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Information Economics and Policy
Volume 25, Issue 4, December 2013, Pages 246-256
Empirical validation of Metcalfe’s law: How Internet usage patterns have changed over time
António​Madureira​
a​
Nico​Baken​
a​d

https://doi.org/10.1016/j.infoecopol.2013.07.002
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Abstract
Few doubt that Digital Information Networks (DINs) such as the Internet constitute the basis of a new technology-driven economic era. A large body of literature tries to understand and quantify the value of DINs to help policy makers justify investments in new or improved infrastructures. The prevailing methodological approach is to depict DINs as an observable production input changing the uncertainty regarding the performance of an economic system. In such context, the value of DINs is typically measured with regression techniques between the penetration rate of DINs and economic growth. This approach provides too little insight on the actual causality between DINs and economic value. We recently developed a framework that identified 13 different ways (“capabilities”) how users convert information into economic value. In this article, we show how a simple quadratic relation (Metcalfe’s law) can be used to quantify how adequate these capabilities are in converting the ability to access information into economic value. To our knowledge, this is the first time that Metcalfe’s law is empirically validated as such.
Introduction
Since the 1980s, the telecommunication sector has been expanding rapidly (Shiu and Lam, 2008). This is mainly caused by the conversion of analoge communication networks designed for telephony or TV services into multi-functional Digital Information Networks (DINs). The exponential growth of services offered over DINs can be explained by many factors, including technological advancements, market liberalization and privatizations. The worldwide extraordinary level of interest in deploying information networks is due to the strong perception that information networks bring economic, social and environmental benefits (Firth and Mellor, 2005). Some authors speculated that DINs may have a similar impact on society as transportation networks had during the 20th century (OECD, 2001). In long wave theory, this information driven economic era is known as the 5th Kondratieff economic cycle (Perez, 2003). A Kondratieff cycle manifests itself by a sinusoidal-like long-term cycle from approximately 40 to 60 years in length with a semi-period of high productivity growth followed by a semi-period of relatively slow growth (Freeman and Louçã, 2001). The benefits of DINs can be observed directly. For example, construction of network infrastructures leads to direct increase in job employment. In addition, the benefits might also be more intangible, such as better quality of health care services, improved education and organizational efficiency. The Organization for Economic Co-operation and Development (OECD) considered broadband DINs as key to enhancing competitiveness and sustaining economic growth (OECD, 2001). Many governments are increasingly committed to extending DINs to their citizens (Katz et al., 2009), particularly in the developing nations (Kagami et al., 2004). Consequently, the levels of interdependency between users and DINs’ providers increased dramatically (Dijk and Mulder, 2005) and the DIN infrastructure became an essential facility for all economic sectors.
In order to justify policy support for further investments in DINs (e.g. in Fiber To The Home (FTTH)), it is necessary to learn from expenditures that have already been made and demonstrate their value. We recently developed a Holonic Framework (HF) which identified and defined so-called “capabilities” of users in DINs (Madureira et al., 2011). Capabilities are mechanisms that users apply to convert information into economic value. In this article, we show how a simple quadratic relation (Metcalfe’s law) can be used to quantify how adequate these capabilities are in converting the ability to access information into economic value. To our knowledge, this is the first time that Metcalfe’s law is empirically validated as such.
The next section describes the state of the art on studies aiming at understanding the value of DINs, including a brief overview of our HF. Section 3 provides the equations with which the behavior of the capabilities of the HF can be quantified. The characteristics of our data source, our conceptual operationalizations and our validation methodology are described in Section 4. The results of our analysis are presented in Section 5, whereas Section 6 discusses them, identifies potential implications, and describes the limitations of our work. The last section is reserved for our conclusions.
Figures
Binning process for adoptability.
Applying Metcalfe’s law to the Eurostat data ( regression, precision, • bin points).
Applying Briscoe’s law to the Eurostat data ( regression, precision, • bin points).
Section snippets
State of the art
We reviewed 24 studies on the value of DINs spanning a period from 1980 to 2010. These studies can be grouped into three classes: (1) macro-economic studies using general equilibrium theories and/or input–output tables (Katz et al., 2009, Greenstein and McDevitt, 2009, Correa, 2006, ACIL Tasman, 2004, CEBR, 2003, Röller and Waverman, 2001, Hardy, 1980); (2) econometric studies not addressing the issue of causality (Thompson and Garbacz, 2008, Thompson and Garbacz, 2007, Shideler et al., 2007,
Model for value generation by users in DINs
We can derive a number (value) for how effective a capability is in creating economic value from how it is used to generate income. For example, if a worker uses DINs for online education, then he uses adoptability to obtain a certain part of his income. The value (yc) generated by a capability c is dependent on the size x of the DIN. With a larger network more value is extracted by a capability. kc is the coupling strength between the size of the network and the value generated by capability c
Data collection
We proxied the value created by the capabilities of the HF individually and their dependence on the size of the DIN using data from Eurostat. Eurostat, the European Union’s official organization to collect statistical data, provides one of the richest data sources about the usage of Information Technology (IT) in enterprises and households. We were allowed to use a significant part of their data set for our research. The data comes in two separate files with a total size of approximately 350
Metcalfe’s law
Fig. 2 shows the results obtained with model (1). All curves fit well within the limits provided by the error bars. The exception is selectibility, which behaves linearly with a slope of approximately 1, meaning that roughly every additional node will use selectibility. This can be theoretically expected. When a quadratic curve following model (1) gets close to the line y = x, it means that the fraction of enterprises or individuals using a capability is equal to the relative size of the network.
Analysis of the models and the results
Both our regression models result in the same ranking of coupling strengths with selectibility on top and perceptability/modelability/decisability at the bottom. Selectibility is followed by adoptability and cooperatibility. Within the error bars, normatibility, coordinatibility, and biddability have the same coupling strength and so does trustability and perceptability/modelability/decisability.
Selectibility and, to a lesser extent, adoptability support the use of Briscoe’s law rather than
Conclusions
To justify further investments in Digital Information Networks (DINs)’ infrastructures (e.g. in FTTH), it is necessary to analyze expenditures that have already been made and demonstrate their value. Madureira et al. (2011) presented a Holonic Framework (HF) which identifies these mechanisms as capabilities and specified 13 of these capabilities. Building upon the HF and Eurostat data, this article demonstrates that the value that these capabilities create by using information shows either a
Acknowledgments
We thank the Royal Dutch KPN, TNO and the Delft University of Technology for funding this research. We thank Eurostat for the data used in this article. Finally, we thank the editors and reviewers of Information Economics and Policy for constructive discussions during the submission process.
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