Show Summary Details

Page of

Printed from Oxford Research Encyclopedias, Physics. Under the terms of the licence agreement, an individual user may print out a single article for personal use (for details see Privacy Policy and Legal Notice).

date: 05 July 2022

# The Economics of Physics: The Social Cost-Benefit Analysis of Large Research Infrastructures

• Massimo FlorioMassimo FlorioDepartment of Economics, Management, Quantitative Methods, University of Milan
•  and Chiara PancottiChiara PancottiCSIL Centre for Industrial Studies and University of Milan

### Summary

In economics, infrastructure is a long-term investment aimed at the delivery of essential services to a large number of users, such as those in the field of transport, energy, or telecommunications. A research infrastructure (RI) is a single-sited, distributed, virtual, or mobile facility, designed to deliver scientific services to communities of scientists. In physical sciences (including astronomy and astrophysics, particle and nuclear physics, analytical physics, medical physics), the RI paradigm has found several large-scale applications, such as radio telescopes, neutrino detectors, gravitational wave interferometers, particle colliders and heavy ion beams, high intensity lasers, synchrotron light sources, spallation neutron sources, and hadrontherapy facilities.

These RIs require substantial capital and operation expenditures and are ultimately funded by taxpayers. In social cost–benefit analysis (CBA), the impact of an investment project is measured by the intertemporal difference of benefits and costs accruing to different agents. Benefits and costs are quantified and valued through a common metric and using the marginal social opportunity costs of goods (or shadow price) that may differ from the market price, as markets are often incomplete or imperfect. The key strength of CBA is that it produces information about the project’s net contribution to society that is summarized in simple numerical indicators, such as the net present value of a project.

For any RIs, consolidated cost accounting should include intertemporal capital and operational expenditure both for the main managing body and for experimental collaborations or other external teams, including in-kind contributions. As far as social intertemporal benefits are concerned, it is convenient to divide them into two broad classes. The first class of benefits accrue to different categories of direct and indirect users of infrastructure services: scientists, students, firms benefiting from technological spillovers, consumers of innovative services and products, and citizens who are involved in outreach activities. The empirical estimation of the use value of an RI depends on the scientific specificities of each project, as different social groups are involved to different degrees. Second, there are benefits for the general public of non-users: these benefits are associated with social preferences for scientific research, even when the use of a discovery is unknown. In analogy with the valuation of environmental and cultural goods, the empirical approach to non-use value aims at eliciting the willingness to pay of citizens for the scientific knowledge that is created by an RI. This can be done by well-designed contingency valuation surveys.

While some socio-economic impact studies of RIs in physics have been available since the 1980s, the intangible nature of some benefits and the uncertainty associated with scientific discoveries have limited the diffusion of CBA in this field until recently. Nevertheless, recent studies have explored the application of CBA to RIs in physics. Moreover, the European Commission, the European Strategy Forum on Research Infrastructures, the European Investment Bank, and some national authorities suggest that the study of social benefits and costs of RIs should be part of the process leading to funding decisions.

### Subjects

• Physics and Economics
• Physics Policy and Management

### 1. Introduction

Large-scale research infrastructures (RIs) in physics, such as the Large Hadron Collider (CERN, Geneva) or the Relativistic Heavy Ion Collider (RHIC; Brookhaven National Laboratory, near New York), are major long-term investment projects that are designed and managed with the objective to create and share knowledge with multiple users. In the past, typical arguments for government funding of large-scale research infrastructures in physics often consisted in top-down agendas related to national security and national ambitions. Examples of Big Science with military implications were the U.S. Manhattan Project, the French Nuclear Program, and the Apollo Program. The rationales for contemporary RIs revolve instead around curiosity-driven science (i.e., for the sake of knowledge per se) or around a range of pre-competitive applications that are mostly identified by scientific communities themselves. This bottom-up perspective, together with a general declining trend of the investment of public resources in R&D, implies that scientific communities need to compete for both national and international funding. Therefore, the ability of the scientific community to convince governments that a large-scale RI project is valuable is crucial.

Since these projects are costly and ultimately funded by taxpayers, two questions arise: Which project should a government target for funding in the first place? What are the benefits for society of supporting these investments and their operations? Governments and taxpayers–when government funds are involved—but also private donors or investors of private funds are mostly interested in knowing (or should be informed about) the expected or achieved socio-economic impact of investment decisions they support. The socio-economic case will usually not be the core argument in the political decision process, as the scientific case takes priority, but its importance in convincing governments cannot be exaggerated.

Typically, the funding of very expensive RIs is promoted by a coalition of scientists who are often supported by peer reviews to convince policymakers of the importance of a new project. This practice, which can be described as lobbying for science, is a common feature of any major public investment-decision process. A wide coalition of stakeholders is often needed to achieve consensus in order to commit public and/or private capital to infrastructures that may pay back investors or citizens, only in some relatively distant, unspecified future, while having immediate costs.

While the expected financial return is the key metric needed to convince private investors to support an infrastructure, the public sector decision-making process is much more complex. In principle, government intervention is needed when markets do not provide efficient solutions for the supply of demanded goods. The provision of “public goods” (Samuelson, 1954) is one of the typical cases of market failure. New scientific knowledge often has the peculiar characteristics of a public good. Its use is non-rival: reading a paper by one individual on the observation of gravitational waves does not decrease the opportunity of reading the same paper by another individual. Moreover, it is costly and often nearly impossible to exclude third parties. For example, scientific papers can be reproduced and circulated at a very low cost, even when a subscription is required to access the journal where they were first published, and there are free repositories such as arXiv. In fact, knowledge, once created, can easily spill over elsewhere. Not everything can be patented or kept secret, and the returns of an agent’s research expenditures may be captured by another agent. Hence, as Romer (1990) claimed in a famous article (leading to the Nobel Prize in Economic Science in 2018), private investors or firms are reluctant to bear such risk. The result is that they invest less in R&D than what would be socially optimal. Governments need to counteract this behavior by funding R&D to the extent that private investors and firms are not willing to. Ultimately, this is why RIs exist: to counteract a market failure.

In this perspective, RIs are becoming a focal ingredient of publicly supported policies aimed at boosting technological and scientific progress. They are at the core of the knowledge triangle of research, education, and innovation. Indeed, there is increasing international competition by countries in hosting facilities at the frontier of science with the expectation that such projects may promote economic competitiveness, even if it is uncertain how and when these scientific discoveries may have such an impact. In this context, governments may have to recur to a decision criterion also based on the expected socio-economic return—that is, the net societal well-being change produced by a given investment. It would certainly be helpful to be able to answer questions such as: What is the value of building and operating a specific RI for society, given that, in financial terms, this project incurs/results in a loss, as there will be costs but no revenues (or extremely modest ones compared to the costs)?

The remainder of this article draws from Florio (2019), where a more detailed treatment is provided. The “Earlier Literature” section briefly takes stock of existing socio-economic impact studies of RIs in physics. The section “What Is Cost–Benefit Analysis?” introduces the cost–benefit analysis (CBA) method and provides some initial remarks about its application. The “Evaluation Framework” section suggests a simple framework to undertake a consistent intertemporal accounting of social welfare effects in the RI context. The model is straightforward: the social value of an RI is the algebraic sum of the benefits, net of costs, for certain social groups of users and for the general public of non-users, where each value is discounted to a base year. All of these values are expressed by a common numeraire and in terms of the expectations computed by the probabilities attached to some critical variables. The “Concluding Remarks” section provides some final considerations.

### 2. Earlier Literature

The first socio-economic impact studies of research infrastructure (RI) in physics date back to the late 1970s. The increasing need for systematic assessments of the scientific performance of large basic research facilities had been pointed out by Martin and Irvine (1983). After reviewing the literature on scientific assessment, the authors argued that, while there are no simple measures of the contributions to scientific knowledge that are made by scientists, there are a number of “partial indicators”—that is, variables that are partially determined by the magnitude of the particular contributions and partially by “other factors.” Based on this, they proposed the method of “converging partial indicators,” which was also tested in an empirical study on four radio astronomy observatories.

One year later, the same authors published a series of three papers (Irvine & Martin, 1984a, 1984b, 1984c), where they attempted to evaluate the overall scientific performance, since 1960, of the three main particle accelerators at CERN and assess future prospects for CERN and its users over the next 10 to 15 years. In the second of their three papers, the authors assessed the scientific performance of the CERN Proton Synchrotron or the Super Proton Synchrotron in terms of their track record in publications compared, respectively, to a similar machine at the U.S. Brookhaven National Laboratory and at the Fermi Lab (as well as other accelerators).

Drawing on studies in radio astronomy and particle accelerators, and in view of the multi-dimensional nature of basic research, Martin (1996) suggested a range of possible indicators to assess the benefits of large basic research facilities. In particular, he proposed (a) scientific contributions to the stock of knowledge, (b) educational-contributions in terms of skills and trained personnel, (c) technological contributions to the development of new or improved technologies, and (d) cultural contributions to the wider society. This multi-indicator approach has been refined and extended several times (see, e.g., Martin & Tang, 2007; Salter & Martin, 2001).

Since the early 2000s, the literature on the socio-economic impact of RIs has split into two branches (for a complete review see, e.g., Giffoni and Vignetti, 2019). On the one hand, there are case studies on specific projects that tend to rely upon a mixture of narratives and quali-quantitative assessments based on a range of different performance indicators (see, e.g., LBNL, 2001; Le Goff, Heuer, Koutchouk, Stapnes, & Stavrev, 2011; OECD, 2014). On the other hand, there is a strand of literature on the macroeconomic returns of investment based on input–output models, output multipliers, and other aggregate indicators (see, e.g., Anderson Economic Group, 2011, on the economic impact of Fermilab; KPMG, 2016, on SNOLAB, a neutrino research facility; and STFC, 2010 on the synchrotron light source in Daresbury, UK). Both strands have some limitations. Case studies and quali-quantitative indicators are often not grounded on consistent economic theory, are not structured as models, and provide results that, while informative, are difficult to compare across different investment projects, as each case study is based on different assumptions and methods. Macroeconomic models are based on aggregate variables and the use of multipliers based on average regional or country-level statistical effects and cannot identify the microeconomic effects of a specific project. Therefore, relatively little is known about social-economic returns at the project level by applying these methods. It may be true that, on average, the increase of an economic input, such as electrical equipment in a country or region, may be associated with an increase in a sort of output, such as cars, and that on average for every dollar invested there is a return of one dollar and twenty cents (a multiplier of expenditure of 1.2). However, an average national or regional effect is not informative regarding the impact of one spent dollar when dealing with a specific project, be it a particle accelerator or a power plant.

In the attempt to devise an approach that would minimize the above-mentioned limitations, cost–benefit analysis has been considered. CBA offers, indeed, an established framework for the evaluation of public investment and consists in comparing its socio-economic costs and benefits at the project level. Generally speaking, CBA wants to assess whether the benefits of a project—to whomever they may accrue—exceed costs—by whomever they may be incurred—thereby demonstrating whether the project represents a net benefit for society as a whole. The key strength of this approach is that it produces information about the project’s net contribution to society, summarized as simple numerical indicators such as the net present value of a project. Clearly, the CBA of a specific RI ought to be intended as a complement to, and not a substitute for, its scientific case, which essentially implies a peer review process.

### 3. What Is Cost–Benefit Analysis?

Occasionally, economists have considered how the methods that have been developed by physicists may be transferred to economics or finance. An interdisciplinary research field, econophysics, applies models and statistical approaches originally developed in physics to solve certain problems in economics. In this section, an attempt is made to answer the opposite question: How may economics be helpful to physicists? More precisely, can applied welfare economics and CBA models help evaluate the socio-economic impact of large research infrastructures in physics?

CBA is a way of thinking about how best to make decisions that involve resources (Brent, 2017; Johansson & Kriström, 2018). As resources are limited, decision makers are required to choose projects that produce the highest utility from those limited resources. Hence, it seems sensible to compare benefits (advantages expressed in monetary terms) and costs (disadvantages expressed in monetary terms). In a nutshell, benefits and costs are, in essence: (quantities) • (prices) = values. The net socio-economic benefit of any project is captured by a (non-linear) function of real variables (quantities, prices, time, discount factors, and other parameters), that is, the net present value (NPV). This is expressed as the difference between benefits and costs, each represented in terms of present time values (PV), to avoid simply adding values that occur now but are related to future events.

The core of the CBA of any project is the empirical estimation of the NPV. This is often reported as a single number, but in fact, as mentioned, it is an empirical function. In a fully developed CBA model, there may be dozens or hundreds of project-specific variables (such as capital expenditures, labor cost, number of doctoral students, etc.) and economy-wide parameters (such as GDP growth, per capita income, unemployment, etc.) determining the NPV. The important outcome is not the resulting single NPV but the underlying assumptions and the range of results generated by the model. Also, because there is uncertainty in forecasting future benefits and costs, whenever possible all variables have to be considered as stochastic and, in turn, associated with probability distributions. Therefore, a project’s NPV should be expressed as an expected value from a probability distribution, conditional to the distribution of input variables. The notation E(NPV), E(PV) is then used when the mean value of a distribution is explicitly considered.

The E(NPV) is simply an empirical assessment of what is known and what is not known, in terms of the expected socio-economic impact of a project. Therefore, it should be read as claiming, for example, that the expected measurable net benefit of a synchrotron light source is one million dollars, or one million dollars in excess of costs in terms of time = 0 (present) dollars. This has nothing to do, of course, with the “profitability” of this investment, which usually, in fact, will lead to losses in financial accounting terms.

CBA should not be confused with a mere financial analysis. The latter refers to market prices and represents the project’s cash inflows and outflows, including funding mechanisms, financial sustainability, and any possible financial revenue accruing to the project. In fact, for many goods, market prices do not exist or do not provide information about their true values in terms of social welfare because they are affected by market distortions. Most environmental, cultural, and scientific goods and services are such that markets do not attribute an empirically observable price to them, yet they have social value. Therefore, a basic principle of CBA is that, when market prices do not exist or are inappropriate for value inputs and outputs, or social benefits and costs in general, such prices must be substituted by empirical estimations of marginal social values—that is, shadow prices. In practice, shadow prices may be estimated by an agent’s marginal willingness to pay (WTP) for a good, by the marginal social production costs, or by a combination of these measures. The marginal WTP is how much you would be willing to pay to obtain an additional small unit of a good. The marginal production cost is the value of the resources needed to produce such an additional unit.

CBA also differs in some forms of “growth accounting,” input–output models, and macroeconomic multipliers. As a matter of fact, CBA does not directly relate to country economic growth objectives. This is partly because CBA includes impacts (e.g., on knowledge spillovers, human capital formation, cultural outreach) that do not figure in gross domestic product (GDP), which is an accounting convention with a number of limitations. However, CBA also relies on measuring costs and benefits to project stakeholders (users, providers, taxpayers). Hence, CBA is applied in microeconomic terms, while concepts such as input–output models and output or employment multipliers are macroeconomic in essence (i.e., they look at aggregate economic variables such as GDP).

The analytical framework of CBA, after its distant origins at the École des Ponts in Paris in the 19th century, has been developed since 1970 by international institutions such as the Organisation for Economic Co-operation and Development (OECD), the United Nations Industrial Development Organization (UNIDO), the World Bank, the European Commission, and several national governments, especially in the United Kingdom, the United States, Canada, France, the Netherlands, and Scandinavian countries, as well as by many agencies. The CBA methodology has been systematically applied to appraise thousands of projects in different fields, starting with transport and moving to energy, telecommunications, health, education, and notably the environment.

Since the mid 2010s, investment in science, including physics, has remained outside of the scope of CBA methods. This is due to a series of factors: the bottom-up identification of priorities by the scientific community, rather than by governments themselves; the international coalitions of funders; shared management; and the intangible nature of some benefits such as knowledge externalities and the uncertainty associated with scientific discoveries. These factors contributed to the diffusion of a belief that an RI is too different from the conventional infrastructure project and therefore cannot be analyzed with the well-established CBA methods that have been developed in other fields.

While it is true that some features of RIs are peculiar to them, several aspects are similar to other categories of infrastructures. In particular, high capital costs in the initial period, long time horizons, the generation of externalities, and the lack of proper competitive markets are all RI features that are common to other infrastructures and are typical CBA issues. The absence of a CBA model—grounded on the principles of applied welfare economics—that can deal with both the generic and the specific features of the RI was indeed the first obstacle to the application of CBA to the R&D field. A first systematic attempt to solve this research gap is represented by a study (2013–2015) by the University of Milan with the support of the European Investment Bank Institute with the aim of developing and testing a CBA conceptual framework for RIs. Since then, other projects have further elaborated and drawn on the methodological framework presented in Florio and Sirtori (2016), which particularly focuses on CERN accelerators but also considers synchrotrons for hadrontherapy, synchrotron light sources, and other facilities.

While CBA will never be the core argument to justify the investment of taxpayers’ money in physics research, it provides an established framework for answering important questions about the net socio-economic benefits and risks of any large-scale RI.

### 4. The Evaluation Framework: A Cost–Benefit Analysis Model

Like other investment projects in any field, the forecast of the socio-economic NPV of RIs over a given time horizon is defined as the expected intertemporal difference between benefits and costs valued at shadow prices, which, in turn, are defined as the marginal social value of goods and services. In the formula:

$Display mathematics$

the $T+1$ terms $1/(1+SDR)t$ (running from year 1 to the final year considered $T$) represent the discounting process. One euro in a distant future, such as $T$, is worth less than one euro today because it could have been invested and earned a return in the years between 1 and $T$. A social discount rate (SDR) is a measure of such potential return that is used to translate future values into present ones. Also, all the benefits and costs to be considered are in incremental terms against a counterfactual scenario, a state of the world without the specific RI project under evaluation.

While the formula is generally valid for every infrastructure, for RIs it is convenient to divide social intertemporal benefits into two broad classes. (The first article to propose such an approach is Florio and Sirtori, 2016, further developed in Florio, 2019.) First, there are use benefits that accrue to different categories of direct and indirect users of infrastructure services. Second, there are non-use benefits that reflect the social value of the discovery potential of RIs, regardless of predictable ex ante actual use. Consequently, the $E(NPV)$ of RIs may be broken down into two parts: the expected net present value $E(NPVu )$ of use benefits $Bu$ and costs $Cu$ and the expected net present value of non-use value of knowledge created, or “discovery” $(Bn)$:

$Display mathematics$

where $u$ and $n$ represent, respectively, a use value and a non-use value.

More specifically, the present value of use benefits $PVBu$ is the discounted sum of benefits to users of the RI services, including the value of publications for scientists ($SC$); benefits to staff, particularly students, arising from human capital accumulation $(HC)$; benefits to firms, defined as technological externalities $(TE)$; information technology externalities $(IT)$; benefits of applied research to external users or other consumers $(AR)$; and benefits to users of cultural goods $(CU)$. Non-use benefits $(Bn)$ refer to the future possible economic effects of any discovery (quasi-option value) and the intrinsic value of the discovery per se, which represents a public good. The present value of costs $PVCu$ is the sum of the economic present value of capital costs $(CAPEX)$, operating costs $(OPEX)$, and negative externalities, if any $(EXT)$:

$Display mathematics$

A discussion of relevant benefits and costs is provided in what follows.

#### 4.1 Dealing With Benefits

When dealing with benefits generated by an RI, the first step consists in benefit identification. In this regard, it is helpful to track the benefits in terms of agents, rather than in other possible ways such as final consumption or added value, investment, government expenditures and taxes, or trade balance. Looking at the economy from the perspective of agents is a structured evaluation strategy used to avoid double counting or picking up redundant indicators having no precise meaning in terms of social impact. In the applied welfare economics literature, a customary partition of economic agents simply includes the following: consumers, employees, taxpayers, and firms. These groups can then be conveniently broken down into subgroups, for example in terms of income of consumers, location of firms, domestic versus foreign ownership of firms, and so on, as needed for a more fine-grained analysis.

Following this partition, and keeping in mind the distinction between use and non-use categories, a possible taxonomy of the benefits deriving from an RI project includes six main measurable use benefits and two non-use benefits. The benefits include:

1.

The value for scientists of increased knowledge outputs $(SC)$, namely, publications and other forms of specialized communication that disseminate new theories, results, methods, and concepts. This is not the final value of knowledge but only a (relatively small) fraction of it, embodied in the value of writing, publishing, reading, and citing papers. For example, in high-energy physics, Carrazza, Ferrara, and Salini (2016) investigated the pattern of the propagation of knowledge outputs related to different colliders (LHC, LEP, and Tevatron) over a wide time span. To do so, they extracted the number of scientific publications (including articles and preprints) as well as the number of citations up to 2012 from the INSPIRE database and forecast the future number of publications (2013–2025) by implementing a double exponential model (Bacchiocchi & Montobbio 2009; Carrazza et al., 2014).

2.

The human capital formation $(HC)$ of PhD students and postdoctoral researchers involved in experiential learning at RIs. Typically, they are affiliated with a university, so there are spillovers from the RI to different university departments. The learning experience at RIs ultimately increases job opportunities and income for early-stage researchers. Bastianin and Florio (2018) have estimated the salary increase or premium over the active work period for people who have been involved in the LHC program like students or early-stage researchers. These are technical students, doctoral students, and post-doctoral researchers under the age of 30 who are enrolled in a CERN education program and registered “Users” who are between 30 and 35 years of age.

3.

Technological and other types of learning and spillover $(TE)$ for firms involved in procurement contracts for the construction and operation of the RI. Such an effect arises when the RI staff, which is intrinsically motivated by non-profit objectives, helps technology suppliers solve new problems arising from procurement contracts. Such solutions may create innovation opportunities for the firms and additional sales in other markets. An example of this benefit is reported by STFC (2010), a study on the socio-economics impact of the Daresbury Synchrotron Radiation Source.

4.

Information technology externalities $(IT)$, which often involve broad communities of users and may also be far beyond the scope of scientific research. Such externalities arise when the policy of the RI managing body is to release free software, or when databases provide open access, and virtually donate to any potential user. For instance, CERN has developed and released IT systems and software that were initially tailored for the needs of high-energy physics into the public domain, proving that such IT tools may be of interest for other application domains. The most famous example is the invention of the World Wide Web $(WWW)$ at CERN in 1989 by Berners-Lee. The WWW browser was originally conceived and developed as a means to improve the sharing of information between scientists working on particle physics experiments in different universities and institutes around the world. Two more examples of software developed by CERN are ROOT (a library of tools for data analysis and visualization) and Geant4 (software to simulate the effects of particles passing through matter that is used, for example, in medicine for simulating radiation damage in DNA and for other industrial applications).

5.

Services directly provided by the RIs to third parties $(AR)$, such as medical research for patients and materials testing for firms. For instance, at CNAO in Pavia (Italy) or MedAustron in Wiener Neustadt (Austria), new protocols are experimented, either with protons or carbon ions for cancer hadrontherapy. These therapies are developed when X-rays are not appropriate and surgery is not possible. Another example of RIs in physics providing research services is represented by the synchrotron light sources, such as the European Synchrotron Radiation Facility (ESRF) in Grenoble (France), the ALBA synchrotron near Barcelona (Spain), and several other similar facilities. In these cases, the main external users are those applying for beam time, including academic teams, research institutes, hospitals, and businesses, with applications for research in biology and medicine, nanotechnology, material science, heritage, chemistry, energy, and environmental sciences.

6.

The RIs may create cultural goods by outreach. There are related benefits which accrue to specific groups of citizens $(CU)$. Del Rosario Crespo Garrido and Catalano (2018) discuss the following types of cultural goods: onsite CERN visitors and visitors of CERN’s traveling exhibitions; the reach of media reporting on LHC; visitors of CERN and LHC experiment websites; users of LHC-related social media (YouTube, Twitter, Facebook, Google+); and other media-related benefits such as movies and non-scientific books. Collins (2017) discussed, in a sociological perspective, the huge impact in the media of the first observation of gravitational waves by LIGO interferometers, in spite of the fact that general relativity is presumably familiar only to a negligible fraction of the public.

As mentioned, there are two possible non-use benefits arising from RIs: the benefit of the unknown future use of the created knowledge (quasi-option value) and the intrinsic value of knowledge as a public good (existence value). The former often remains hidden by our ignorance and cannot be given a value ex ante. For example, nobody knows whether and to what extent the discoveries of the Higgs boson or of gravitational waves will generate useful applications. Instead, there may be a perceived generic social value of a discovery or a research project per se, arising from individual preferences for useless knowledge. It is an empirical matter to observe median taxpayer’s willingness to pay for such knowledge, similarly to the study of preferences for the conservation of the natural environment or cultural heritage. Hence, while the quasi-option value is simply assumed to be non-negative and conservatively set to zero out of ignorance (hence also excluding potential negative effects of knowledge), the existence value may be considered and estimated through the appropriate methods.

After the benefits identification, for each benefit there are two further crucial steps in implementing a social CBA: estimating the benefit in quantitative terms and valuing it through a shadow price, which expresses the social value of a marginal change in the availability of the good. For each benefit, these two steps are briefly discussed in what follows.

Knowledge outputs $(SC)$ are not be confused with the final value of knowledge embodied in a publication. First, scientists—those directly employed either by the body managing the RI or by universities and other institutions—are simultaneously producers and users of such outputs. Second, both publications and their citations have measurable direct value. The marginal social value of this benefit is thus measured by the opportunity cost of both producing and using a publication. This is represented by the value of the time scientists spend on these activities. As the empirical evidence on the market price of scientific publications and on the willingness of scientists to pay to be published, read, and cited are not reliable in terms of marginal social value, adopting the marginal cost approach is justified. Taking the marginal cost of a service as an empirical proxy of its benefit is a standard practice in CBA when the marginal WTP for such goods is not available. From an operational standpoint, the estimation of this benefit consists in computing the sum of the present value (in terms of the value of time) of papers authored by the RI’s scientists, and of the value of subsequent flows of papers produced by other scientists using the results of the RI’s scientists, which is divided by the number of references they contain as a proxy of the subsequent waves of papers citing the RI’s literature output, and eventually the value of the citations that each paper receives as a proxy of the social recognition that the scientific community acknowledges/attributes to the paper. For an application of this to LHC literature, see Florio, Forte, and Sirtori (2016).

Human capital accumulation $(HC)$ is valued as the increased earnings (called premium) gained by former RI’s students and former employees, starting from the time they leave the RI project, against a suitable counterfactual scenario. The premium is a salary and employability that are an effect of the acquired skills, reputation, and networking effects, along with other benefits to students and young researchers in general (postdocs, junior scientists, etc.), deriving from the value that is added to their curricula by their experience in the RI environment. An empirical estimation of the premium attached by students at LHC and experiments is provided in Camporesi, Catalano, Florio, and Giffoni (2017), who show that experiential learning is the key determinant of incremental salary expectations. The premium is estimated in the range of 5%–12% over an entire career, compared to peers who did not have the opportunity to be involved in LHC experiments, by means of a multivariate analysis. Bastianin and Florio (2018), assuming a maximum career length of 42 years, predict that the 2038 cohort of early-stage researchers (ESRs) at the High-Luminosity LHC will enjoy a salary premium until 2080. Using the yearly arrival rate of ESRs and the average time of stay at CERN, they estimate how many ESRs start a professional career elsewhere every year and then compute the time discounted value of the benefit for ESRs.

The value of technological spillovers $(TE)$ is given by the incremental profits (after the initial contract) gained by companies pertaining to the RI’s supply chain or other economic agents who have benefited from a learning externality. In this regard, three considerations are important. First, the initial core impulse of this benefit is a learning event in the procurement relation between firms and the RI. Second, the knowledge created thanks to this event leads to firms’ R&D and innovations, generating productivity and profitability changes in the long term and well beyond the initial contact. Such changes can relate to R&D management, organization practice, project accounting, commercialization techniques, etc. Third, such changes may ultimately produce profits that are evaluated in terms of social profits. These are usually different from private profits because, in principle, they are gross of taxes and interest and because of the possible wedge between market and shadow prices. A number of studies have been conducted in the last five years to investigate the long-term impact on firms’ economic performance of entering a technological procurement relationship with CERN (see, Castelnovo, Florio, Forte, Rossi, & Sirtori, 2018; Florio, Giffoni, Giunta, & Sirtori, 2018).

Turning to externalities from information technologies, two approaches may be adopted to attribute a value to open source, free software, and databases released by the RI in the public domain $(IT)$. One is the avoided cost by using, respectively, open data or by obtaining free, possibly open source, software or IT-based services for professional users. Such avoided costs, which are ultimately based on savings in terms of wages and the working hours of computer scientists and professionals in communities outside the RIs, are a practical way to estimate the implicit minimum WTP. The second approach is to explicitly search for the maximum WTP of certain users through either stated or revealed preference methods. For a practical application of the avoided cost approach to estimate the benefits of externalities generated by ROOT and Geant4 software developed at CERN, see Florio et al. (2016). For a cost-based approach to evaluate open source software, see Boehm et al. (2000).

The value of benefits produced by (mainly applied) RIs on external users (e.g., businesses, government bodies, other research teams, patients) and the economic value of services provided by the RI $(AR)$ are project-specific. Therefore, the approaches to value these benefits depend on the types of new services or products. These methods, in principle, are again generally based on the WTP, marginal cost, or avoided cost approaches and are often well established in CBA. Battistoni et al. (2016) provides an example of how to value health benefits for patients of the CNAO hadrontherapy center in Pavia. As a final remark on $AR$ benefits, it is worth noting that the main problem encountered in their valuation is that a causal relation is often difficult to detect. In most cases, innovations are indeed the result of the combination of discoveries and knowledge created from different sources, not only from one specific RI.

Outreach activities that are directly and indirectly carried out by the RI produce different cultural goods for different categories of the general public $(CU)$. The produced goods can be valued by estimating the willingness to pay of general public visitors (or other proxies) for such activities provided by scientific facilities such as exhibitions in museums of science and elsewhere, access to their websites, users of traditional and new (social) media, and so on. The WTP for these cultural goods is different across these groups and requires different estimation strategies. For onsite visits the travel cost method approach is helpful and was initially proposed by Hotelling (1949) and Clawson (1959) for national parks and outdoor recreation. For applications to RIs in physics, see Florio et al. (2016) and Pancotti et al. (2015).

Finally, concerning the estimation of existence value, it is worth noting that curiosity is a social attitude that supports knowledge creation per se. Not only are scientists curious about nature, but also hundreds of millions of citizens are occasionally interested in knowing something about research in physics and astrophysics, including something that has no known use to them, such as (just to cite some popular subjects) the origins of the universe, antimatter, black holes, gravitational waves, quarks, and quantum computing.

The government funding of science, including that of basic research in physics, astrophysics, and astronomy in particular, is also a reflection of these widespread cultural attitudes. As mentioned, the existence value of discovery is similar to the concept of existence value in environmental economics, a non-use value of natural resources that citizens want to be protected, whether or not they plan to use them in the future. In general, non-use values may be proxied by the stated or revealed WTP of taxpayers for potential discovery. While the intrinsic or existence value concept is not new, its application to RIs’ evaluation is novel. On this topic, see Florio, Giffoni, and Catalano (2020), and Florio and Giffoni (forthcoming), who report the results of contingent valuation experiments with samples, respectively, of students in four countries (in relation to LHC) and of French taxpayers (in relation to future accelerators at CERN).

#### 4.2 Dealing With Costs

The costs of RIs in physics can be broadly defined as the amount of money that has to be paid (cash outflows) or the resources that are employed (in-kind contribution) for the design, preparation, construction or set-up, operation, maintenance, and upgrade of a facility. However, many RIs not only sustain cash outflows but also recur to forms of in-kind support, such as the use of donated scientific equipment or the exploitation of personnel costs. For example, the U.S. Department of Energy will contribute to the High Luminosity LHC with some newly designed quadrupoles and crab cavities. Such arrangements correspond to the use of real resources that do not appear in the budgetary cost as a cash flow of the RI. They are however relevant indications of costs and, as a general rule, should be considered at their current market price, if available.

Like other investment projects in any field, the costs of RIs in physics may be broadly classified in capital $(CAPEX)$ and operating expenditure $(OPEX)$. The former includes costs for the acquisition of durable assets, such as construction costs, acquisition of experimental equipment, and intangible fixed assets such as intellectual property rights. Among annual operating expenditures, there are labor costs (including the costs of scientific personnel and other administrative and technical staff), materials, energy and other utilities, communication, and maintenance. Decommissioning costs should also be considered in some cases, for example, when there is radioactive waste to be disposed of after the shutdown of a facility.

RIs in physics are often designed to perform a range of different experiments or scientific activities. Synchrotron light sources, for example, allocate slots of beam time at their various beamlines to a large number of experimental teams every year. As a result, the research projects generally consist of several interrelated, but relatively self-standing, components, and several problems may arise when appraising their costs. The challenge is represented by the delimitation of RI project borders and, in turn, their financial and social costs. Such an exercise is not always as straightforward as it may appear at a first glance.

An individual scientific project may require a complex of facilities and experiments that are often managed through international collaborations involving different legal entities. For example, a particle accelerator without at least one detector cannot deliver any experimental data. Accelerators and detectors can be run by different collaborations involving legal bodies with separate juridical (and accounting) arrangements. Another example is distributed RIs, consisting of a network of hubs and nodes located in different countries. An example is the SKA radio telescope, which will be located in South Africa and Australia, with headquarters in the United Kingdom. As long as all those components, including the hub and nodes of a distributed digital grid, are necessary to enable the RI to achieve its mission, the costs of such a project are the sum of the costs of each component, regardless of its geographical location, ownership, and other legal and accounting arrangements. In these cases, the definition of the unit of analysis requires the careful aggregation and apportionment of several components, which may be under different contractual arrangements. This entails gathering data from the financial account of all the involved entities, so some harmonization may be necessary before aggregating cost items.

At the opposite side, an individual large-scale scientific site, like a National Laboratory in the United States, can manage a portfolio of various facilities and research projects, each with its own objective. The Lawrence Berkeley National Laboratory is managed by the University of California under a contract with the Department of Energy. The site hosts 76 buildings, over 4,000 staff, and 20 scientific divisions in different domains including computing sciences, physics, earth and environmental sciences, biosciences, energy sciences, and technologies. When a single experimental facility is part of a larger complex, like at Berkeley Lab, some costs are shared with other facilities and projects and should be carefully apportioned to the individual infrastructure under examination. In other words, if different facilities are hosted in the same site, through some functional interrelation—for example, energy and personnel—costs that are common to all facilities must be apportioned to the various entities according to transparent criteria.

Moreover, some RIs take advantage of facilities, land, or equipment in use by existing infrastructures. For example, the Large Hadron Collider (LHC) at CERN uses the 27-km-long tunnel that was excavated for its predecessor, the Large Electron-Positron Collider (LEP). If a new infrastructure re-uses a component of a previous facility, such a component should be considered as sunk and therefore not be included in the cost computation of the new RI. Accordingly, the LEP costs should not enter the LHC costs, as the new accelerator did not sustain costs to use the previous tunnel but only had to invest in certain improvements and other civil engineering adjustments to adapt the existing tunnel and detector sites.

From a socio-economic perspective, the financial costs of an RI may not appropriately reflect the opportunity cost of employed resources. Hence, the social cost of an RI may be different from its financial cost. This is due to market distortions, which may affect some input prices (such as personnel wages), and calls for the use of shadow prices and to the existence of negative externalities $(EXT)$ during construction and operation, which are to be valued in appropriate ways.

In general, it could be argued that there are four main types of RI cost that may require correction in socio-economic terms: land acquisition or use of certain public facilities; labor cost in locations affected by high levels of permanent unemployment; some utilities; and some environmental externalities.

First, many RIs are provided with land or facilities owned by public sector entities either for free or at a lower price than the market rate. When this is the case, there is a hidden subsidy and a cost to society that does not appear in the financial accounting. Second, there are situations where the labor market is affected by structural imbalances, so salaries paid to personnel may be higher or lower than the opportunity cost of labor. In locations with high unemployment (South Africa for SKA is an example), the shadow wage for workers employed in construction activities may be lower than the market wage. Wages of scientists, according to Romer (1990), are often below the value of marginal productivity because of the difficulty for an organization, which may be either a firm or an RI, to fully capture the potential of economic innovations arising downstream of R&D. Moreover, the intrinsic motivation of physicists working at the frontier of science may lead them to accept salaries that are lower than those they could earn in industry or finance. Third, occasionally the price of some utilities, particularly electricity, may deviate from long-run marginal costs because of regulated tariffs, and this should justify a possible correction to the RI’s financial accounts. Finally, there may be social costs related to externalities such as traffic congestion, e.g., during the construction and decommissioning phases, and some emissions of pollutants, including radioactivity. For most of these externalities, there are well-established methods in CBA practice on how to value externalities (see, e.g., European Commission, 2014), but for others further research is needed. An example is the cost of the pollution of space with orbital debris from satellites and rocket stages.

### 5. A Real Case Application

The surprising finding of recent applications of the above-mentioned framework to large-scale research infrastructures in physics (see Bastianin & Florio, 2018) is that a facility as costly as the high luminosity upgrade of the Large Hadron Collider (around \$1 billion in construction costs alone) and entirely devoted to discovering new physics without any identified practical use, passes a standard cost–benefit test ($E(NPV)>0$ with high probability). This result is obtained under conservative assumptions and without considering the unknown future use value, if present, of discoveries.

The aim of the HL-LHC project is to extend the discovery potential of the LHC after 2025. Two scenarios were considered: a baseline scenario with the HL-LHC upgrade and a counterfactual scenario that includes the operation of the LHC until the end of its life without the upgrade. In both scenarios, the total costs include past and future expenditures attributed to the LHC accelerator complex and by the four main LHC experiment collaborations: ATLAS, CMS, LHCb, and ALICE. The difference between the total cost (which includes capital and operational expenditures) in the two scenarios is about 2.9 billion Swiss francs.

The types of benefits considered (and their relative share over the total net benefits) are: human capital formation, created by the acquisition of additional knowledge, skills, competencies by students and ESRs (40%); scientific publications that scientists use as basis for further research and career growth (6%); industrial spillovers for firms involved in HL-LHC procurement (29%); IT externalities (9%); cultural benefits for the general public (6%) (including the economic value created through science tourism based the visits to CERN and travelling exhibitions, as well as benefits deriving from media products, which may causally be related to the LHC and HL-LHC programs); and the public good value for taxpayers of human knowledge advancements through scientific exploration (11%). The difference between the total benefit in the two scenarios is about 5.2 billion Swiss francs. The key benefit for such a positive socio-economic impact is the attractiveness of HL-LHC for ESRs. The NPV of the HL-LHC was calculated as the difference between the flow of discounted net benefits generated by the HL-LHC and the flow of discounted net benefits generated by LHC without high-luminosity upgrading. The resulting NPV is 2,217 MCHF, which is the sum of all annual discounted net benefits (green bars in Figure 1) over the 1993–2038 period. The ratio between incremental benefits and incremental costs of the HL-LHC with respect to continue operating the LHC under normal consolidation is slightly over 1.7.

After Montecarlo simulations of different scenarios for the most critical variables, including construction costs, the probability of a negative NPV is small (6%), even under very conservative assumptions on the potentials for the generated benefits. Further work is going on about testing the CBA approach to the Future Circular Collider (Bastianin & Florio, 2019), where the construction costs may be much larger than for the HL-LHC, given the need of a new 100-km tunnel (see Abada et al., 2019) while as mentioned the construction costs of the LEP were not included in the CBA of the HL-LHC.

### 6. Concluding Remarks

The necessity of a socio-economic impact assessment of large-scale research infrastructures in physics cannot be exaggerated. The history of the demise of the Superconducting Super Collider (Riordan, Hobbeson, & Kolb, 2015) suggests that governments are not always prepared to foot the bill of any investment project in physics, particularly when the costs are higher than expected compared to other fields and when benefits are not quantified and valued in a proper way. Hence it seems useful to adopt a quantitative framework for the assessment of socio-economic benefits and costs associated with an RI that are measurable by means of a common metric. As demonstrated by the examples cited in the article, such a cost–benefit analysis lends itself well to assess large RIs in physics. After identifying the relevant impacts, valuing them in monetary terms, and discounting them through a social discount rate, the resulting net effect is expressed in monetary terms as an economic $E(NPV)$. This is a way to represent the social welfare effects generated by a project that is constrained by the information that was available at the time of the assessment in probabilistic terms. Clearly, a positive net benefit can only reinforce the scientific case, as a signal that the project’s costs to society are more than recouped by its benefits.

Nevertheless, the NPV should be estimated by means of sound theoretical assumptions and robust and up-to-date empirical methods as much as possible, using, for example, appropriate econometric techniques to deal with data about impacts on firm profits and patents, students’ wage premia, travel costs for onsite general public visitors, willingness to pay for science by taxpayers, and other socio-economic variables. It is also important that RI managers or funders recur to independent evaluators, with the appropriate professional expertise in CBA, as the analysis needs to be credible and pass the peer review scrutiny.

The mentioned example of HL-LHC does not imply that all research infrastructures would pass a social benefit–cost test. However, a negative $E(NPV)$ per se does not warrant a negative funding decision. As a matter of fact, (1) the empirical estimation of the E(NPV) is an informationally constrained measure of our knowledge in terms of the real resources that are needed and expected to be created by a project, and (2) the scientific case should often be more important than the socio-economic impact argument in convincing prospective funders. However, it cannot be damaging to show that—along with the scientific case—there are some socio-economic benefits against the costs.

In conclusion, it may be argued that large-scale RIs in physics may take advantage from the scrutiny of social CBA. This can either be used to complement the scientific case before a decision is taken or be performed several years later to assess the ex post impact of the investment decision. The net socio-economic benefits may be positive, modest, or even negative, but this can only be determined after a serious empirical analysis and not as an a priori rhetorical argument, given the increase in competition within science itself and the budgetary constraints of governments and funding agencies. Long-term uncertain benefits of discoveries should remain outside the CBA, as they are unmeasurable ex ante. Some socio-economic benefits will be known only after decades and will be an ex post surprise to future generations, as it happened with the practical applications of electromagnetism, general relativity, or quantum mechanics. What is interesting, however, is to gauge to what extent the measurable benefits of some large-scale investments in physics may already pay back costs, even before the long-term unknown effects are visible.

#### References

• Abada, A., Abbrescia, M., Abdussalam, S. S., Abdyukhanov, I., Abelleira Fernandez, J., Ambramov, A., . . . Zurita, J. (2019). FCC-ee: The lepton collider. European Physical Journal Special Topics, 228(2), 261–623.
• Anderson Economic Group LLC. (2011). Economic impact of Fermi National Accelerator Laboratory.
• Bacchiocchi, E., & Montobbio, F. (2009). Knowledge diffusion from university and public research. A comparison between US, Japan and Europe using patent citations. Journal of Technology Transfer, 34(2), 169–181.
• Bastianin, A., & Florio, M. (2018). Social cost benefit analysis of HL-LHC. No. CERN-ACC-2018-0014. CERN Future Circular Collider Publication.
• Bastianin, A., & Florio, M. (2019). Initial guidelines for a social cost-benefit analysis of the FCC programme. No. CERN-ACC-2019-0037. CERN Future Circular Collider Publication.
• Battistoni, G., Genco, M., Marsilio, M., Pancotti, C., Rossi, S., & Vignetti, S. (2016). Cost–benefit analysis of applied research infrastructure. Evidence from health care. Technological Forecasting and Social Change, 112, 79–91.
• Boehm, B., Abts, C., Winsor Brown, A., Chulani, S., Clark, B. K., Horowitz, E., . . . Steece, B. (2000). Software cost estimation with COCOMO II. Englewood Cliffs, NJ: Prentice Hall.
• Brent, R. J. (2017). Advanced introduction to cost–benefit analysis. Cheltenham and Northampton: Edward Elgar.
• Camporesi, T., Catalano, G., Florio, M., & Giffoni, F. (2017). Experiential learning in high energy physics: A survey of students at the LHC. European Journal of Physics, 38(2), 025703.
• Carrazza, S., Ferrara, A., & Salini, S. (2016). Research infrastructures in the LHC era: A scientometric approach. Technological Forecasting and Social Change, 112, 121–133.
• Carrazza, S., Ferrara, A., & Salini, S. (2014). Research infrastructures in the LHC era: A scientometric approach. Research Project Cost/Benefit Analysis in the Research, Development and Innovation Sector. EIB University Research Sponsorship Programme.
• Castelnovo, P., Florio, M., Forte, S., Rossi, L., & Sirtori, E. (2018). The economic impact of technological procurement from large-scale research infrastructure: evidence from the large hadron-collider at CERN. Research Policy, 47(9), 1853–1867.
• Clawson, M. (1959). Method for measuring the demand for, and value of outdoor recreation. Reprint, No.10, Resources for the Future, Washington, DC.
• Collins, H. (2017). Gravity’s kiss: The detection of gravitational waves. Cambridge, MA: MIT Press.
• Del Rosario Crespo Garrido, I., & Catalano, G. (2018). Cultural effects at CERN. No. CERN-ACC-2018-0048. CERN Future Circular Collider Publication.
• European Commission. (2014). Guide to cost-benefit analysis of investment projects economic appraisal tool for cohesion policy 2014–2020. Directorate-General for Regional and Urban Policy.
• Florio, M., Forte, S., & Sirtori, E. (2016). Forecasting the socio-economic impact of the Large Hadron Collider: A cost–benefit analysis to 2025 and beyond. Technological Forecasting and Social Change, 112, 38–53.
• Florio, M., & Sirtori, E. (2016). Social benefits and costs of large-scale research infrastructures. Technological Forecasting and Social Change, 112, 65–78.
• Florio, M., & Giffoni, F. (2020). A contingent valuation experiment about future particle accelerators at CERN. PLoS ONE 15(3): e0229885.
• Florio, M., Giffoni, F., & Catalano, G. (2020). Should governments fund basic science? Evidence from a willingness-to-pay experiment in four universities. Journal of Economic Policy Reform.
• Florio, Massimo. (2019). Investing in science. Cost-benefit analysis of research infrastructures. Cambridge, MA: MIT Press.
• Florio, M., Giffoni, F., Giunta, A., & Sirtori, E. (2018). Big science, learning, and innovation: evidence from CERN procurement. Industrial and Corporate Change, 27(5), 915–936.
• Giffoni F., & Vignetti S. (2019). Assessing the Socioeconomic Impact of Research Infrastructures: A Systematic Review of Existing Approaches and the Role of Cost-Benefit Analysis, L’Industria, 1, 75-102.”
• Hotelling, H. (1949). Letter to the National Park Service. In The economics of public recreation: An economic study of the monetary evaluation of recreation in the national parks. Washington, DC: National Park Service and Recreational Planning Division.
• Irvine, J., & Martin, B. R. (1984a). CERN: Past performance and future prospects: CERN’s position in world high-energy physics. Research Policy, 13(4), 183–210
• Irvine, J., & Martin, B. R. (1984b). CERN: Past performance and future prospects: II. The scientific performance of the CERN accelerators. Research Policy, 13(5), 247–284.
• Irvine, J., & Martin, B. R. (1984c). CERN: Past performance and future prospects: III. CERN and the future of world high-energy physics. Research Policy, 13(6), 311–342.
• Johansson, O., & Kriström, B. (2018). Cost–benefit analysis. Cambridge, U.K.: Cambridge University Press.
• KPMG. (2016). The Perimeter Institute for Theoretical Physics. Final Evaluation Report, KPMG LLP.
• Le Goff, J.-M., Heuer, R., Koutchouk, J.-P., Stapnes, S., & Stavrev, S. (2011). Particle physics, a key driver for innovation: Facing Europe’s socio-economic challenges.
• LBNL–Ernest Orlando Lawrence Berkeley National Laboratory. (2001). Economic impact 2001. Berkeley, CA: Technology Transfer Department, University of California.
• Martin, B. R., & Irvine, J. (1983). Assessing basic research: Some partial indicators of scientific progress in radio astronomy. Research Policy, 12(2), 61–90.
• Martin, B. R. (1996). The use of multiple indicators in the assessment of basic research. Scientometrics, 36(3), 343–362.
• Martin, B. R., & Tang, P. (2007). The benefits from publicly funded research. SPRU Working Paper Series N. 161, University of Sussex.
• OECD. (2014). Report on the impacts of large research infrastructures on economic innovation and on society. Paris: OECD.
• Pancotti, C., Battistoni, G., Genco, M., Livraga, M., Mella, P., Rossi, S., & Vignetti, S. (2015). The socio-economic impact of the National Hadrontherapy Centre for Cancer Treatment (CNAO): Applying a cost-benefit analysis analytical framework. In DEMM Working Paper n. (2015–05).
• Riordan, M., Hoddeson, L., & Kolb, A. W. (2015). Tunnel visions: The rise and fall of the superconducting super collider. Chicago: University of Chicago Press.
• Romer, P. M. (1990). Endogenous technological change. Journal of Political Economy, 98(5), S71–S102.
• Salter, A. J., & Martin, B. R. (2001). The economic benefits of publicly funded basic research: A critical review. Research Policy, 30(3), 509–532.
• Samuelson, P. (1954). The pure theory of public expenditure. Review of Economics and Statistics, 36(4), 387–389.