Three factors determine the total number of registered domains: First, the ultimate driver of domain name registrations is the demand for virtual space by businesses, organizations or individuals that offer Internet-based information and services to Internet end users. More than 20 years after the inception of the Internet, the total head count of these virtual dwellers (Pop) is still expanding rapidly. While the exact amount of space demanded per dweller is difficult to quantify and also likely to change over time, it is safe to assume that Pop and total demand for virtual space are positively correlated: For instance, doubling the number of virtual dwellers is expected to lead to twice the demand for space (keeping all other factors equal).
Second, the registration fees and other fixed costs (K
reg
) associated with owning a domain name are negatively related to total registration numbers. The fixed costs are comprised of the wholesale domain registration fees charged by the company that administers the domain registry, the markup added by competing middlemen re-selling domains to end users, and by additional costs for hosting and related services. While the direct costs of owning and hosting a domain have been falling year after year due to intense competition between service providers,Footnote 4 it is safe to assume that K is identical for all registrations in a cross-sectional study.Footnote 5
Ultimately, each end user of a website needs exercise an effort E to access an online location. This commuting cost depends on domain specific factors like the recognizability and ease of recollection of a specific name and also on the general competitive position of domains versus other forms of virtual space. If the required effort of commuting to a location is low, owning this location is desirable as it is possible to attract end users easily. Locations with high required efforts are less attractive since fewer end users visit. New domains get registered as long as the utility gained from owning marginal domains given a marginal effort level E
marginal
required by any user exceeds registration costs. In sum, the total number of registrations of domain names can be formalized as
$$ Registrations=a\frac{bPop}{(cK)\left({dE}_{marginal}\right)} $$
(1)
with a, b, c, d being scaling parameters accounting for the overall attractiveness of domain names versus other forms of virtual space (a) and the elasticities of registrations with respect to general demand (b), registration costs (c), and maginal efforts or commuting costs (d).
The marginal effort E
marginal
is assumed to increase in registration numbers. Domain name registrations exhibit a pecking order regarding domain quality: names that had been registered relatively early tend to be of higher quality than those registered later. Marginal domain registrations, on average, contain out of more characters, are less descriptive and more difficult to memorize than the existing stock, requiring higher efforts by end users as registrations increase. Those high quality and easy to access locations that are claimed first in land rush markets tend to trade for higher values in secondary markets subsequently.
The marginal level of effort required by users as more and more lower quality domains get registered, can be generalized as
$$ {E}_{marginal}=g\kern0.5em {Registrations}^h $$
(2)
where g and h are scaling factors. The choice of a power function is motivated by Zipf’s observation that the frequency at which a word is used is inversely proportional to this word’s rank in the frequency table (Zipf 1936) and that the rank is a particular power function of word frequency (Zipf 1949). If domains are registered along the rank suggested by the keyword frequency table, the marketing potential of domains will also follow a power law. This notion is supported by Cunha et al. (2011) finding that the frequencies of Twitter hashtags are governed by a Zipfian power distribution.
Assuming identical registration costs for all domains, and plugging (2) into (1) can be solved for Registrations and simplified to
$$ Registrations=mPo{p}^n $$
(3)
where where m and n are products of earlier used constants (and therefore constants as well): m = (ab/cKg)– (1+h) and n = − (1 + h).
This study assumes the same level of use intensity for all domains. While the classical, traditional monocentric model does include variable density, that is not a necessary feature of the monocentric model. All the essential elements of the monocentric model still come through with a fixed, constant density as shown in Geltner et al. (2001, Chapter 4). In addition, Lindenthal and Loebbecke (2014) have already documented that more valuable domains are more likely to be developed into more extensive websites, which represents a higher use intensity or “density” compared to registrations of lower quality domains without further development.
Owner-operated websites are not the only form of cyberspace available to virtual dwellers. Alternatively, they can connect with their audiences through shared spaces like social media platforms, wikis, online market places or direct communications and marketing. For instance, the increasing role of social networks in connecting companies and its customers could weaken the demand for domains in general. A local business might find it more cost-effective to promote its Facebook profile instead of steering customers towards their website. Reversed, changes to search engine algorithms could make it easier for users to find relevant content on millions of individual websites, tilting the balance in favor of owning domains. The competitive position of domains versus other options is, among other factors, accounted for in factor m.
This framework also allows investigating demand levels for segments of domains by employing subset specific values for E. For instance, the relative commuting costs for a domain under the COM Top Level Domain (TLD) could differ from the cost of accessing a NET or ORG domain, resulting in the different demand levels for each TLD, documented by Lindenthal (2014).
The empirical part of the paper splits a cross-section of domain registrations into subsets for which the level of demand Pop is quantifiable and the number of registered domains is known. The fixed cost K is identically distributed for all domains in cross-section and can therefore be omitted. In a future study, the price sensitivity of domain registrations could be estimated by analyzing longitudinally different values for K.
Figure 2 visualizes the approach: For each group of domains, the intersection of the demand curve D1 and D2 and supply curve S1 can be observed as the number of registered domains, R1 and R2. Demand for domains from group 2 is higher than demand for domains from group 1, as indicated by an upward shifted demand curve and higher values for R2 than for R1. This analysis is only feasible if data on fundamental demand levels and registration numbers per segment can be directly observed.
The relationship between the number of potential domain registrants Pop and actual Registrations can now be estimated empirically in the following log-log regression specification:
$$ \ln \left( Registration{s}_{\mathrm{i}}\right)=\upalpha +\beta ln\left(Po{p}_{\mathrm{i}}\right)+{\upvarepsilon}_{\mathrm{i}} $$
(4)
The regression coefficient β estimates the elasticity of Pop and Registrations, α is a constant and ε
i
an identical and independently distributed error term.
Since the price for a domain registration is constant, the elasticity of registrations with respect to Pop should equal 1 by theory if the supply of domains was effectively unconstrained. The regression coefficient β would then have a value of 1. A coefficient estimate significantly below 1, however, would supports the hypothesis of virtual space scarcity:
-
H1-
The relative increase in the number of registered domains is smaller than the relative increase in the number of potential domain registrants.
Defining E at the domain level also allows accounting for any differences in linguistic quality between domains and the resulting differences in commuting costs and registrations. Zipf (1936) shows that shorter words tend to appear more frequently in natural languages than long expressions. Similarly, the length of Twitter hashtags is inversely related to their usage frequencies (Cunha et al. 2011). If his principle of least effort also holds true in domain space, shorter domains will be registered more often than long domain names. For instance, bearers of long surnames are less likely to register a domain containing their name than somebody with a relatively short name. To give a simplifying example, domains derived from the keywords “Pennington Associates Milwaukee” might be more tedious to type than any from “Carr Associates Miami”, making the former less likely to appear in registrations.
If domain length is a valid proxy for the effort required by users to access a virtual location, then an inverse relation between the length of a string and the number of registrations containing this string can be expected.
-
H2-
The likelihood of a character string being registered as a domain name decreases in the length of the string.
To test H2, the variable domain Length is added to (4):
$$ \ln \left( Registration{s}_i\right)=\upalpha +{\upbeta}_1 \ln \left(Po{p}_i\right)+{\upbeta}_2 \ln \left({Length}_i\right)+{\upvarepsilon}_i $$
(5)
A negative estimate for the regression coefficient β
2
can be interpreted as evidence for different levels of effort required by users – or for the equivalent to commuting costs required by the monocentric city model.
In a similar fashion, the number of keywords within a domain name can be interpreted as an additional measure for commuting costs, as more keywords require more effort when memorizing and recalling. However, combining multiple keywords results in a trade-off between brevity and descriptiveness. In case the domains “pizza.com” or “pizzaboston.com” are already taken, “tastypizzaboston.com” might still be available as the electronic storefront of a local pizza place. Theoretically, each additional keyword increases the number of potential domain names by several orders of magnitude: If the total number of viable single keywords is W, then W
2 two-keyword combinations, or W
3 three-keyword combinations are possible. Whoever is willing to accept the higher effort required to access a domain consisting of many keywords has plenty of choice. This trade-off between availability and domain quality reconciles the view of seemingly unconstrained domain supply and the observation that short, low-effort domains are not easy to come by: Just add a few more keywords and you can have any domain you want.
This notion motivates one last hypothesis:
-
H1-
Domain space is less constrained for combinations of multiple keywords than for single-keyword domains.
To test H3 empirically, the domain registrations for each surname or MSA i are further subdivided into 4 subgroups k, where k denominates the number of keywords in each name. For instance, Registrations
Boston,2
counts the number of COM registrations containing BOSTON and one additional keyword, Registrations
Boston,3
is the number domains with two additional keywords, and so forth. The dummy variables D
n
are defined as 1 if k = n and 0 otherwise. All β’s are regression coefficients:
$$ \mathit{\ln}\left({Registrations}_{i,k}\right)=\alpha +{\beta}_1\mathit{\ln}\left({Pop}_i\right)+{\sum}_{k=3}^{k=5}{\beta}_{2,k}{D}_{i,k}\mathit{\ln}\left({Pop}_i\right)+{\sum}_{k=2}^{k=5}{\beta}_{3,k}{D}_{i,k}+{\beta}_4\mathit{\ln}\left({Length}_i\right)+{\epsilon}_i $$
(6)