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Spectrum Concentration and Performance of the U.S. Wireless Industry


This paper estimates the empirical relationship between concentration in mobile carriers’ holdings of radio spectrum and the performance of the U.S. wireless industry. Reduced-form regressions that use a 2012–2013 cross-section of approximately 700 Cellular Market Areas reveal a robust inverted-U relationship between spectrum HHIs and subscriber penetration rates—a measure of consumer welfare. The marginal effect of spectrum concentration is positive throughout the range of sampled markets—contrary to the conventional concentration-performance hypothesis. This pattern persists when spectrum concentration is separately measured for bands below 1 GHz and for rural areas. It is also shown not to be biased by the potential endogeneity of spectrum HHIs. This paper is distinguished by relating subscriber penetration rates to the quality and coverage of operator networks that supports efficiency explanations for operator size, and hence the benefits of structural concentration. These findings cast doubt on federal policies adopted as early as the 1927 Radio Act that attempt to equalize ownership of spectrum. Instead, our empirical results recommend measures that promote investment in wireless infrastructure and other non-spectrum factors.

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  1. 47 U.S.C. 4—Radio Act of 1927 (Feb. 23, 1927), section 17.

  2. U.S. Department of Justice, Ex parte submission of the U.S. Department of Justice, in the matter of Policies Regarding Spectrum Holdings, WT Docket 12-269, 11 April 2013 (“DOJ Ex Parte”).

  3. The FCC adopted this paradigm in its annual assessment of wireless competition. FCC, Implementation of section 6002(b) of the Omnibus Budget Reconciliation Act of 1993, Annual Report and Analysis of Competitive Market Conditions with Respect to Mobile Wireless, Including Commercial Mobile Services (Mobile Wireless Competition Report). Available at Beginning with the 2004 publication of its 9th Mobile Wireless Competition Report (2004), the FCC arranged its analysis of the industry under the three chapter headings of structure, conduct, and performance. That arrangement continued through the release of its 16th Report in 2013. Beginning with 17th Report in 2014, the FCC deviated somewhat from this organizational structure.

  4. Note that the simple correlation between the HHI of spectrum holdings and the HHI of subscribers is 0.1292.

  5. For example, in its AT&T-Qualcomm Order, the FCC states that it is concerned by possible aggregation of “…below 1 GHz spectrum, that has technical attributes important for other competitors to meaningfully expand their provision of mobile broadband services or for new entrants to have a potentially significant impact on competition.” See FCC, Application of AT&T Inc. and Qualcomm Inc. for Consent to Assign Licenses and Authorizations, WT Docket No. 11-18, Order, (2011) at ¶ 51.

  6. They separately fitted the relationship for the largest 50 CMAs and also for CMAs outside the largest 50. Also, they came to similar conclusions when the spectrum HHIs were computed for holdings below 1 GHz.

  7. Note also that, for some specifications, they found a U-shaped relationship between mobile prices and industry HHIs with the average industry HHI on the downward portion—contrary to the market power hypothesis.

  8. In 2011, Cox and SpectrumCo proposed to transfer AWS-1 licenses to Verizon in various CMAs, and also to make exchanges of Lower 700 MHz, PCS and AWS-1 licenses between Verizon and Leap Wireless. To address competitive concerns, the Commission conditioned the transaction on Verizon’s transferring many of its acquired AWS-1 licenses to T-Mobile (and receiving a few in return). See FCC, Memorandum Opinion and Order and Declaratory Ruling in the Matter of Applications of Cellco Partnership d/b/a Verizon Wireless and SpectrumCo LLC et al., WT Docket Nos. 12-4, 12-175, adopted Aug. 21, 2012, available at

  9. The combined surplus derived by individual consumers from mobile access is likely to underestimate aggregate welfare. Like other communications technologies, mobile services convey “network effects” in direct relation to the fraction of the population that adopts them. In that case the benefits of increased mobile penetration will be amplified when it generates spillovers for existing subscribers. The magnitude of this source of consumer welfare will likely be smaller for smaller geographic areas (e.g., CMAs) compared to larger ones such as that entire nationwide market.

  10. The 1992 version of the FTC/DOJ Horizontal Merger Guidelines endorsed the use of HHI for assets in addition to output and sales to evaluate mergers. See Section 1.41 of the FTC-DOJ Horizontal Merger Guidelines, reprinted in 4 Trade Reg. Rep.

  11. In response to a Circuit Court remand of its rules on ownership of PCS-band licenses, the FCC conducted an analysis of spectrum concentration in which it used spectrum HHIs. See FCC, Amendment of Parts 20 and 24 of the Commission’s Rules—Broadband PCS Competitive Bidding and the Commercial Mobile Radio Service Spectrum Cap, Report and Order, FCC 96-278 (Jun. 24, 1996), at ¶¶ 96–100 and Appendix A (showing a calculation of spectrum HHIs without weighting the bandwidth by population). More recently, however, the Commission has declined to use spectrum HHIs; the Commission noted that it “would mark a substantial departure from our traditional approach.” See FCC, In the Matter of Policies Regarding Mobile Spectrum Holdings, Expanding the Economic and Innovation Opportunities of Spectrum Through Incentive Auctions, Report and Order, 29 FCC Rcd 6133 (2014) (Mobile Spectrum Holdings R&O), at ¶ 249.

  12. See, e.g., Angrist and Pischke (2008, p. 213): “If you can’t see the causal relationship in the reduced form, it’s probably not there.” See, also, Angrist and Krueger (2001, p. 80): “Most importantly, if the reduced form estimates are not significantly different from zero, the presumption should be that the effect of interest is either absent or the instruments are too weak to detect it.”

  13. Daughety (1990) varies industry structure, and the HHI, by increasing the fraction of firms that behave as Cournot leaders competing with each other and with the remainder of the firms that behave as Cournot followers.

  14. There are 722 CMAs in the U.S. The first 305 of these included metropolitan areas (MSAs) that are defined by the Office of Management and Budget; the Gulf of Mexico was added later; the remaining 416 Rural Service Areas (RSAs) were established by the FCC. Collectively these areas are referred to as “CMAs.” See FCC, Cellular Market Areas, DA 92-109 (Jan. 24, 1992).

  15. Discrepancies with regard to boundaries between some adjacent CMAs resulted in misaligned subscription counts. In those cases, two or three CMAs were combined into one area so as to preserve the information. As a result of this aggregation, 12 mostly rural CMAs were absorbed, which further reduced the sample size.

  16. Burton et al. (2000) described the ways in which resellers increase competition in mobile services markets.

  17. Located at:

  18. These same control variables (income, education, commute travel time) have been used in several studies of cellular subscription demand. See, e.g., Parker and Roller (1997), Busse (2000), Rodini et al. (2003), Ward and Woroch (2010), Seim and Viard (2011), and Macher et al. (2017).

  19. The FCC has often measured the extent of wireless deployment in terms of “road miles” that are covered by the networks. It is likely that travel time and road miles are highly correlated.

  20. The few CMAs that are located in Alaska and Hawaii were dropped from the estimation sample due to incomplete data.

  21. See Mackey (2012) for state and local taxes that are applied to mobile wireless services in mid-2012. Those taxes ranged from a low of 7.67% in Oregon to a high of 24.49% in Nebraska exclusive of the federal USF rate of 5.82%.

  22. Sun (2016) constructed a comprehensive dataset for the state of Connecticut and estimated a structural model that shows that increases in a carrier’s base station density result in a greater market share for the carrier and reduced shares for its rivals.

  23. The F-tests of the joint hypotheses that both coefficients are zero are not reported here because they parallel the outcomes of the tests of the margins that are found at the bottom of Table 2.

  24. Unexpected coefficients such as this could also be caused by severe multicollinearity. As a check I computed the Variance Inflation Factors for variables in the base regression and found the VIF for log of travel time to be 2.81. None of the control variables suggested a problem, as they had VIFs ranging from 2.47 to 5.84. As expected, the VIFs of the linear and squared terms were enormous. Thanks to Jim Prieger for suggesting this check.

  25. See 20th Mobile Wireless Competition Report (2017) at ¶ 35 and DOJ Ex Parte at 12–13.

  26. In addition, we cannot reject the null hypothesis that both the linear and quadratic coefficients on low-frequency HHIs are both equal to zero.

  27. See DOJ Ex Parte at 12–14.

  28. The FCC adopted this criterion in the context of spectrum policy making. See FCC, Facilitating the Provision of Spectrum-Based Services to Rural Areas and Promoting Opportunities for Rural Telephone Companies to Provide Spectrum-Based Services, WT Docket No. 02-381, Report and Order and Further Notice of Proposed Rule Making, 19 FCC Rcd 19078, 19123 (2004) ¶¶ 2, 79–80.

  29. Spectrum licenses have since been issued for a variety of geographic areas including basic and major trading areas, economic areas, partial economic areas, and counties, among other delineations. Auctions that allow combinatorial bidding further obscure the boundaries of the geographic regions that are covered by spectrum licenses.

  30. Hausman (1997) adopted this method to construct instruments for endogenous prices.

  31. Three conditions must hold to ensure consistent estimation of treatment effects: conditional independence; treatment overlap; and independence of outcomes across treatment groups. See, e.g., Cameron and Trivedi (2005, Section 25.4). The assumption of conditional independence—the assignment of CMAs to treatment groups is as-if random conditional on covariates—is not testable. It helps to have an abundance of covariates, and that is one reason that I included state fixed effects in the model. The overlap assumption—CMAs with similar covariate values receive all three treatments—is easily confirmed in our data.

  32. Demsetz (1973, p. 3) observed that “… output will tend to be concentrated in those firms fortunate enough to have made the correct decisions.” U.S. antitrust case law had earlier carved out an exception for firms that grew large as a result of such superior business decisions. Courts cautioned antitrust enforcers to make the distinction between “the willful acquisition or maintenance of that power as distinguished from growth or development as a consequence of a superior product, business acumen, or historic accident.” United States v. Grinnell Corp., 384 U. S. 571 (1966).

  33. While it was not the focus of their paper, Zhu et al. (2015) noted that Verizon had higher penetration in markets where its signal strength was above its nationwide average, and where AT&T’s signal strength was below its average.

  34. These included its “Binge On” feature in November 2015 and its unlimited “ONE Plan” in August 2016.

  35. FCC, 20th Mobile Wireless Competition Report (2017), Table II.C.1.

  36. Id., Chart II.B.5.

  37. Presumably, the coverage of 4G technology includes both LTE (Long Term Evolution) standard and non-LTE technologies.

  38. See, e.g., Lhost et al. (2015).

  39. DOJ Ex Parte at 11, and FCC, 2000 Biennial Regulatory Review Spectrum Aggregation Limits for Commercial Mobile Radio Services, WT Docket No. 01-14, Report and Order (2001), ¶ 44 and fn. 148.

  40. E.g., in the recent 600 MHz incentive auctions, the FCC set aside up to a “30 MHz reserve” for non-dominant bidders, which meant that less bandwidth was available for large carriers to bid on. Op. cit., Mobile Spectrum Holdings R&O, at ¶ 146.

  41. The (forward) incentive auctions offered bidding credits of 15% or 25% for qualifying small businesses and rural service providers. See FCC, Expanding the Economic and Innovation Opportunities of Spectrum Through Incentive Auctions, GN Docket No. 12-268, Report and Order, 29 FCC Rcd 6567, 6833-47 (2014) at ¶ 475.

  42. The FCC first imposed spectrum caps on Commercial Mobile Radio Services (CMRS) in 1994. FCC, Implementation of section 3(n) and 332 of the Communications Act—Regulatory Treatment of Mobile Services, GN Docket No. 93-252, Third Report and Order, 9 FCC Rcd (1994). Subsequently, it placed caps on licensed broadband PCS and Specialized Mobile Radio (SMR) spectrum. Over time it eliminated the various spectrum caps. See, e.g., the phase out of the CRMS cap in 2003, FCC, 2000 Biennial Regulatory Review Spectrum Aggregation Limits for CMRS, WT Docket No. 01-14, Report and Order, 16 FCC Rcd 22668, 22,710-11, ¶ 93 (2001).

  43. See FCC, Verizon Wireless-SpectrumCo Order, FCC 12-95 (2012) at ¶ 59 and FCC, Verizon Wireless-ALLTEL Order, 23 FCC Rcd 17,473 (2012) at ¶ 54. The FCC has added to, and subtracted from, the suitable and available bands over time. See, e.g., Mobile Spectrum Holdings R&O, ¶¶ 70–134.

  44. As specified in the incentive auctions, entities with less than 45 MHz of sub-1-GHz spectrum in a given service area were eligible to bid on a reserved block up to 30 MHz in size depending on initial spectrum clearing targets. Mobile Spectrum Holdings R&O, at ¶ 146.

  45. Mobile Spectrum Holdings R&O, at ¶¶ 279–289.

  46. For instance, in the recent incentive auctions, 28 rural telephone carriers qualified for a bidding credit of 15%. See FCC, Broadcast Television Spectrum Incentive Forward Auction, Attachment A, Qualified Bidders, July 15, 2016.

  47. Concerns over the physical limits of radio spectrum date back at least to the 1927 Radio Act. In the 1929 Congressional hearings on Continuing Power of the Act, Sen. Frederic Sackett (R-KY) stated “The spectrum of these wavelengths—I suppose it is called the spectrum—is very short.” Quoted in De Vries and Westling (2017).

  48. This incremental bandwidth will come from licenses to portions of the 24 GHz, 28 GHz, 37 GHz, 39 GHz, and 47 GHz mm-wave bands. See FCC, Use of Spectrum Bands Above 24 GHz For Mobile Radio Services, Report and Order and Further Notice of Proposed Rulemaking, 31 FCC Rcd 8014 (10), Aug. 29, 2018.

  49. Aaron Pressman, The FCC Just Wrapped Its First 5G Airwave Auction, Fortune, Jan. 24, 2019.

  50. It is estimated that at this time 715.5 MHz is suitable and available for mobile wireless use. See 20th Mobile Wireless Competition Report (2017), Table II.E.1.

  51. Nick Fox, “Say hi to Fi: A new way to say hello.” Official Google Blog (April 22, 2015) at:

  52. Comcast Introduces Xfinity Mobile: Combining America's Largest, Most Reliable 4G LTE Network and the Largest Wi-Fi Network, Comcast Corp. (Apr. 6, 2017) at

  53. FCC, Accelerating Wireless Broadband Deployment by Removing Barriers to Infrastructure Deployment, Third Report and Order and Declaratory Ruling, WT Docket No. 17-79 (Sep. 26, 2018).

  54. For instance, Sun (2016) has suggested that antitrust authorities should consider efficiencies that are derived from consolidation of base stations when reviewing mergers of mobile operators.

  55. MetroPCS subscriptions appeared in a separate category even though its acquisition by T-Mobile USA was officially completed in May 2013. It is likely that integration of the networks and customer bases took many months—if not years—to complete.

  56. Estimates of county populations for 2012 were extracted using the Census Bureau’s American Factfinder data tool:

  57. See GSMA Wireless Intelligence-United States, Data Dashboard (May 14, 2014). London: GSM Association. Available at In this article, GSMA states that U.S. consumers owned 1.57 wireless devices as of 2012. In its other data series, however, GSMA reports that Americans had 1.51 wireless connections—apparently making the distinction that not all wireless devices have an active connection.

  58. Located at:

  59. In some instances, multiple carriers were assigned the full spectrum holdings in the Cellular A and Cellular B bands. In that case the spectrum limit was divided equally among the license holders.

  60. See Description of the Transaction and Public Interest Statement, Exhibit 1, Appendix D, “Sprint Non-2.5 GHz Spectrum.” For the SMR band only Sprint’s spectrum holdings are considered.

  61. I imposed a 55.5 MHz cap on carrier holdings of these BRS bands according to the FCC’s determination of how much of this spectrum was usable. The portion of the 55.5 MHz cap that is not held by Sprint is assumed to be held by the residual Other category.

  62. U.S. Bureau of the Census, American Community Survey, 5-Year Estimates.

  63. The typography code for land surface form topography runs from 1 through 21 as the land surface form varies from “flat plains” to “high mountains.” See the “Natural Amenities Scale” published by the U.S. Department of Agriculture:


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My thanks to Gerry Faulhaber, Tom Hazlett, Michael Katz, John Mayo, Jim Prieger, Mike Ward and Larry White for their helpful comments on earlier versions of this paper. A version of this paper was presented at the January 2016 meetings of the Transportation and Public Utility Group in San Francisco.

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This Appendix provides additional detail on the collection and preparation of the dataset that was used for the regression analysis of spectrum concentration and subscription penetration.

Subscription Penetration

Data on wireless connections were collected for each Cellular Market Area (CMA) by the market research firm, Link Analytics, as of the end of 2013 for the four national carriers plus three regional carriers: US Cellular, Leap Wireless, and Metro PCS.Footnote 55 There was an eighth residual category for subscribers of all other carriers.

To calculate penetration of wireless services, we start with Census Bureau estimates for 2012 population of each county.Footnote 56 These figures include all persons in the CMA regardless of age—including infants and children who are too young to use a cell phone. To approximate better the addressable population, we reduce the CMA population by the Census Bureau’s estimates of the percentage of persons who are aged less than 14 years old.

It is not uncommon for consumers to have more than one wireless subscription—whether that is a second cell phone or more likely a connected tablet. This is one reason why estimates of active SIM cards in a country sometimes exceed its entire population. To adjust for this effect, we use data from the GSM Association’s Wireless Intelligence unit, which reported that the average American had 1.51 wireless connections in 2013.Footnote 57 Accordingly, each 1.51 connections that are provisioned by a carrier is treated as a single “subscriber.”

After these two adjustments to the county population figures, the counties are consolidated into the respective CMAs. Penetration rates for each carrier are then simply the number of subscribers (after adjusting for average wireless connections per capita) divided by the estimate of the number of adults (14 years and older). The sum of all carriers gives the overall penetration rate in each market. In a few instances, the penetration rate exceeds 100%. This likely occurs because of discrepancies for the CMA in terms of its actual wireless connections per capita or estimates of the size of its adult population.

Spectrum Metrics

Data were downloaded for radio spectrum holdings for each of the 3100 + U.S. counties from the FCC’s Universal Licensing System (“ULS”) for the fourth quarter of 2012.Footnote 58 License ownership was recorded for each of six carriers: AT&T, Sprint, T-Mobile, U.S. Cellular, and Verizon Wireless, plus a residual category of all other owners. Licenses that were held by each carrier in the cellular, 700 MHz, PCS, AWS, and WCS spectrum bands were downloaded from the ULS. The ULS reports spectrum holdings at the county level, so these were then aggregated to CMAs to be compatible with the subscribership data.

The ULS ownership records were reformatted, and the names of license owners were mapped to the parent carriers. All spectrum that was not attributed to one of the five carriers in a frequency band was assigned to the “Other” category. Leases to mobile spectrum were not captured. Holdings by partnerships were assigned to the largest license owner when its share exceeded 50%. In cases when two carriers owned portions of a band in the same county, they were assigned a fraction of the band limit in proportion to each one’s bandwidth. When the sum of carriers’ holdings exceeded the band limit, ownership was allocated in proportion to the carriers’ bandwidth holdings.Footnote 59 For the SMR spectrum band, Sprint’s holdings were taken from its Form 603 filings with the FCC for its consolidation with Clearwire.Footnote 60 Spectrum holdings for the BRS/EBS spectrum bands are extracted from the ex parte filed in the Sprint/Softbank docket.Footnote 61

As is typically done for spectrum rights, the bandwidth of holdings (expressed in MHz) was multiplied by county population estimates to make them comparable across CMAs. The resulting amounts, in units of MHz-Pops, were then summed up for each carrier for those counties that comprise each CMA, and the carriers’ spectrum shares were computed for each CMA.

The spectrum shares were then used to form the Herfindahl–Hirschman index (HHI) of spectrum concentration for each CMA. This was done for the cellular, SMR, 700 MHz, PCS, AWS, BRS, and WCS mobile spectrum bands. The HHIs were computed taking the “Other” category as though it were a single carrier. Since that category often represented shares of several carriers, the computed spectrum HHI would tend to overstate the extent of spectrum concentration.

In order to address concerns about the unique advantages of low-frequency spectrum, the HHIs for holdings that fall below 1 GHz (i.e., cellular, SMR, and 700 MHz bands) were computed. The same was done for spectrum bands that are higher than 1 GHz (i.e., the PCS, AWS, BRS, and WCS bands).

Demand and Cost Shifters

Most of the variables that are used to control for demand for mobile services are derived from estimates that are published by the Census Bureau. Their county-level averages of income, household composition, home ownership and tenancy, and education are aggregated up to the CMA.

Also included were characteristics of the CMA that in other contexts have been known to be strongly related to mobile subscribership, such as average travel time to workFootnote 62 and an index of the land topography.Footnote 63 To better control for variation in demand conditions, average travel time was computed as a population-weighted average across the counties that make up each CMA. The average land topography was computed by taking the land area-weighted average of the TypoCodes of counties that make up each CMA.

Network Quality and Coverage

Measures were developed using two industry sources that produce indices of technical performance of mobile wireless networks: Mosaik and RootMetrics.

RootMetrics generates a host of technical indicators of voice, data, and text services with the use of a sophisticated collection methodology. Twice per year, measurements were taken for the largest 125 of the Census Bureau’s “urbanized areas” (UAs) for the four national mobile carriers. Tests were conducted at all times of the day, inside and outside of buildings, while driving in cars, and at major airports. To perform their tests, RootMetrics used unmodified handsets that were purchased from the carriers. Dozens of metrics were collected in each test that are designed to quantify service reliability (e.g., blocked and dropped calls, establish and maintain a network connection) and speed (e.g., time to connect to an IMAP server, file download and upload times, delay in sending/receiving texts). I use the high-level indices—the Overall, Reliability, and Speed scores—that are weighted averages of the several metrics. Each major carrier received a score on a 100-point scale for each of the 125 urbanized areas. Those areas were imputed to CMAs after determining whether they had counties in common. This matching reduced the sample to about 200 CMAs, which include about 60% of the U.S. population.

Mosaik Solutions reports the coverage of different kinds of wireless network technologies that are deployed by the major carriers. This was done in terms of the size of the land area and the size of the population that can receive the service. I limited the analysis to fourth-generation mobile technologies, including: LTE, HSPA, and WiMAX. When a carrier deployed more than one technology in the same area, I took the one that had the greatest coverage. In addition to the four national carriers, the Mosaik data tracked Leap Wireless and U.S. Cellular.

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Woroch, G.A. Spectrum Concentration and Performance of the U.S. Wireless Industry. Rev Ind Organ 56, 73–105 (2020).

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  • Spectrum concentration
  • Industry performance
  • Mobile wireless services

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