Was the bell system a natural monopoly? An application of data envelopment analysis

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1 Ann Oper Res (2006) 145: DOI /s Was the bell system a natural monopoly? An application of data envelopment analysis Hsihui Chang Raj Mashruwala Published online: 23 June 2006 C Science + Business Media, LLC 2006 Abstract Examination of the relation between scale economies and natural monopoly has been a central issue in public policy research. The paper employs Data Envelopment Analysis (DEA) methodology to re-examine the issue of natural monopoly for the Bell system with annual time series data for Results from the DEA-based statistical tests reveal the prevalence of increasing returns to scale for the Bell system, implying that there were economies of scale for the Bell system. This evidence suggests that the Bell data was indeed consistent with a natural monopoly. Further, the results indicate that the low level of overall efficiency primarily results from allocative inefficiency rather than technical and scale inefficiency. Keywords DEA. Bell system. Returns to scale. Inefficiency 1. Introduction Examination of the relation between scale economies and natural monopoly has been a central issue in many public policy related studies. Conventional wisdom for this relation has been that a natural monopoly has economies of scale that are large relative to the size of the market. However, we do not deal with market size here. Instead, we direct our study to the exchanges on this topic such as those that occurred in the context of the U.S. Justice Department studies conducted for their case against AT&T that led to the breakup of the Bell System. In particular, we deal with the studies of Evans and Heckman (1983, 1984, 1988) and the resulting exchanges with Charnes, Cooper, and Sueyoshi (1988) as well as other studies that we will cite. Nothing was said about the size of the market in these exchanges probably H. Chang ( ) Whitman School of Management, Syracuse University, Syracuse, NY swhchang@syr.edu R. Mashruwala Olin School of Business, Washington University in St. Louis, St. Louis, MO mashruwala@wustl.edu

2 252 Ann Oper Res (2006) 145: because it was regarded as a non-issue due to the huge size of the market served by Bell. Not only did Bell serve the entire U.S., it also extended that market to the entire world on its transatlantic and transpacific services and, due to regulatory activities, competition by other firms was not allowed. This approach was rationalized by the natural monopoly arguments in economics that revolve around the returns-to-scale considerations that are dealt with in this paper. To investigate whether the Bell system exhibited characteristics of a natural monopoly, we employ Data Envelopment Analysis to examine the returns to scale from the production function perspective. Increasing returns to scale suggests that a proportionate change in the level of inputs results in a more than proportionate change in the level of outputs. More specifically, if a firm has increasing returns to scale then the firm s average costs can be further reduced by increasing its scale of operation. Therefore, increasing returns to scale implies that there are economies of scale, which in turn, implies a natural monopoly. Following the divestiture of AT&T in 1984, there has been substantial debate among researchers whether the Bell system was in fact a natural monopoly. The issue remains important in the contemporary telecommunications economics literature (Majumdar and Chang, 1996; Cave, Majumdar, and Vogelsang, 2002). As part of the econometric evidence in supporting the Justice Department s action to break-up Bell, Evans and Heckman developed a test for a natural monopoly that employs regression analysis of a translog cost function specification. They applied this test to the Bell system for the years 1958 through 1977 and found that subadditivity did not hold. Based on this evidence, Evans and Heckman claimed that the Bell system did not have a natural monopoly over any of the output configurations which were realized between 1958 and Evans and Heckman used these findings in laying out the plan that the courts subsequently followed in breaking up AT&T into (1) AT&T itself and (2) the local phone companies, which came to be known as baby Bells. However, Evan and Heckman s test of subadditivity for the Bell system cost function has led to considerable debate. Their findings contradict those of related studies such as Charnes, Cooper, and Sueyoshi (1988) and Roller (1990), among others. For instance, Charnes, Cooper, and Sueyoshi (1988, hereafter referred to as CCS) use the same data and employ the same functional form (e.g. a translog cost function) as Evans and Heckman but reach the opposite conclusion. In fact, the resulting estimates of CCS reversed every one of the findings of Evans and Heckman. 1 Note that Evans and Heckman used central tendency estimates derived from regressions to reach their conclusions while CCS used frontier estimates obtained from a goal-programming-constrained regression model which permits only one-sided deviations. CCS noted in their work that the economic assumptions of efficiency used by Evans and Heckman played a crucial role in reaching their conclusions. They believed that the use of OLS regressions that yield only central tendency estimates was not up to what was required to reflect these assumptions. Importantly, though, neither the approach of Evans and Heckman nor that of CCS circumvented the problems associated with the use of the translog function and like approximations. These can be serious as shown by Charnes, Cooper, and Schinnar (1982) who show that good approximations with a translog function in one region of a production possibility set will yield bad approximations in other regions of that set. This suggests that good statistical fits in one region will yield bad extrapolations to other regions. 1 We thank Professor William W. Cooper for providing us with a historical perspective of the literature surrounding the break-up of AT&T.

3 Ann Oper Res (2006) 145: Clearly, no consensus seems to have emerged from these studies and this still remains an open question: was the pre-divestiture Bell system indeed a natural monopoly? To address this issue we employed a nonparametric Data Envelopment Analysis (DEA) approach to estimate the production function for Bell system prior to its break-up and to assess its production characteristics, particularly the pattern of returns to scale. Our choice of using nonparametric DEA methodology to examine this issue is guided by two reasons. Firstly, DEA enables us to directly estimate a production set with multiple inputs and multiple outputs (e.g., three inputs and two outputs) instead of estimating it indirectly by assuming a specific structure for the production function as in parametric regression analyses. Although flexible functional forms such as translog can be used to approximate the unknown true production function, these estimations involve several assumptions and various robustness problems as argued by CCS and Roller (1990). Moreover, the methodologies used in earlier studies examining this issue assume that the chosen functional form holds for the data over time. This assumption ignores the possibility that technological progress can change the functional form itself over time. These problems, which are inherent in parametric estimation methods, can be overcome by using DEA. More importantly, since DEA specifies only a broad structure on the production function, the estimates and statistical test results obtained using DEA are likely to be more robust than those of traditional parametric methods (Banker and Maindiratta, 1988). DEA is thus better suited to modeling and testing for a natural monopoly than parametric methods. The second reason for employing DEA is that previous studies that have worked with the Bell data have stayed within the parametric world. As CCS suggest, it is prudent to employ different methodologies to examine whether the results are consistent with each other. 2 The CCS goal programming-constrained regression estimates were criticized by Evans and Heckman for lack of statistical characterizations and associated tests of significance. Banker (1993) showed that DEA estimates like we are using can be associated with statistical sampling distributions and, under the same assumptions that guided Evans and Heckman, these estimates can be submitted to statistical tests of significance. Hence, our use of non-parametric DEA estimates possess statistical properties which allow the use of statistical tests of significance. To evaluate the hypotheses for returns to scale, we follow the work of Banker and Chang (2002) and propose two DEA-based statistical test procedures. Monte Carlo studies have shown that these DEA-based statistical tests are more robust than those of conventional parametric tests in small sample sizes (Banker and Chang, 1995, 2002). We find strong evidence supporting the hypothesis that the Bell system was indeed a natural monopoly. The evidence we obtain is not even neutral to the technological changes because the nature of production function had shifted from labor intensive to capital intensive. The relative share of capital increased while the relative share of labor showed a corresponding decrease. In addition, our results also indicate that the lower level of overall inefficiency is primarily due to lower allocative efficiency. Given increasing returns to scale prevailing for the Bell system, our results are consistent with the findings of CCS and Roller (1990). The remainder of the paper is organized as follows. In Section 2, we describe Data Envelopment Analysis and the hypothesis tests for returns to scale. We also propose two DEA-based test procedures to test our hypothesis. In Section 3, we describe the data used in the study and present the analysis and empirical results that support the finding that the pre-divestiture Bell system was a natural monopoly. Finally, we present our main findings and concluding remarks in Section 4. 2 Our study is very much in the spirit of avoiding the methodological bias associated with using only one approach that is noted as a motive in the article by Charnes, Cooper, and Sueyoshi (1988).

4 254 Ann Oper Res (2006) 145: Data envelopment analysis and hypothesis tests DEA provides a nonparametric approach to estimate the production function and evaluate the production efficiency of similar decision making units (DMUs) from observed data. Let Y and X be the observed output and input for DMUs. We can represent the production possibility set as: T ={(X, Y ) Y 0 can be produced from X >= 0}. (1) The inefficiency is measured radially by the reciprocal of Shephard s (1970) distance function. Thus, the inefficiency of an observation (X 0, Y 0 ) T is given by: θ(x 0, Y 0 ) = sup{θ (X 0 /θ, Y 0 ) T } (2) Banker (1993) specifies the following structure for the production set T and the probability density function f (θ) for the inefficiency θ: Postulate 1: Convexity If (X 1, Y 1 ) T and (X 2, Y 2 ) T then (λ 1 X 1 + λ 2 X 2, λ 1 Y 1 + λ 2 Y 2 ) T for all λ 1, λ 2 0 such that λ 1 + λ 2 = 1. Postulate 2: Monotonicity If (X 1, Y 1 ) T, X 2 X 1 and Y 2 Y 1 then (X 2, Y 2 ) T. Postulate 3: Envelopment If θ<1 then f (θ) = 0. Postulate 4: Likelihood of Efficient Performance If δ>0then 1+δ 1 f (θ)dθ >0. To estimate pure technical efficiency e v = 1/θ v, the following DEA model of Banker, Charnes, and Cooper (1984) (BCC hereafter) may be employed: subject to θ v (X 0, Y 0 ) Max θ (3.0) N λ j X j X 0 /θ 0 (3.1) j=1 N λ j Yj Y 0 (3.2) j=1 N λj = 1 (3.3) j=1 θ and λ j 0. (3.4) Banker (1993) shows that the DEA estimator of θ v using the BCC model described in (3) is statistically consistent and the asymptotic empirical distribution of the DEA estimator retrieves the true distribution of θ v under the assumptions embodied in the four postulates.

5 Ann Oper Res (2006) 145: These postulates are consistent with variable returns to scale in that they do not impose the constraint of constant returns to scale. We shall refer to such an inefficiency measure as θ v. If additional information that the production set exhibits constant returns to scale is imposed, then by adding the postulate 5 below, we obtain the so-called CCR inefficiency estimates θ c (Charnes, Cooper, and Rhodes, 1981) by solving the same linear program as before except (3.0) is maximized subject only to (3.1) (3.2) and (3.4). Postulate 5: Constant Returns To Scale If (X, Y ) T then (kx, ky) T for anyk > 0. The CCR estimator is also statistically consistent under the maintained assumptions reflected in postulate 1, 2, 3, 4, and 5. We refer to the CCR inefficiency measure as θ c. Since the CCR model enables us to estimate overall technical and scale inefficiencies and the BCC model helps us estimate the pure technical inefficiency of a DMU at the given scale of operation, we can divide the aggregate inefficiency obtained from CCR by the pure technical inefficiency from BCC to obtain the scale inefficiency estimate θ s. As described earlier, DEA estimators are statistically consistent. Therefore, under the null hypothesis of constant returns to scale, the asymptotic empirical distributions of DEA estimators θ v and θ c are identical, each retrieving the true distribution of θ. The asymptotic correspondence between the empirical distributions of θ v and θ c under the null hypothesis of constant returns to scale motivates the following two statistical tests: (i) If we maintain the assumption that θ is exponentially distributed over [1, ) with mean 1 + σ, then the sum (θ j 1)/σ over all N sample observations follows the chi-square distribution with 2N degrees of freedom and our test-statistic T 1 (θ c j 1)/ (θ v j 1) is evaluated by the F-distribution with (2N, 2N) degrees of freedom. (ii) If we maintain the assumption that θ follows a half-normal distribution over the range of values [1, ) with mean 1 + σ, then the sum of squares (θ j 1) 2 /σ 2 over all N sample observations follows the chi-square distribution with N degrees of freedom and our test statistic T 2 (θ c j 1) 2 / (θ v j 1) 2 is evaluated by the F-distribution with (N, N) degrees of freedom. To test whether increasing (decreasing) returns to scale holds for the sample, we impose non-decreasing (non-increasing) returns to scale on the production set to obtain the inefficiency estimator by solving the BCC model in (3) with (3.3) less (greater) than or equal to 1. We refer to the inefficiency measure as θ i (θ d ). Since the non-decreasing (non-increasing) returns to scale production frontier envelops the observed data less closely than the variable returns to scale production frontier, the resulting inefficiency measure θ i (θ d ) is greater than or equal to that calculated from the variable returns to scale production set. For any DMU, equality implies the prevalence of non-increasing (non-decreasing) returns to scale and inequality implies the more restrictive property of increasing (decreasing) returns to scale. The test statistics can be constructed similar to those for constant returns to scale except in this case θ i (θ d ) is substituted into the numerator (numerator) under the null hypothesis of non-increasing (non-decreasing) returns to scale. Alternatively, since the constant returns to scale production frontier envelops the data less closely than non-decreasing (non-increasing) returns to scale, its inefficiency estimate θ c is greater than or equal to that calculated from nondecreasing (non-increasing) returns to scale. The test statistics are again similar to those for constant returns to scale except that θ i (θ d ) is substituted into the denominator (denominator) if non-decreasing (non-increasing) returns to scale is assumed. In addition, the returns to scale

6 256 Ann Oper Res (2006) 145: can be identified as decreasing, constant, or increasing on the basis of the value of N j=1 λ j, where λ j is the optimal value of λ j obtained from the CCR model described earlier. Decreasing returns to scale are indicated for N j=1 λ j > 1, constant returns to scale are indicated for N j=1 λ j = 1, and increasing returns to scale are indicated for N j=1 λ j < 1 over all possible solutions. Returns to scale, nevertheless, is a dynamic concept since changes in technology can alter the efficient scale in an industry (Majumdar and Chang, 1998). Such changes not only affect the cost structure of existing firms relating to the shift in the substitution between inputs, but also the range of outputs over which the returns to scale can apply. It is, therefore, meaningful to examine the inefficiency impact of misallocation of input resources at different points of time with all factors of production also varying. To investigate allocative inefficiency when substitution possibilities have not been utilized, we employ the estimation procedure of Banker and Maindiratta (1988), 3 maintaining the DEA assumptions embodied in the four postulates. Specifically, we first estimate the efficient cost C (Y 0, P 0 ) for an observation with outputs Y 0 and input prices P 0 using the following linear program: subject to C (Y 0, P 0 ) Min x N P 0 X (4.0) j=1 N λ j X j X 0 (4.1) j=1 N λ j Y j Y 0 (4.2) j=1 and λ j 0. (4.3) The allocative efficiency is then estimated by dividing the overall efficiency, C (Y 0, P 0 )/P 0 X 0, by the aggregate technical and scale efficiency estimated using the CCR model. 3. Empirical results and analysis The data used in this study is reproduced from Charnes, Cooper, and Sueyoshi (1988) and presented in Table 1. Each individual year, from 1947 to 1977 is considered as a DMU in the application of DEA. The inputs and outputs are similar to those used in CCS and Roller (1990). Inputs consist of capital, labor, and material quantity indices, whereas outputs are the quantity indices of local calls and toll calls. Real cost and R&D index are also included in Table 1. Traditionally, returns to scale in telecommunications has been identified as arising from two main sources. The first is from economies in the physical provision of basic services. Given the network of lines developed as part of the Universal Service infrastructure, it is 3 Banker and Maindiratta (1988) also show that if only the convexity and monotonicity assumptions are maintained then point estimates of the efficiency measures are not possible and only a range of values can be obtained.

7 Ann Oper Res (2006) 145: Table 1 Bell system quantities and prices data (Base period: 1967) a Local Toll Real Year Capital Labor Material output output cost b R&D t X1 P1 X2 P2 X3 P3 Y1 Y2 ($10 6 ) Index a Source: Charnes, A., W. Cooper and T. Sueyoshi. (1988). A Goal Programming/Constrained Regression Review of The Bell System Breakup. Management Science, 34, b Real cost (in $10 6 ) is derived from the formulations of R. W. Shephard (1970) by means of the following identity C t = 3 i=1 p it q it, where the cost is calculated with all prices relative to 1967 as a base period. See the row for 1967 in Table 1 and note that all prices are set at unity in this row to give the real cost shown on the right for this year. thought to be more efficient to have one single connection to each end use location, rather than 160 million telephones in the U.S. connected to each other which would result in a lot of duplication. Hence, higher-order connectivity is required, with transmission lines connected to switches that provide the network for the exchange or communication. This presupposes that returns to scale in switching and transmission of signals enables service to be best provided within a local area through one or more switches, giving rise to a minimum efficient network size (Littlechild, 1979).

8 258 Ann Oper Res (2006) 145: Table 2 DEA-based statistical test results of returns to scale Test statistic Null Hyp. Alt. Hyp. F-Statistic P > F Panel A: When the inefficiency is assumed to be exponentially distributed / 31 j=1 ( ˆθ C 31 j 1) j=1 ( ˆθ j B 1) CRS VRS / 31 j=1 ( ˆθ C 31 j 1) j=1 ( ˆθ j I 1) NDRS DRS / j=1 ( ˆθ j D 1) j=1 ( ˆθ j B 1) NDRS DRS / 31 j=1 ( ˆθ C 31 j 1) j=1 ( ˆθ j D 1) NIRS IRS / j=1 ( ˆθ j I 1) j=1 ( ˆθ j B 1) NIRS IRS Panel B: When the inefficiency is assumed to be half-normally distributed 31 j=1 ( ˆθ C j 1) 2/ 31 j=1 ( ˆθ j B 1) 2 CRS VRS j=1 ( ˆθ C j 1) 2/ 31 j=1 ( ˆθ j I 1) 2 NDRS DRS j=1 ( ˆθ j D 1) 2/ 31 j=1 ( ˆθ j B 1) 2 NDRS DRS j=1 ( ˆθ C j 1) 2/ 31 j=1 ( ˆθ j D 1) 2 NIRS IRS j=1 ( ˆθ j I 1) 2/ 31 j=1 ( ˆθ j B 1) 2 NIRS IRS CRS: Constant returns to scale; VRS: Variable returns to scale; NDRS: Non-decreasing returns to scale; DRS: Decreasing returns to scale; NIRS; Non-increasing returns to scale; IRS: Increasing returns to scale. Second, there can be managerial economies of size such as in network planning. A larger network may be able to handle randomly varying demand more efficiently by reallocating capacity between switching and transmission equipment (Majumdar, 1998). Planning and managing network resources may be cheaper, and if there are fixed costs of network management they can be spread over a greater number of lines in a bigger network (Greenwald and Sharkey, 1989). In reality, however, capacity is not static and constant adjustments to plant and equipment are being made. Technological change may change the mix of how technology and human capital interact over time which can also lead to observations of scale returns at differing output levels because of the substitution of labor by capital (Gold, 1981). In production economic theory the notion of increasing returns to scale is equivalent to scale economies since increasing returns to scale implies that average costs of producing a given level of different output mix can be further reduced by increasing the size of operation. Therefore, a natural monopoly holds if the production process displays increasing returns to scale since this implies that scale economies exist. We present the DEA-based statistical test results for returns to scale in Table 2. Panel A of Table 2 reports the results of constant, non-decreasing and non-increasing returns to scale under the assumption that the inefficiency estimates are exponentially distributed. We find that the null hypothesis of constant returns to scale is rejected at the 1% significance level, the null hypothesis of non-decreasing returns to scale cannot be rejected at any conventional level, and the null hypothesis of non-increasing returns to scale is rejected at the 1% significance level. Panel B of Table 2 provides results of the tests assuming that the inefficiencies follow a half-normal distribution. The results are similar to those reported in Panel A of the same table in that all support increasing returns to scale. Collectively, the results provide evidence supporting increasing returns to scale for the Bell system. This, in turn, implies the existence of scale economies based on which we can conclude that the Bell system was a natural monopoly.

9 Ann Oper Res (2006) 145: Table 3 Returns to scale characteristics ( ) Scale pattern CRS IRS DRS Number of observations Year observations 1953, 1956, 1957, 1947, 1948, 1949, 1970, 1971, 1972, 1958, 1960, 1962, 1950, 1951, 1952, , 1969, 1974, 1954, 1955, 1959, 1975, 1976, , 1963, 1967, 1965, 1966, 1967 CRS: Constant returns to scale. IRS: Increasing returns to scale. DRS: Decreasing returns to scale. Table 3 reports the number of DMUs that exhibit constant, increasing, and decreasing returns to scale. We find that 12 and 15 out of 31 year periods, respectively, are in constant and increasing returns to scale regions and only 4 are in the region of decreasing returns to scale. This implies that economies of scale could be further exploited in most periods by increasing the scale of operation since the actual operation size is less than the most productive scale size (Banker, 1984). Thus, were the Bell system to increase in size, further cost savings could be achieved. Again, this evidence is consistent with the natural monopoly hypothesis. We present the efficiency estimates in Table 4 and plot them graphically over the sample period in Fig. 1. Figure 1 suggests that the estimate of technical efficiency fluctuates over time and the scale efficiency measure does not change too much after However, the estimate of allocative efficiency increases over time until The results in Table 4 also indicate that the elimination of both technical and scale inefficiencies is likely to result in a less than two percent improvement on average. In contrast, a 12.16% reduction in costs would be realized if all allocative inefficiencies were eliminated. These results suggest that Efficiency Year TECH SCALE ALLOC OVERALL Fig. 1 Efficiency over Time ( )

10 260 Ann Oper Res (2006) 145: Table 4 Efficiency estimates TECH: DEA technical efficiency estimates. SCALE: DEA scale efficiency estimates. ALLOC: DEA allocative efficiency estimates. OVERALL: DEA overall efficiency estimates. YEAR TECH SCALE ALLOC OVERALL Mean Std. dev the overall inefficiency is a result of allocative inefficiency rather than technical and scale inefficiency. Table 5 reports the correlation matrix for efficiency estimates, the R&D index and time trend. The results reveal that the scale efficiency is highly correlated (at the 1% significance Table 5 Correlation matrix of efficiency estimates and R&D index and year (p-values in parentheses) TECH SCALE R&D YEAR TECH (0.0000) (0.0033) (0.9694) (0.9121) SCALE (0.1072) (0.0000) (0.0016) (0.0016) R&D (0.9424) (0.0128) (0.0000) (0.0001) YEAR (0.8363) (0.0001) (0.0001) (0.0000) Spearman correlations are above the diagonal and Pearson correlations are below the diagonal. Tech: DEA technical efficiency estimates. Scale: DEA scale efficiency estimates. R&D: R&D Index.

11 Ann Oper Res (2006) 145: Table 6 Ratio of optimal relative input to actual relative input Year CL LM MC CL: [Optimal Capital Input (X1 )/Optimal Labor Input (X2 )] / [Capital Input (X1)/Labor Input (X2)]. LM: [Optimal Labor Input (X2 )/Optimal Material Input (X3 )] / [Labor Input (X2)/Material Input (X3)]. MC: [Optimal Material Input (X3 )/Optimal Capital Input (X1 )] / [Material Input (X3)/Capital Input (X1)] Mean Std. dev level) with the R&D index and time trend. That is, the improvements in scale efficiency can be primarily attributed to the spending on R&D and the time trend. Technical efficiency, on the other hand, had little association with the R&D index and the time trend. This result supports Waverman s (1989, see pg. 89) assertion that Evans and Heckman, and CCS represented technological advance for AT&T s toll and local outputs by a proxy-the yearly research and development expenditures of Bell Labs. This proxy is not related to the actual pace of technological advance of specific components of telecommunications plant and thus its use in the empirical investigations added unknown bias to the results. Waverman argues that specific components of a telecommunications plant can have varying scale economies. For instance, microwave plants on a route-by-route basis have few scale economies, while cable and fiber optics have far greater economies of scale. Even so, given the lack of data on usage of specific components, Waverman uses Bell Labs research and development expenditures as a proxy for technical change in estimating the cost function of AT&T. Thus, like Waverman,

12 262 Ann Oper Res (2006) 145: we are restricted to Bell system data and therefore use research expenditures as a proxy for technological change. 4 The ratio of optimal relative inputs to actual relative inputs is given in Table 6. It shows the effects of technological advances on the firm s use of inputs, cost structures, and returns to scale. The implications of the shift in production technology are significant. Not surprisingly, first, the direction of technological change had been labeled capital intensive rather than labor intensive since the optimal mix of inputs requires more capital than labor. Second, the Bell system had adjusted the input mix to reflect the need of technological change. For instance, a higher share of the total cost was accounted for by capital. This observation also helps explain why the allocative efficiency as reported in Table 4 is increasing over time because the efficiency of input resources utilization is improved. Finally, since a capital intensive production technology (having significant fixed costs) could increase the returns to scale, our results supporting the increasing returns to scale hypothesis, exhibited by the statistical test procedures reported in Table 2, are not neutral and can also be attributed to technological advancement. This last finding is particularly interesting since it calls into question the assumption of the same production technology over time imposed either explicitly or implicitly in most previous studies using the Bell data including Evans and Heckman (1983, 1984), Charnes, Cooper, and Sueyoshi (1988) and Roller (1990). 4. Summary and conclusion In this paper we have employed the nonparametric Data Envelopment Analysis approach to address the question whether the Bell system represented a natural monopoly prior to its break-up. We argue that if a convex production set exhibits increasing returns to scale then economies of scale exist. This, in turn, suggests the existence of a natural monopoly. To test the hypothesis of returns to scale, we have employed two DEA-based statistical test procedures based on the consistency property of DEA estimators (Banker, 1993). We find strong evidence supporting increasing returns to scale for the Bell system. This evidence suggests that there were scale economies for the U.S. telephone industry prior to the Bell system break-up since it is less costly to provide local and toll calls services jointly by Bell system than to specialize and provide each separately by different firms. This is consistent with the natural monopoly hypothesis. Further, our results indicate that the increasing returns to scale is not Hicks-neutral to the shift in production technology. In fact, technological change has resulted in the production process becoming more capital intensive. This finding invalidates the underlying assumption imposed in most previous Bell system studies that the same functional form holds for the data over time. Acknowledgments We express our sincere gratitude to Professors William W. Cooper and Rajiv D. Banker for their helpful suggestions and comments. We appreciate the comments of Professor Wade D. Cook and two anonymous reviewers. 4 The breakup of Bell has been followed by a massive burst of technological change. Most of this activity has occurred in relatively new high tech industries, external to Bell, and much of it did not even exist at the time of these studies. There seems to be no compelling reason to believe that these developments were a result of the breakup of Bell.

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