This past February, we released a paper entitled Wireless Competition After Spectrum Exhaust.  As far as we can tell, this paper was the first serious attempt to model the effect of spectrum exhaust on mobile wireless competition.  We found that the addition of a binding capacity constraint (i.e., spectrum exhaust) to the standard Cournot model of competition reveals that that fewer—not more—firms would lead to lower price, more investment, and more jobs.  Our paper, not unexpectedly, raised a few eyebrows.  (For a CliffsNotes summary of our paper, see my February 8, 2012 blog post.)

This weekend, Steven Crowley at GigaOm, a consulting engineer, posted some comments on our paper.  He describes the paper as “some fresh, thought-provoking thinking on mobile competition analysis,” but then challenges the idea there is spectrum exhaust. For three reasons, I think it is appropriate to respond to Steven’s commentary:  (1) Steven is a credentialed and prolific consulting engineer focused on mobile wireless technology; (2) Steven took the time to actually read our paper and provide written comments; and (3) a response provides an opportunity to offer some clarifications to our analysis which may make it more compelling.

First, let’s review what our paper said.  In Wireless Competition After Spectrum Exhaust, we appended to the basic Cournot Model of competition (which finds that more competitors leads to lower prices) an industry-shared resource (e.g., spectrum) that could effectively constrain the capacity of the Cournot competitors.  We also assumed that there was a type of “scale economy” in this shared resource, so that doubling the amount of spectrum a firm had more than doubled its capacity.  We demonstrated that if the capacity-constraint was binding (i.e., a “spectrum crunch” or “spectrum exhaust”), then the standard more-firms/lower-price outcome of the Cournot Model was no longer valid.  In fact, fewer firms led to lower prices!  Given that the FCC contends there is a spectrum shortage, yet it also depends heavily on the standard Cournot result that more competitors leads to lower prices (see, e.g., its CMRS Reports and its review of the AT&T-T-Mobile merger), it’s plain that this result is of significant policy relevance, forcing (we hope) the FCC to rethink its competitive model for the industry.

With this review in mind, let’s turn to Steven’s commentary.

Most of what Steven says about our paper is based on his belief that spectrum exhaust is not a problem because of “trends in the mobile network architecture that intended [sic] to address the capacity crunch.”  Steven goes on to state that “[o]ne concern I have with the study … is the need for there to be a condition of ‘spectrum exhaust’ for the model to work.”  To begin with, Steven’s assessment of our model is technically incorrect.  Our model encompasses the case of both a binding and non-binding spectrum constraint (as just described).   That is, the model “works” whether the constraint is binding or not.  In fairness, I think Steven’s point is that the Cournot result is not “turned on its head” in the absence of a binding constraint, but we make this point clear in our paper.  Indeed, that’s what makes the paper interesting—the constraint matters, and it matters a lot.

As detailed in the paper, my blog post, and above, absent spectrum exhaust, our paper admittedly offers nothing new, and perhaps this is the point Steven is trying to make.  But even if you don’t believe there is exhaust (either now or in the near future), we believe it is worth keeping one thing in mind—the White House, the FCC, Congress and much of the industry are all operating on the assumption that currently allocated spectrum resources are inadequate to continue supporting the volume of consumer demand (both now and especially in the future).  Consequently, it is important to model spectrum exhaust in order to fully understand its implications, since the exhaust mindset is driving policy and investments.

Let’s turn now to why Steven is unconcerned about spectrum exhaust.  First, he argues that capacity is not simply a function of the amount of spectrum.  He is correct.  A finite quantity of spectrum can yield greater capacity using, for example, “increased antenna sectorization at the base station.”  It is well documented that the companies clamoring for more spectrum are also deploying interim technical solutions to extract more capacity from existing allocations.  However, this reality doesn’t materially affect the findings in our paper; either the constraint is binding or it is not.  If sectorization removes the constraint, then the standard Cournot result applies (at least in theory).  Keep in mind, however, that sectorization is not a costless way to increase capacity, and consumers must eventually bear all costs.  The costs for additional infrastructure deployment and other tools to extract more capacity from existing supplies may be so high as to be non-economic.  There is a FCC study on this very issue (though I suppose Steven might take it to task, as would I on some issues).  Moreover, as I understand it, most RF engineers agree that even with interim steps to do more with existing supplies, commercial wireless networks will simply need more raw spectrum to support the expected demand for more wireless broadband.  In fact, Steven has a number of blog posts related to finding more spectrum for U.S. carriers (which I would take to be a waste of time if there was no capacity issue).

Steven also argues that the capacity of spectrum can be increased using “Wi-Fi and small-cell offloading.”  However, these options do nothing to increase the capacity of spectrum, they merely shift traffic from one network to another (that is, offloading targets demand rather than fundamentally altering supply, unlike sectorization which targets supply).  Further, the point ignores the reality of Wi-Fi hot spots themselves becoming overwhelmed with traffic and becoming a less viable solution for consumers. In contrast to Steven’s argument, I believe offloading is good evidence that spectrum exhaust is a reality today.  Otherwise, why would carriers bother?

A few comments in Steven’s blog suggest a bit of clarification on our behalf is perhaps needed.  First, Steven states that we “present a model that happens to show two [wireless competitors] as optimal.”  This is not the case.  Steven’s statement is based on Figure 1 in the paper where we illustrate graphically the relationships between price and quantity and industry concentration both with and without a binding capacity constraint.  We stated in the paper that the figure was based on purely arbitrary assumptions that were required to convert the theory into something that could be illustrated in a graph.  Perhaps we did a poor job of making that clear enough (though Steven quotes the relevant text).  Steven correctly notes that, “a different set of assumptions, equally arbitrary, could indicate a higher or lower number than two”—this is correct and the essence of arbitrary parameter selection.  So, while Steven points to an article suggesting a “Rule of Three,” and also suggests that “[m]aybe two, as shown in the Phoenix Center model, isn’t that far off,” if it turns out that two is optimal, we unfortunately can’t claim foresight.

Steven also discusses the example used in my blog post to explain the “scale economies” assumption in spectrum.  The example reads,

“Say you have 100 MHz of spectrum and you divide it among 4 firms so that each gets 25 MHz. Say this generates 100 units of capacity. If instead you divided 100 MHz among two firms, so that each gets 50 MHz, then the amount of total capacity would be something like 150.”

Steven then asks, “Why 150 instead of, say, 105 or 200? We aren’t told.”  The reason “we aren’t told” is that it doesn’t matter.   It’s a numerical example designed to illustrate a technical point.  As for the theory, as long as there is some “scale economy” in spectrum holdings, no matter how small, you get the same result (note that the size of the price response depends on the size of the scale effect, but size is an empirical question, not a theoretical one).

Steven offers a number of other but less substantive comments on the paper.  For example, he argues that some of the Wall Street analyst reports we cite in the paper regarding “too much competition” are more than two years old.  We note that the theme of excess competition in mobile wireless sector is a current one.  An excellent “live” discussion of the topic with respected industry analysts at our 2011 Symposium is available on our website (second video; and watch the first video, at 1.04, for my presentation of the Spectum Exhaust paper).  Steven also didn’t care for us citing the FCC’s technical report on spectrum exhaust, which he has taken to task on his blog.  As the analysis was targeted at FCC policies, we view using the FCC’s own documents to support the agency’s claims on spectrum shortages was sensible.  If you don’t like the report, there is other evidence about spectrum exhaust from reputable engineering sources, industry and financial analysts, and, most notably, the recent expenditure of huge political capital from both the White House to virtually every segment of the wireless industry to help pass legislation that gives the FCC the authority to hold voluntary incentive auctions for broadcast spectrum.  Whether or not exhaust is a reality or a fabrication is a debate that likely will continue, and while we tend to side with the reality crowd, we respect the rights of those who believe otherwise.

Finally, we must respectfully disagree with Steven’s statement that our “analysis, in its present form, is [not] ripe for influencing policy.”  To the contrary, spectrum exhaust, whether a reality or a fabrication, is a key driver of federal communications policy and industry investments, and likely will be for the foreseeable future.  Besides, we are confident the paper is already influencing policy.

We appreciate Steven taking the time to review our study and providing some insightful comments and suggestions.  Such dialogue among industry professionals is essential to good policy.  I hope this conservation moves the ball forward.

Also, for those interested in the economics of this problem, Professor Luke Froeb, an economist at the Vanderbilt Department of Mathematics, pointed me to a couple of his papers (here and here) that reach similar conclusions in entirely different contexts using entirely different methodologies.

 

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