs, tollcalls have negative marginal cost for a large number of the observations. When weestimate the non-heterogeneity specification using three outputs, local calls have

19 Data that account for the intensity of the traffic and other operating characteristics of LECs areunavailable. The missing information, however, is likely a source of unobserved heterogeneity andshould be reflected in the associated controls for unobserved heterogeneity.

20 Parameter estimates for firm dummies are not reported but available upon request.


Table 3aParameter estimates

Spec. 1 Spec. 2 Spec. 3 Spec. 4

Estimate S.E. Estimate S.E. Estimate S.E. Estimate S.E.

Intercept 0.1554 0.0160 0.2292 0.0158 0.1569 0.0157 0.2273 0.0185

PL 0.3280 0.0091 0.3857 0.0116 0.3268 0.0091 0.3959 0.0151

PK 0.3466 0.0043 0.3218 0.0075 0.3473 0.0044 0.3178 0.0079

LC 0.0052 0.0136 0.0592 0.0166 * * * *

TC 20.0196 0.0082 20.0064 0.0053 * * * *

AL 1.0049 0.0232 0.7403 0.0357 0.9901 0.0096 0.8019 0.0305

PM * * * * 0.0810 0.0357 0.1214 0.0285

TK 20.2697 0.0707 20.0680 0.0399 20.2242 0.0686 20.0849 0.0420

CO 0.0134 0.0098 0.0027 0.0059 0.0113 0.0095 0.0035 0.0056

LL 0.0032 0.0129 20.0004 0.0191 0.0036 0.0128 0.0044 0.0202

TREND 20.0141 0.0027 20.0165 0.0015 20.0146 0.0027 20.0166 0.0015

BELL 20.0467 0.0144 * * 20.0520 0.0135 * *

1/2*PL2 0.1890 0.0026 0.1964 0.0033 0.1894 0.0026 0.1966 0.0022

1/2*PK2 0.2323 0.0014 0.2211 0.0037 0.2331 0.0015 0.2226 0.0026

1/2*LC2 20.0371 0.0103 0.0104 0.0167 * * * *

1/2*TC2 0.0021 0.0035 0.0129 0.0052 * * * *

1/2*AL2 20.0211 0.0221 0.0424 0.0296 20.0038 0.0022 20.0002 0.0102

1/2*PM2 * * * * 20.1735 0.0527 0.4058 0.0784

1/2*TK2 20.0417 0.1355 20.8542 0.1925 0.0499 0.1167 21.1015 0.2018

1/2*C02 0.0004 0.0025 0.0154 0.0041 20.0022 0.0022 0.0130 0.0041

l /2*LL2 20.0014 0.0044 0.0482 0.0170 20.0035 0.0039 0.0489 0.0153

1/2*TREND2 0.0003 0.0002 0.0006 0.0002 0.0003 0.0002 0.0005 0.0002

PL*PK 20.1101 0.0024 20.1071 0.0035 20.1107 0.0024 20.1080 0.0019

PL*LC 0.0048 0.0075 0.0431 0.0102 * * * *

PL*TC 20.0094 0.0046 20.0011 0.0030 * * * *

PL*AL 0.0046 0.0122 20.1495 0.0211 20.0007 0.0046 20.1157 0.0201

PL*PM * * * * 0.0496 0.0203 0.0388 0.0177

PK*LC 20.0020 0.0043 20.0213 0.0058 * * * *

PK*TC 0.0071 0.0025 0.0029 0.0019 * * * *

PK*AL 20.0038 0.0065 0.0785 0.0103 0.0022 0.0025 0.0632 0.0105

PK*PM * * * * 20.0341 0.0118 20.0313 0.0093

PL*TK 20.1358 0.0359 0.0461 0.0217 20.1210 0.0350 0.0393 0.0235

PK*TK 0.0714 0.0202 20.0230 0.0126 0.0656 0.0194 20.0223 0.0124

PL*CO 0.0052 0.0050 20.0018 0.0026 0.0043 0.0048 20.0018 0.0028

PL*LL 0.0074 0.0065 0.0164 0.0108 0.0072 0.0064 0.0213 0.0126

PK*CO 20.0033 0.0028 20.0009 0.0013 20.0030 0.0028 20.0009 0.0015

PK*LL 20.0048 0.0037 20.0020 0.0045 20.0045 0.0038 20.0039 0.0065

PL*TREND 20.0096 0.0012 20.0123 0.0009 20.0094 0.0012 20.0120 0.0009

PK*TREND 0.0052 0.0006 0.0061 0.0005 0.0051 0.0006 0.0061 0.0005

PL*BELL 20.0354 0.0083 * * 20.0353 0.0078 * *

PK*BELL 0.0186 0.0041 * * 0.0185 0.0039 * *

LC*TC 0.0046 0.003 8 20.0048 0.0062 * * * *

LC*AL 0.0318 0.0149 20.0176 0.0196 * * * *

TC*AL 20.0091 0.0062 20.0130 0.0092 * * * *


Table 3. Continued

Spec. 1 Spec. 2 Spec. 3 Spec. 4

Estimate S.E. Estimate S.E. Estimate S.E. Estimate S.E.

PM*AL * * * * 0.0048 0.0111 20.0061 0.0132

LC*TK 0.0095 0.0255 0.0475 0.0391 * * * *

TC*TK 0.0130 0.0151 0.0316 0.0245 * * * *

AL*TK 20.0380 0.0413 20.0563 0.0546 20.0129 0.0144 0.0499 0.0218

PM*TK * * * * 20.0869 0.0766 20.0850 0.1013

LC*CO 0.0004 0.0032 20.0013 0.0036 * * * *

LC*LL 0.0021 0.0060 0.0065 0.0099 * * * *

TC*CO 20.0019 0.0029 0.0039 0.0041 * * * *

TC*LL 0.0008 0.0036 20.0020 0.0043 * * * *

AL*CO 0.0024 0.0051 20.0180 0.0065 0.0030 0.0020 20.0129 0.0040

AL*LL 20.0060 0.0086 0.0010 0.0121 20.0047 0.0024 0.0017 0.0070

PM*CO * * * * 0.0078 0.0108 20.0156 0.0127

PM*LL * * * * 0.0143 0.0150 20.0147 0.0224

LC*TREND 20.0017 0.0009 20.0037 0.0013 * * * *

TC*TREND 0.0001 0.0005 20.0019 0.0007 * * * *

AL*TREND 0.0025 0.0016 0.0091 0.0021 0.0004 0.0005 0.0024 0.0007

PM*TREND * * * * 20.0012 0.0021 20.0046 0.0022

TK*TREND 0.0106 0.0054 0.0291 0.0074 0.0080 0.0052 0.0368 0.0073

CO*LL 0.0039 0.0030 20.0200 0.0056 0.0054 0.0026 20.0168 0.0055

CO*TK 0.0061 0.0150 0.0010 0.0190 20.0013 0.0128 20.0137 0.0195

LL*TK 20.0040 0.0235 0.0392 0.0298 20.0108 0.0194 0.0527 0.0304

CO*TREND 20.0011 0.0006 20.0036 0.0009 20.0004 0.0006 20.0032 0.0006

LL*TREND 0.0005 0.0008 0.0036 0.0011 0.0002 0.0007 0.0032 0.0007

LC*BELL 0.0043 0.0057 * * * * * *

TC*BELL 0.0043 0.0022 * * * * * *

AL*BELL 20.0045 0.0078 * * 0.0042 0.0031 * *

PM*BELL * * * * 0.0081 0.0122 * *

TK*BELL 0.0557 0.0208 * * 0.0260 0.0194 * *

CO*BELL 20.0006 0.0028 * * 20.0008 0.0028 * *

LL*BELL 0.0052 0.0041 * * 0.0018 0.0040 * *

BELL*TREND 0.0006 0.0007 * * 0.0015 0.0007 * *

a Spec. 1 is the specification with traditional three-output variables and no controls for unobservedheterogeneity. Spec. 2 is the same as Spec. 1 with controls for unobserved heterogeneity included.Spec. 3 and Spec. 4 are the specifications with the alternative output treatment (access lines and productmix). Spec. 3 has no controls for unobserved heterogeneity, while Spec. 4 has controls for unobservedheterogeneity included. The variables are as follows: PL stands for the wage rate, PK stands for theprice of capital, LC stands for local calls, TC stands for toll calls, AL stands for access lines, PM standsfor product mix, TK stands for technology, CO stands for central offices, LL stands for average looplength, BELL stands for Bell Operating Companies, and TREND stands for the time trend. Asterisksmean that the variable was not included in the corresponding specification.


negative marginal cost for over 35% of observations and toll calls have negative21marginal cost for all observations. When we consolidate local calls and toll calls

into a product mix measure, the set of specifications with the product mix variabledo not exhibit negative marginal cost. Nonetheless, apart from differences insatisfying regularity conditions, our specifications with heterogeneity controlsyield similar parameter estimates, whether we use the product mix variable or thethree outputs.

4.1. Heterogeneity models

For the product-mix specification, all linear terms have the signs that areconsistent with our priors, although neither the number of central offices noraverage loop length is significant. Although these insignificant estimates appear tobe counter-intuitive, they are plausible. Central offices and network loops are fixedfacilities. Once the central offices and local loops are in place, these facilitiesthemselves do not incur any incremental costs; it could well be that the variablecosts incurred in operating and maintaining these facilities are small compared to

22other costs so that their marginal impact on LECs’ production costs is negligible.For the three-output specification, most linear terms have the expected signs and

are statistically significant. The parameter estimate of the first-order term foraccess lines is 0.8 for the product-mix specification and 0.74 for the three-outputspecification. These results suggest there are scale economies associated with thenumber of access lines.

The parameter estimate for product mix variable is positive and significant(0.12), which implies that the costs of LEGs depend significantly on the productmix. An increase in the proportion of local usage results in a cost increase while anincrease in the proportion of toll usage reduces production costs ceteris paribus.The significant second-order term for product mix suggests that production costsincrease at an increasing rate with the proportion of local calls. One plausibleexplanation for these estimates is that there may exist economies of scope in thejoint production of local and toll calls. As Gabel and Kennet (1994) pointed out,‘To a large degree, these economies of scope arise from the public input nature ofthe local loop.’ A network built for providing local services can be used inproviding toll services without incurring additional costs. For that reason, a greater

21 Since our estimate of the linear parameter for toll calls is insignificant, marginal cost of toll calls atthe mean value is zero. Away from the mean values, however, there are observations with negativemarginal cost. Although most of these negative marginal costs are statistically zero on an individualbasis, they are jointly non-zero. This may well result from the multicollinearity problem between outputvariables that traditional treatment of these variables cannot resolve.

22 See Gabel and Kennet (1994).


proportion of toll services may indicate that the network is more effectively23utilized.

We use two variables to proxy technological change. The level of electronicswitching equipment is used to represent the observed component, and a time

24trend is used for the unobserved component. The first-order parameter estimatesfor these two variables (from the heterogeneity specifications) are negative and ofsmall magnitudes. These indicate that technology has slight cost-reducing effectsover the sample period. The negative second-order parameter estimates forelectronic switching equipment suggest that its cost-reducing effects diminish aselectronic switching equipment increases. The estimate of the second-order termfor the time trend has such a small magnitude (with all specifications) that itseffects on LECs’ costs are negligible. These estimates of small magnitudes are notsurprising. First, electronic switches are widely used by the LECs in the sample.Note that the mean value of the technology proxy is 0.952 (see Table 2), and manyLECs have 100% electronic switches. These estimates suggest diminishing returnsto the deployment of electronic switches. Second, technological change can beprocess-oriented, which helps reduce production cost, or product-oriented, whichhelps LECs produce new services. The small magnitude of the first-order andsecond-order estimates for the time trend may be an indication that the technologi-cal progress witnessed so far in the telecommunications industry has been moreproduct-oriented than process-oriented.

Parameter estimates for the linear term on central offices and average looplength are insignificant for the heterogeneity specifications. This suggests that themarginal effects of number of central offices and average loop length arenegligible on LECs’ costs. Examining the interactive terms between factor prices,access lines, and product mix, we see that labor shares decrease with the numberof access lines and increase with the proportion of local calls. However, capitalshares increase with access lines and decrease with the proportion of local calls.These estimates suggest that larger LECs with more access lines and handling agreater proportion of toll calls in their product mix tend to be more capital-intensive while those handling large volumes of local calls over smaller (and

25probably congested) networks appear to be more labor-intensive. Finally, theinteractive terms between factor prices and time trend from heterogeneity

23 Since on average the proportion of toll calls accounts for only 16.8% of the total number of localand toll calls combined (see Table 2), this explanation is plausible within the confines of the networkconfigurations found in the current sample. It may be questionable if the proportion of toll calls isgreater than 50%.

24 We also tried using year dummies, which yield very similar results.25 Note that we are commenting on smaller telephone networks greater labor-intensiveness relative to

larger telephone networks, not to other industries.


specifications indicate that labor shares have been declining, while capital shareshave been increasing. These results are consistent with the stylized facts thattelecommunications are becoming increasingly capital-intensive, and telecom-munications firms have been investing heavily in new production facilities and

26down-sizing their workforce.

4.2. Non-heterogeneity models

The non-heterogeneity specifications yield several parameter estimates that arequantitatively different from those of the heterogeneity models. Among thedisparities, the first obvious difference is the estimated coefficient for access lines.For the product-mix specification, the parameter estimate is 0.99 (versus 0.80 in itsheterogeneity counterpart), and for the three-output specification it is 1.00 (versus0.74). These estimates imply that there are no scale economies associated withaccess lines (at mean values of the other variables). Another difference is theparameter estimates for electronic access: 20.22 and 20.27 from both non-heterogeneity specifications vs. 20.085 and 20.068 from the two heterogeneityspecifications. The former pair is three to four times as large in magnitude as thoseresulting from the heterogeneity specifications. These results along with thosepresented in the previous subsection point to the extreme sensitivity associatedwith the treatment of unobserved heterogeneity. The sensitivity is even morepronounced in the results of subadditivity tests.

5. Subadditivity

Our parameter estimates based on the heterogeneity specifications suggest thatlocal telephone companies exhibit scale economies. The estimates based on thenon-heterogeneity specifications suggest that there are no scale economies. Wenow assess whether the cost structure estimated with these LEC data are consistentwith natural monopolies. In so doing, we simulate costs and conduct a series ofsubadditivity tests similar to those of Evans and Heckman (1983, 1984) and Shinand Ying (1992). Conceptually, a firm is a natural monopoly if and only if its costfunction is globally subadditive. A typical subadditivity test determines whetherthe following inequality holds:

A BC(Y) , C(Y ) 1 C(Y ), (6)

A Bwhere Y is an output vector of a monopoly and Y and Y are the output vectorsA Bof hypothetical firms (A and B) such that Y 5 Y 1 Y . If the inequality holds, the

26 The three-output specification controlling for heterogeneity yields similar implications.


firm’s cost function is subadditive, and the firm is considered to be a naturalmonopoly.

We conduct subadditivity tests on all four cost specifications. For the three-output specifications, the hypothetical multiple-firm industry structure with firms Aand B, the outputs are defined as:

AY 5 (l Y , l Y , l Y ),1 1 2 2 3 3 (7)BY 5 ((1 2 l )Y , (1 2 l )Y ), (1 2 l )Y ),1 1 2 2 3 3

where Y , Y , and Y represent local usage, toll usage, and access lines and l , l ,1 2 3 1 2

l 5 (0.1, 0.2, . . . , 0.9). For the product-mix specifications, we have two sets of3

tests with different treatments of the product mix. In our first set of tests, we holdproduct mix as constant and use access lines as the only output variable Y . The1

two hypothetical industry outputs are defined as:

AY 5 (uY ),1 (8)BY 5 ((1 2u )Y ),1

where u 5 (0.1, 0.2, . . . , 0.9). This is equivalent to varying the hypotheticaloutputs without changing the product mix. In the second set of tests, we allow theproduct mix to vary. Using Y , to represent the product mix, we then define2

outputs for firms A and B as:

AY 5 (u Y , u Y )1 1 2 2 (9)BY 5 ((1 2u )Y , (1 2u )Y ),1 1 2 2

where u , u 5 (0.1, 0.2, . . . , 0.9). By constraining ls and us to this range, we rule1 2

out zero outputs and specialized product mix (a reasonable restriction in thisindustry). All remaining variables are held constant. Since competitive entry is amore likely policy option than breaking up incumbent local monopolies, weconduct subadditivity tests by allowing each hypothetical firm to have the same

27number of central offices as the monopoly firm.We have altogether 401 valid observations, each with 365 unique hypothetical

output configurations for the three-output specification, and 41 unique hypotheticaloutput configurations for the product-mix specifications (when we allow theproduct mix to vary). Our subadditivity tests yield a measure of cost subadditivity(S defined below) for each pair of 146 365 (401*365) output configurations in the

27 Considering that access lines are connected to and switched in central offices, we alsoexperimented with varying central offices of each hypothetical firm. We give hypothetical firms thesame proportions of central offices to their proportions of access lines. That is, if firm A is given 10%of the access lines, its proportion of the central offices is also 10%. Our test results are similar to whatis presented.


case of the three-output specifications, and for each pair of 16 441 (401*41) outputconfigurations in the case of the product-mix specifications. The hypothetical costsavings (or increases) owing to breaking up monopolies are computed as:

A BC(Y ) 1 C(Y ) 2 C(Y)]]]]]]]S 5 100. (10)

C(Y)

Note that S . 0 implies subadditivity (i.e., percentage cost increases from breakingup a monopoly), whereas S , 0 indicates superadditivity (i.e., percentage costsavings from replacing monopoly production with multiple-firm production).

In examining subadditivity in the three-output model, we compare the results ofour subadditivity tests from the three-output specifications with and withoutheterogeneity controls. Because of the extensive data, we summarize the results inthe text and present the results for various levels of local and toll call usage (i.e.,

28we vary l and l ), holding the distribution of access lines constant at l 50.5.1 2 3

When using parameter estimates from the non-heterogeneity three-output model,we find LEC costs are generally superadditive. Approximately 58% of thesimulated output configurations exhibit superadditive costs. The simulated costchanges incurred by replacing single-firm production with two-firm productionrange from 29.21% to 3.47% with an average value of 20.78%. (Tables 4 and

295) Superadditivity of costs is more pronounced when we test the product-mixspecifications without heterogeneity controls. (See Table 5 for details.) Spe-cifically, the simulated cost changes from replacing single-firm production withtwo-firm production range from 268.92% to 211.32% when product mix isallowed to vary, with an average value of 232.44%.

These results are qualitatively consistent with empirical findings by Evans andHeckman (1983) and Shin and Ying (1992), although the magnitudes of costchanges differ. For instance, across different specifications the percentage costchanges by multiple-firm production simulated by Evans and Heckman (1983)range from 217% to 25%, but none of these figures are statistically different from

30zero. Hence, they conclude that the cost function is locally additive. The averagepercentage cost savings by multiple-firm production obtained by Shin and Yingrange from 0.94% to 3.8%, depending on whether positive marginal costs and thenumber of central offices are controlled for in simulating the cost function.

28 We have conducted all subadditivity tests described in the text. The tables are available from theauthors upon request.

29 These are mean values of simulated cost changes. Note that negative cost changes are costreductions; therefore, 3.47% is a cost increase whereas 29.21% a cost reduction. We present the resultsof our subadditivity tests in this format. (See Tables 4 and 5.)

30 Evans and Heckman also point out, however, that subadditive cost function is possible at outputvectors other than those realized in their sample. They state explicitly that their results are ‘tooimprecise to evaluate the relative costs of particular industry configurations.’


Table 4Percentage change in costs from multiple-firm versus single-firm production with traditional output

atables (l 5 0.5)3

l 5 0.2 l 5 0.4 l 5 0.5 l 5 0.62 2 2 2

Spec. 1 Spec. 2 Spec. 1 Spec. 2 Spec. 1 Spec. 2 Spec. 1 Spec. 2

l 5 0.2 20.4011 12.4002 20.9108 12.0535 21.0078 12.0858 21.0344 12.21831

(0.2656) (3.1277) (0.2624) (3.0640) (0.2622) (3.0602) (0.2583) (3.0694)

l 5 0.4 0.4272 13.6255 0.0383 13.1076 20.0140 13.07981

(0.1860) (2.9808) (0.1885) (2.9149) (0.1912) (2.9095)

l 5 0.5 0.4475 13.8209 0.1061 13.2377 0.0727 13.18501

(0.1928) (2.9700) (0.1948) (2.9023) (0.1974) (2.8962)

l 5 0.6 0.2982 13.8004 0.0008 13.15691

(0.1866) (2.9865) (0.1886) (2.9165)

l 5 0.8 20.8262 12.98401

(0.2529) (3.1464)

a Standard errors are in the parentheses.

When using parameter estimates from the heterogeneity models, we find verydifferent results in that LEC costs are subadditive in general. Out of 146,365output configurations from the three-output specification, only 1411 (i.e., less than1%) exhibit superadditive costs. The hypothetical cost changes range from a low

31of 1.96% to a high of 15.37%. The average value of cost increases is 10.53%. Asfor the product-mix specification, the subadditivity of costs appears to be much

Table 5aPercentage change in costs from multiple-firm versus single-firm production with product mix

u 5 0.2 u 5 0.4 u 5 0.5 u 5 0.62 2 2 2

Spec. 3 Spec. 4 Spec. 3 Spec. 4 Spec. 3 Spec. 4 Spec. 3 Spec. 4

u 5 0.2 218.8319 19.5479 223.8140 11.4752 227.9456 12.1749 233.3002 15.67641

(0.7704) (5.0478) (1.1476) (4.3308) (1.2956) (4.7024) (1.4124) (5.4970)

u 5 0.4 228.5417 31.1406 226.5510 15.9096 227.5145 15.16681

(1.0004) (7.1920) (1.2424) (5.0693) (1.3020) (5.0497)

u 5 0.5 233.5351 35.5294 228.0795 16.9485 227.4638 15.50861

(1.1125) (8.1016) (1.2872) (5.2923) (1.3028) (5.0901)

u 5 0.6 238.6209 39.1235 229.7085 17.29571

(1.2233) (8.9419) (1.3304) (5.4369)

u 5 0.8 249.1158 43.76181

(1.4415) (10.4594)

a Standard errors are in the parentheses.

31 These are mean values of simulated cost increase. Due to the small proportion of superadditivecases, cost reductions are ‘averaged’ away. Note that Tables 4 and 5 only present a selected sample ofthe subadditivity results, for the complete set of subadditivity test results is too large to present. It isavailable upon request.


more pronounced. The hypothetical cost increases range from a low of 3.19% to a32high of 122.5%, with an average value of 29.82% when product mix varies. (See

Table 5 for details.) These results are qualitatively consistent with findings by¨Charnes et al. (1988) and Roller (1990a,b). According to Charnes et al., for

instance, the hypothetical costs of multiple-firm production are 15% to 34% higherthan single-firm production on average, and the maximum cost increase due to

¨multiple-firm production is 86%. Depending on the specifications used, Roller(1990a) finds that multiple-firm production costs 7% to 47% more than single-firmproduction.

These results strongly suggest that subadditivity tests are sensitive to thespecifications of cost functions. Therefore, they raise serious questions about thevalidity of the premise that local telephone markets are unnatural monopolies.

6. Concluding remarks

Recent telecommunication policy has been based at least in part on the findingthat costs in the industry are not subadditive. This finding suggests that theindustry is not a natural monopoly and that there is no loss of efficiency fromopening entry to local exchange markets. A review of the previous literaturesuggests that subadditivity is far from a resolved issue and calls into question thepremise of such a policy. In particular, some previous research has yielded costfunctions that exhibit negative estimates of marginal costs and nonconcavities. Inaddition, still other research suggests that there are a number of deficiencies in theeconometric specification of cost functions in this literature. While we do not claimto have fully addressed the issues raised by the previous research, due to datalimitations, we have attempted in this paper to take steps to overcome some of thedifficulties attributed to the previous research.

The central objective of our research is to reexamine the natural monopoly issuepertaining to local telephone markets. We use the most recent data available toestimate cost functions for LECs with and without controls for unobservedheterogeneity in costs and factor shares. We also introduce alternative treatmentsof output and compare those with some of the recent research. The resultingestimates enable simulations of the costs of LECs and allow subadditivity tests tobe conducted on all specifications. The results of the subadditivity tests aresensitive to heterogeneity controls but not to the treatment of output. Inspecifications with controls for unobserved heterogeneity incorporated, LEC costsappear to be subadditive; however, without these controls, LEC costs appear to besuperadditive. These findings hold regardless of the alternative treatments ofoutput.

32 Again, these are mean values of simulated cost increases.


These findings have strong policy implications. The subadditive costs of LECssuggest that it may be premature to deregulate the local telephone markets andsubject LECs to competitive entry. It is likely that regulated incumbent localexchange carriers are natural monopolies. Therefore, forcing them to open theirmarkets for competitive entry may result in undue competition and efficiency loss.

The diametrically different results we obtained, again, strongly suggest thatsubadditivity tests are sensitive to the specifications of cost functions. Given thestrong empirical evidence in favor of heterogeneity controls and the results of oursubadditivity tests, we believe that future research needs to be targeted not only atidentifying the sources of currently unobserved heterogeneity, but also at develop-ing data and measures of these sources.

Acknowledgements

The authors gratefully acknowledge comments from Bruce Blonigen, DavidFiglio, Larry Singell, Jim Ziliak and an anonymous referee on this research, andthank Tae Hoon Oum and Yimin Zhang for providing information on data sourcesand alternative variable measures.

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Telecommunications deregulation and subadditive costs: Are local telephone monopolies unnatural?

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