Earth’s Orbits at Risk

3. An environmental economics framework for measuring the cost of space debris

Chan Hee Lee, Seoul National University, Korea

Keewon Kim, Seoul National University, Korea

Jong Ho Hong, Seoul National University, Korea

Abstract

This chapter applies an environmental analytical framework and econometric model for estimating the cost of space debris, providing global and national perspectives. Total cost is broken down into three separate domains and the chapter presents the equation and variables for each domain. The chapter notably closely considers external costs and suggests economic measures to internalise them.

Introduction

Since the launch of the first artificial satellite, the Union of Soviet Socialist Republics’ (USSR’s) Sputnik 1 in 1957, humanity and its space programmes have come a long way. Attempts have been so numerous in the past 60 years that a primary concern has now ironically become the over-exploration of the formerly unexplored. The scenario in which collisions between space objects, including debris and functional objects, end up causing a cascade where each collision creates debris heightening the risk of further collisions, the “Kessler Syndrome”, is transforming from a distant possibility to a daunting reality for today’s space community. Meanwhile, tens of thousands of satellites, individually or in the form of mega-constellations, are allegedly in the pipeline to be launched in the next decade. Despite heightened awareness of the problem and the many technical and normative developments, the global response remains insufficient to turn the tides.

This gap between the level of action required for meaningful change and that actually taken is not new. It has been repetitively raised in relation to various environmental problems, a most recent and salient example of which is climate change. As witnessed, some are still largely unaware of or have denied the problem, while others acknowledge the importance yet remain reluctant to change (or incapable of changing) their own behaviours. The analogy can be taken further: both the problems of space debris and climate change are attributable to different countries to different extents, but the damage is transboundary or global in nature. Contrary to early beliefs, neither the space environment nor the natural environment was found to be sufficiently vast enough to be unbounded and immune to unrestrained human activity. Often classified as public goods, characterised by their non-rivalry and non-excludability, both have been prone to overexploitation by human populations, generally assumed to be self-interested. Presumably under similar lines of reasoning, Gerard Brachet, former Chairman of the United Nations Committee on the Peaceful Uses of Outer Space, has also compared the situation to overfishing and marine pollution, a classic case of the tragedy of the commons (Newman and Williamson, 2018[1]).

Accordingly, the perspective and approach developed in the field of environmental economics may prove useful in the discussion on space debris and preserving space sustainability. Having extensively grappled with how to understand the cause (e.g. lack of property rights, externalities), measure the associated costs and benefits, and find both non-market and market solutions (e.g. Pigouvian tax or subsidy, cap-and-trade system) related to various environmental problems using economic theory, environmental economics holds a unique strength in capturing the most important aspects of a complex problem and providing practical guidance for decision making. Undoubtedly, the approach also has limits, particularly in regard to the assumptions and resulting inability to fully incorporate the uncertainties of the real world. Such issues and limitations will be clarified when relevant and possible throughout this chapter.

Given this, this preliminary research aims to quantify the cost of space debris in monetary terms and introduce economic tools or approaches to solve the problem. It begins, in the next section, by presenting the framework used here to quantify the cost of space debris and identify the impacts or cost categories that require consideration. Rather than starting from scratch, this study reviews and builds upon the socio-economic impacts outlined in Undseth, Jolly and Olivari (2020[2]). The following section presents ways to quantify the identified cost categories, bringing in valuation methods developed in the field of environmental economics, especially those concerning the valuation of non-market goods, resources or services. Although numbers or ranges cited in previous literature will be included when appropriate and possible, this chapter does not intend to present a decisive monetary estimate of its own, for significant differences will inevitably exist depending on the precise context and conditions of the space mission under evaluation. The last section presents the conclusion and overall discussion, particularly from the perspective of Korea, a latecomer in terms of exploring outer space.

Modelling the cost of impact events

A model from a global perspective

What is the cost of space debris? How should the costs be defined? Suppose a piece of debris hits satellite A and a piece of resulting debris from satellite A collides with satellite B. In the perspective of the country or company that operates satellite A, only the damage to satellite A will count; the damage costs associated with satellite B will not. However, from a global perspective, the damage inflicted on both satellites will count. The costs will further differ depending on the spatial and temporal scope, such as whether the consideration is confined to outer space or includes the Earth and whether the entire history of space exploration, only selected time periods or implications in the future are covered. 

As this study aims to develop a model that is both comprehensive and practical, the cost of space debris centres on the costs incurred as a result of collision events, only after which tangible costs arise, and covers both the space and terrestrial environment. This section will present a model for estimation from the global perspective, while the following section will also suggest a method to apply the model at the national level. 

The total cost (${\mathit{C}}_{\mathit{t}}$): Considering the pace at which the space industry and the number of objects in space have grown, the space environment is also expected to change within short time periods. Therefore, this study presents a model that estimates the total cost on a yearly basis, broken down into the costs pertaining to all operating satellites, space stations and shuttles (e.g. the International Space Station, ISS), and the Earth. Put into an equation, the annual cost of space debris in year t is:

$\begin{array}{c}{C}_t=C_{St}+C_{It}+C_{Et} \#\left(1\right)\end{array}$

where $C_{St}$ represents the costs associated with satellites, $C_{It}$, the impact on space stations and shuttles, and $C_{Et}$, the impact on Earth. 

The impact on satellites (${\mathit{C}}_{\mathit{S}\mathit{t}}$): The costs related to satellites, specifically attributable to the problem of space debris, can be largely grouped into the additional costs incurred during the stages of development, operation and maintenance on the one hand, and the damage costs resulting from collision events on the other.

The additional development and operational costs arise from the need to avoid collision with space debris or to reduce the level of damage, should a collision inevitably take place. Improving satellite and/or constellation designs and enhancing shielding can increase development costs, while the increased mass may also increase launch costs. Insurance costs may increase due to heightened risks and it may be necessary to secure additional resources to obtain information on approaching objects promptly, as well as to perform evasive manoeuvres.

The most substantive consequence of a collision with space debris would be the loss or impairment of payloads. However, the direct and indirect damage costs may also include the interruption of satellite services (e.g. communication and broadcasting), loss of research data and a decrease in investments in related industries.

In modelling such costs, this study makes several assumptions. First, only those collisions that result in the complete loss of satellite functions are considered. This implies that minor scratches, dents or other types of inconsequential damage to satellites or satellite parts are disregarded, if the satellite remains functioning. This is because “impacts that do not have any value to human beings are not counted” in cost‑benefit analysis (Boardman et al., 2018[3]). The second relates to when costs are assumed to arise and hence accounted for. Development costs will have begun to arise well before the launching stage, yet are accounted for in sum in the first year of the satellite’s lifespan. Operational and maintenance costs that arise each year are assumed to be paid for at the beginning of each year, as this is usually when budgets are set. Lastly, in comparison to costs, the benefits obtained from satellites are assumed to occur at the end of each year. 

Given the above, the annual cost borne by satellites can be modelled as:

$\begin{array}{c}{C}_{St}=m_t\stackrel{-}{D}+n_t\stackrel{-}{O}+{\alpha }_t\sum _{k=0}^{\stackrel{-}{y}}\{<!--\; -->\frac{\stackrel{-}{V}}{\stackrel{-}{l}}\times \frac{1}{{\left(1+r\right)}^{\stackrel{-}{l}-k}}\} \#\left(2\right)\end{array}$

where $\stackrel{-}{D}$ stands for average development costs and $\stackrel{-}{O}$ for average annual operational and maintenance costs; both are confined, however, to those costs additionally incurred due to the space debris phenomenon. $m_t$ refers to the number of newly launched satellites in year $t$ and $n_t$ to the total number of satellites in operation in year $t$, which includes both newly and formerly launched satellites. ${\alpha }_t$ is the number of satellites that lost their function as a result of a collision with space debris in year $t$. $\stackrel{-}{V}$ stands for the average monetary value of satellites, $\stackrel{-}{l}$ for the average lifespan of satellites and $\stackrel{-}{y}$ for the average number of years satellites have been in operation. Finally, $r$ is the social discount rate, which is used in cost-benefit analysis to convert future values into present values. In the context of this equation, it comes into account when estimating the benefits obtained from the continued operation of satellites in the future. It must be further noted that, with the exception of $\stackrel{-}{D}$, all average values are the average of all operating satellites; in the case of $\stackrel{-}{D}$, the average will concern only newly launched satellites. 

Conceptually, the annual cost borne by satellites is the sum of the additional development, operational and maintenance costs arising from the space debris phenomenon and the expected benefits lost due to collision events.

The impact on space stations and shuttles (${\mathit{C}}_{\mathit{I}\mathit{t}}$): Although there have not been any fatal incidents so far, the ISS has been under increasing threat of collision with space debris. In 2020 alone, several narrow incidents were reported, followed in the next year by actual or near collisions creating a hole in the station’s robotic arm and forcing astronauts on board to prepare for evacuation (see Kettley (2020[4]) and Ali and Gorman (2021[5])). Further implications exist concerning the invaluable research conducted at the ISS. With rising attention to space tourism, the threat may extend to various other types of crewed vehicles in the future.

The costs that arise in such cases can be modelled as:

$\begin{array}{c}{C}_{It}={\beta }_t\left({\stackrel{-}{P}}_I+{\stackrel{-}{L}}_I\right) \#\left(3\right)\end{array}$

where ${\beta }_t$ refers to the number of collision events in year $t$, ${\stackrel{-}{P}}_I$ the average cost of damage to space stations and shuttles (including material and non-material aspects), and ${\stackrel{-}{L}}_I$ the average cost related to the loss of lives. All are limited to collisions with space debris.

The impact on Earth (${\mathit{C}}_{\mathit{E}\mathit{t}}$): Existing literature rarely takes into account the impact of space debris on Earth when calculating the related costs, presumably because there have not been many reported cases of serious damage to terrestrial ecosystems and creatures. However, such cases, where resources, property or human lives on Earth were indeed affected, have continuously occurred. In 2002, a six-year-old Chinese boy was reported to have been injured from a falling space object while sitting under a tree (Maley, n.d.[6]). A more serious and recent case involves a region in Guangxi, People’s Republic of China, where debris identified to have broken apart from Long March 3B’s rocket booster fell and exploded on the ground, posing severe health risks to local residents. Many more cases exist, involving damages of various types and magnitudes to land and property across the globe (e.g. Lemoine (2016[7])). Although USD 6 million was the amount filed by the Canadian government against the USSR for the damage caused by radioactive debris traceable to the state’s satellite in 1978,1 the extent of the damage can be expected to be much higher in present values and if the collision involves populated areas. In addition, the threats are expected to loom larger with growth in the number of space debris.

Put into an equation, the annual costs to Earth can be modelled as:

$\begin{array}{c}{C}_{Et}={\gamma }_t\left({\stackrel{-}{P}}_E+{\stackrel{-}{L}}_E\right) \#\left(4\right)\end{array}$

where ${\gamma }_t$ refers to the number of collision events on Earth in year $t$, ${\stackrel{-}{P}}_E$ the average cost of damage to property and resources on Earth, and ${\stackrel{-}{L}}_E$ the average cost related to the loss of lives on Earth. 

Combining equations (1)~(4), the annual cost of space debris in year $t$ can be expressed as shown below. Table 3.1 presents a summary of the variables. 

$C_t=C_{St}+C_{It}+C_{Et}$

$\begin{array}{c}=[m_t\stackrel{-}{D}+n_t\stackrel{-}{O}+{\alpha }_t\sum _{k=0}^{\stackrel{-}{y}}\{<!--\; -->\frac{\stackrel{-}{V}}{\stackrel{-}{l}}\times \frac{1}{{\left(1+r\right)}^{\stackrel{-}{l}-k}}\}]+{\beta }_t({\stackrel{-}{P}}_I+{\stackrel{-}{L}}_I)+{\gamma }_t({\stackrel{-}{P}}_E+{\stackrel{-}{L}}_E) \#\left(5\right)\end{array}$

Table 3.1. Variables for estimating the cost of space debris at the global level

Variable type	Variable	Description	Unit
Count	mt	Number of satellites launched in year t
	nt	Number of satellites in operation in year t (including satellites launched in year t )
	αt	Number of satellites that lost their function due to space debris in year t
Frequency	βt	Number of collisions between space stations/shuttles and space debris in year t
	γt	Number of collisions on Earth in year t
Cost	D-	Average increase in development costs due to space debris	per satellite
	O-	Average increase in operational and maintenance costs due to space debris	per satellite
	P-	Average cost of non-human damage	per collision
	L-	Average cost of human damage	per collision
Value	V-	Average monetary value of satellites	per satellite
Duration	l-	Average lifespan of satellites (years)	per satellite
	y-	Average number of years satellites have been in operation (years)	per satellite
Rate	r	Social discount rate (%)

Applying the model to the national level

The problem of space debris is inevitably a global issue: the action of one country or company carries repercussions for all others around the globe that cannot but share the space environment and Earth’s orbits. However, in the perspective of each country, a major concern would be the cost of space debris that each country specifically faces. Alternatively, in the process of finding global solutions or evaluating impacts, comparisons between countries may surface as a matter of interest. The equation below is the result of converting the variables in equation (5) into national units and reflects the cost of space debris for country $j$ in year $t$.

$C_{jt}=C_{Sjt}+C_{Ejt}$

$\begin{array}{c}=[m_{jt}{\stackrel{-}{D}}_j+n_{jt}{\stackrel{-}{O}}_j+{\alpha }_{jt}\sum _{k=0}^{{\stackrel{-}{y}}_j}\{<!--\; -->\frac{{\stackrel{-}{V}}_j}{{\stackrel{-}{l}}_j}\times \frac{1}{{\left(1+r\right)}^{\stackrel{-}{l}-k}}\}]+{\gamma }_{jt}({\stackrel{-}{P}}_{Ej}+{\stackrel{-}{L}}_{Ej}) \#\left(6\right)\end{array}$

As apparently noticeable, a large difference is the exclusion of the impact on space stations and shuttles. One reason is attributable to the fact that the ISS is a joint venture of only 15 countries and plans for it after 2024 (or, at most, 2028) are unclear. If astronauts or tourists from a particular country face injuries or death, such costs can be added to the equation on an individual basis (Table 3.2). 

Table 3.2. Variables for estimating the cost of space debris at the national level

Variable type	Variable	Description	Unit
Count	mjt	Number of satellites launched by country j in year t
	njt	Number of satellites operated by country j in year t (including satellites launched in year t )
	αjt	Number of satellites operated by country j that lost their function due to space debris in year t
Frequency	γjt	Number of collisions on country j ’s territory in year t
Cost	D-j	Average increase in development costs due to space debris for country j	per satellite
	O-j	Average increase in operational and maintenance costs due to space debris for country j	per satellite
	P-Ej	Average cost of non-human damage due to space debris in country j	per collision
	L-Ej	Average cost of human damage due to space debris in country j	per collision
Value	V-j	Average monetary value of satellites operated by country j	per satellite
Duration	l-j	Average lifespan of satellites operated by country j (years)	per satellite
	y-j	Average number of years satellites operated by country j have been in operation (years)	per satellite
Rate	r	Social discount rate (%)

Discussion on the OECD’s impact categories

As noted in the introduction, the cost categories or variables considered in this study build upon the impact categories outlined in the OECD policy paper. Some categories were merged into a single variable to simplify the model, while some others were removed because they were beyond scope or irrelevant. Table 3.3 presents how the original categories can be reclassified according to the model of this study.

Table 3.3. The OECD’s impact categories reclassified

Time frame	Type of impact	Description	Reclassified
Current impacts	Debris-related damage	Loss of functionality or loss of entire satellites. Many incidents go unreported.	V-
	Satellite and constellation design	Costs associated with satellite shielding, collision avoidance capabilities, safe hold modes and redundancies (i.e. launch extra satellites as spares). Satellite constellations increasingly include spares for system resilience, but this solution often becomes part of the problem.	D-
	Operational costs	Costs of space situational awareness activities, services and software. Data blackouts when conducting avoidance manoeuvres.	O-
	Orbit clearance costs	In the geostationary orbit: Relatively low, equivalent to about three months of station‑keeping. In the low-earth orbit (LEO) above 650 km altitude: Very high and requiring specific satellite subsystems (on-board computer).	Removed
	Insurance costs	Overall, limited use of in-orbit insurance by operators for space debris. Space debris collisions have historically been considered low-probability and not affecting insurance premiums.	O-
Potential future impacts	Loss of unique applications and functionalities	Space observations from some of the orbits most vulnerable to space debris are often the best or only source of data and signals in their domain. This applies in particular to polar-orbiting weather and earth observation satellites. The loss of polar‑orbiting weather satellite observations would heavily affect the southern hemisphere, where there are fewer terrestrial observations.	V-
	Loss of lives	The International Space Station is located at an altitude of about 400 km. Although debris at that altitude decays naturally, it still poses a real collision threat.	L-
	Interrupted time series for earth science and climate research	Uninterrupted time series are crucial for the accuracy and reliability of weather prediction and climate models.	V-
	Curbed economic growth and slowdown in investments in the sector	Satellite broadband is widely considered to become a key driver of space activities and revenues in the coming decades. More than ten broadband satellite constellations are in different stages of development. Practically all LEO communication services would be affected, on orbit and/or during orbit-raising, as most constellations are located near or above the thickest LEO debris belts. Reduced access to venture finance, with investors preferring more affordable and less risky terrestrial alternatives.	V-
	Distributional effects	The loss or perturbation of certain LEOs could be felt more heavily in rural low‑density residential areas and low-income countries.	Removed

The variable $\stackrel{-}{D}$ includes the cost increase due to the addition of shielding or spare parts noted in the OECD report and may further include other costs that arise during the stages of development and launch. Likewise, the variable $\stackrel{-}{O}$ captures the operational and insurance costs identified in the OECD policy paper and may further include other maintenance costs previously overlooked (e.g. following the increase in staffing to monitor and respond to collision risks more closely).

The convergence of various categories into the variable $\stackrel{-}{V}$, however, may raise questions: how can the interruption experienced by the research community, the impact on the economy and investments, or other intangible benefits be reflected? Although the answer would ultimately depend on the specific valuation method applied (more details can be found in the next section), it is indeed possible to measure the entire value of satellites that encompasses such intangible, indirect or non-use values. For instance, when surveying the public’s willingness to pay for a particular satellite (service), researchers only need to clearly explain such aspects, which will then be reflected in the responses. At the same time, many of the categories are, in effect, the value of data transmitted from different types of satellites and do not need to be treated as distinct categories.

Two categories have been removed in the context of this study. Orbit clearance costs were removed because collision events with space debris do not necessarily entail the act of clearing orbits. While related activities can be viewed as efforts to reduce the risks and, hence, costs of space debris, including such costs can also give rise to double counting. This is because the cost of damage caused by a certain problem and the cost of alleviating it are essentially two different sides of the same coin.

Distributional effects, the other removed category, largely refers to the problem in which the degree of loss or damage varies depending on the economic level of a country. This matter is undoubtedly important and requires attention; however, such inequalities should be reflected in the process of estimating the costs, rather than treated as a separate cost category. When applying the model of this study, for instance, the cost of space debris at the national level will vary widely depending on the context of each country, such as one’s income level and the extent to which one’s space industry has developed.

Estimating the costs 

Economic valuation is understood as attaching a monetary value to things based on the preference and welfare of individuals. This is most often measured by how much individuals would be willing to pay to receive a certain service or benefit (willingness to pay, WTP) or, at times, by how much individuals would be happy to accept as compensation for a decrease in benefit or welfare (willingness to accept, WTA). Such individual preferences can be measured based on either a revealed or stated preference. Revealed preference refers to preferences that have been observed and thus revealed to the world, such as prices in the market; stated preference, on the other hand, refers to preferences that have been self-reported by, for instance, survey respondents. Generally, economists tend to trust and prefer revealed preferences, which are believed to reflect “the world as it is” or the “real” behaviour of economic actors.

Notwithstanding the limitations, stated preference methods are, however, often the only option possible for valuation purposes. This is the case when no observable price exists, which is true of many environmental goods and services, as well as health interventions, cultural heritage sites and other public goods. In such cases, applying the contingent valuation or choice experiment method is gaining popularity and increasing support in terms of validity.

Among the variables included in this study’s model to estimate the cost of space debris, development, operational and maintenance costs ($\stackrel{-}{D}$ and $\stackrel{-}{O}$) are assumed to be easily observable and, thus, rather straightforward. The main challenges, therefore, are expected to surround the value of goods and services for which prices are not easily observable, such as the value of satellites ($\stackrel{-}{V}$) or the environment (included in $\stackrel{-}{P}$), and values that are intangible or immeasurable, such as the value of human lives ($\stackrel{-}{L}$). The remainder of this chapter will explore such contentious subjects, based on the developments thus far in the field of environmental economics.

The value of satellites ($\stackrel{-}{\mathit{V}}$)

The largest and most serious impact of space debris and incidents thereof is the destruction of or damages to operational satellites, leading to the loss of functionalities either entirely or partially. Following the observations of Murtaza et al. (2020[8]), even millimetre-sized debris can cause substantial damage due to the hypervelocity (typically 8~10 km/s) and uncontrolled nature that characterise space objects. The precise extent of the loss and how it can best be measured, however, would vary depending on the characteristics of the satellite (e.g. function, altitude, service area, etc.).

The value of satellites that provide communication or broadcasting services, for example, would mostly concern direct use value. Therefore, the welfare enjoyed by individuals in monetary value can be estimated using market transactions data, such as the bills paid for telephone and Internet services. How about satellites performing earth observation missions? Weather forecasting services are generally provided without charge, while the scope and application of obtained data and information are extremely vast (see Häggquist and Söderholm (2015[9]) for a non-exhaustive list of areas for which geological information is used). Although likely an underestimation of actual benefits, a simple approach based on revealed preferences would be to use the total revenue enjoyed by satellite operators from data and information sales.

An alternative method, based on stated preference, is to run a survey using the contingent valuation. Eom and Hong’s work (2011[10]) is an example, where the value of a geostationary satellite expected to provide improved information on atmospheric pollution was measured through a survey with a sample size of 1 000. Respondents were given an easily understandable scenario explaining the situation (with vs. without the improved information) and the potential effects the improved information could have on individuals, then asked to respond to a series of questions following the dichotomous choice method. As a result, the average WTP per household was estimated to be approximately USD 3.6 (KRW 4 200).2 Once such a WTP has been drawn, the value of a satellite can be estimated by the product of the WTP and the beneficiary population.

Nonetheless, the amount would differ for different types of satellites. Accordingly, to estimate the global average value, $\stackrel{-}{V}$, the average value for and the proportion of each type must be considered as shown in the following equation:

$\begin{array}{c}{\stackrel{-}{V}}_t= \sum _{f=1}^{n_f}{w}_{ft}{\stackrel{-}{v}}_{ft} \#\left(7\right)\end{array}$

where ${\stackrel{-}{V}}_t$ refers to the global average value of satellites in year $t$, $n_f$ the number of different types of satellites, $w_{ft}$ the proportion of satellite type (or function) $f$, and, ${\stackrel{-}{v}}_{ft}$ the average value of satellite type $f$.

The value of property and resources ($\stackrel{-}{\mathit{P}}$)

An impact event that causes damage to public/private property and/or resources, including the natural environment, has much in common with natural disasters in the sense that neither can be fully prevented, while the consequences can be truly devastating. Methods commonly used to estimate the cost of damage due to natural disasters have been based on either insurance claims, clean-up costs or recovery costs.

The catastrophic flooding in Western and Central Europe in July 2021, for instance, has been estimated to have cost at least USD 20 billion in Germany alone and based solely on insurance claims (Aon, 2021[11]). This approach is most accessible in that the data are readily available and can reflect the damages to property; however, in many cases, the numbers are likely to be gross underestimations of actual damage costs as other types of damages (e.g. to unowned land or resources) are not accounted for.

In the aforementioned example, in which the Canadian government filed a case against the USSR under the Liability Convention, the requested USD 6 million amounted to roughly half of the costs borne to clean up the radioactive debris generated. Such an approach has an advantage over the method based on insurance claims in terms of measuring the impact on the environment.

Recovery costs can include all types of costs incurred to undo the damages and return property, the natural environment, etc. to their original state. Therefore, this method has the potential to be the most comprehensive, but, for the same reason, can show the largest variance. For instance, the amount would differ depending on how far ahead in time recovery efforts are recognised or whether non-material damages, such as the psychological damages to families and communities, are also considered (see Bonanno et al. (2010[12]) for a discussion on this topic).

Once the appropriate method is chosen and the damage costs estimated, the global average, $\stackrel{-}{P}$, can be calculated by the following:

$\begin{array}{c}{\stackrel{-}{P}}_t= \frac{\sum _{i=1}^{n_c}{p}_i}{n_{ct}} \#\left(8\right)\end{array}$

where ${\stackrel{-}{P}}_t$ stands for the global average cost of damage to property and resources in year $t$, $n_{ct}$ the number of collision events in year $t$, and, $p_i$ the damage costs incurred for collision event $i$.

The value of statistical life ($\stackrel{-}{\mathit{L}}$)

The mere idea of putting a price tag on human lives can be extremely controversial. Earlier methods of estimation based on wages as a proxy for one’s lifetime lost (“forgone earnings”) only aggravated the problem, since, following such a logic, the value of one’s life would differ according to one’s paycheck. The value of statistical life (VSL), on the other hand, does not measure the value of one’s time or life per se, but rather reflects the WTP of individuals for a reduction in the risk of death or the WTA for bearing an increase; hence, the term “statistical”. In theory, the VSL can be conveniently calculated by the function below, where $a$ is the WTP or WTA and $w$ is the change in risk (Boardman et al., 2018[3]).

$\begin{array}{c}VSL=\frac{a}{w} \#\left(9\right)\end{array}$

For the purpose of illustration, let us assume that an individual can choose to buy a private alarm system that notifies its users of any approaching (space) object well enough in advance to safely evacuate. If the system increases the probability of survival by 1/100 000 and costs USD 300 to install (or lifetime service), the VSL in this specific case – reducing the risk of death due to a space debris collision – would be USD 30 million.

Despite the seeming simplicity, however, this method would be altogether impractical when either a or w or both cannot be identified. Under the status quo, much uncertainty remains over $w$, underscoring the need to obtain precise estimates of the probability of fatal space debris collisions as a prerequisite. In the meantime, the VSL can be estimated through a benefit transfer, which refers to the practice of plugging in estimates from earlier findings. Through a meta-analysis that was adjusted for publication selection bias, Viscusi and Masterman (2017[13]) suggest a US VSL of USD 9.6 million; using this as a base value and taking into account the respective income elasticities of each country, the authors further suggest the VSL for “lower income, lower middle-income, upper middle-income, and upper income countries to be USD 107 000, USD 420 000, USD 1.2 million, and USD 6.4 million, respectively” (Viscusi and Masterman, 2017, p. 226[13]).

Discussion and conclusions

To quantify the cost of space debris, this chapter presented an analytical framework and econometric model for estimation, which is the first such attempt to the best of the researchers’ knowledge. Valuation methods developed in the field of environmental economics were further elaborated on so that the developed model can be of practical use.

Emphasis was put on making a model that is easily understandable and readily applicable. Therefore, the framework first broke up the cost of space debris into three domains: the impact on satellites, that on space stations and shuttles, and that on the Earth. Based on extant research and records, the specific variables under each domain focused on the most relevant and substantial impacts. In the process, a number of cost categories previously discussed were merged into a single variable or removed. Finally, the model estimates costs on a yearly basis, so that situational changes can be reflected promptly.

Another contribution of this study is the inclusion of previously excluded cost categories. In developing the analytical framework, the researchers found satellites to be both the largest victim and perpetrator of the problem: not only are satellites the most heavily affected by space debris, they are also the predominant cause. Accordingly, launching an additional satellite into space inevitably increases the density of orbits and thus heightens the collision risk for all other operating payloads. However, the researchers observed that most cost-benefit analyses of satellite projects do not consider this fact and instead exclusively centre on those costs directly borne by operators (i.e. development and operational costs). While this may relate to an underestimation of the costs, previous calculations may also be guilty of overestimating the benefits. For the same reason – the collision risk with space debris – the expected benefits can be much smaller if a satellite is damaged before its life expectancy is reached. Such uncertainties and the resulting costs, both internal and external, are incorporated into the study’s model.

Taking it a step further, this study extends the consideration of externalities to the possible impact of space debris on the Earth’s environment. For instance, in the process of developing and launching satellites, various materials and resources, including potentially hazardous substances and fossil fuels, are needed in large volumes. When re-entering Earth’s atmosphere and ultimately landing either on the ground or in water, hitherto uninvestigated air, marine and soil pollution may occur and accumulate over time. The environmental consequences, however, are not limited to the pollution directly resulting from falling space debris, as the ecological footprint begins from resource extraction. In terms of carbon, emissions due to rocket launches have been reportedly increasing by 5.6% each year (see Gammon (2021[14])). With climate change worsening, this study calls for heightened attention to these matters. Table 3.4 shows the suggested categories for a more comprehensive cost-benefit analysis of satellite projects.

The internalisation of external costs can, therefore, be an effective approach to restrain launch behaviour and alleviate the problem of space debris. For instance, as suggested by Rao, Burgess and Kaffine (2020[15]), an orbital fee equal to the gap between the collision rate under open access and the optimal collision rate could be introduced. According to the authors, such a measure will not only correct incentives for launching satellites, but also quadruple the value of the space industry. Alternatively, as with the case of carbon, an emissions trading system could be introduced. Whatever the response, however, the contribution of each country in generating space debris must be considered. The more a country has launched rockets and satellites, the more it has conducted anti-satellite missile testing, the more responsibility it necessarily holds.

Table 3.4. An improved framework for cost-benefit analyses of satellite projects

Benefit		Cost
Protection of property and infrastructure		Development costs (including R&D)
	Safety of life		Satellite body
	Protection of property		Payload
Added value to the economy			Ground station
Private use by citizens			Launch cost
		Operational costs
			Insurance
			Space situational awareness
			Other maintenance costs
		Collision risks
			Damage/loss of my satellite
			Damage/loss of other satellites
			Other possible damages (e.g. human lives, property, etc.)
		Environmental impacts on Earth
			Carbon emissions
			Other pollution (e.g. air, marine, soil)

While the model in this study can be useful in the discussion of economic incentives or as a tool to solve the problem, limits and avenues for improvement also exist. First, the key variables of the current model (i.e.${\alpha }_t$, ${\beta }_t$, ${\gamma }_t$) are based on counting or frequency, implying that the model is less suitable for predictions. Attempts to replace the values with functions would be promising. Second, for simplicity, most variables are defined as gross averages, while several assumptions were also made, according to which damages that do not seriously affect a satellite’s function were excluded. Therefore, much room exists for sophistication. For such reasons, the researchers were wary of presenting an explicit estimate in this study. Related prospects would be more encouraging with further accumulation of data and modelling improvements.

References

[16] Aganaba, T. (2021), “If a satellite falls on your house, space law protects you – but there are no legal penalties for leaving junk in orbit”, The Conversation, 19 May, https://theconversation.com/if-a-satellite-falls-on-your-house-space-law-protects-you-but-there-are-no-legal-penalties-for-leaving-junk-in-orbit-160757.

[5] Ali, I. and S. Gorman (2021), “Russian anti-satellite missile test endangers space station crew – NASA”, Reuters, 17 November, https://www.reuters.com/world/us-military-reports-debris-generating-event-outer-space-2021-11-15.

[11] Aon (2021), Global Catastrophe Recap: July 2021, Aon, http://thoughtleadership.aon.com/Documents/20211008_analytics-if-july-global-recap.pdf.

[3] Boardman, A. et al. (2018), “Introduction to cost–benefit analysis”, in Cost-Benefit Analysis, Cambridge University Press, https://doi.org/10.1017/9781108235594.003.

[12] Bonanno, G. et al. (2010), “Weighing the costs of disaster”, Psychological Science in the Public Interest, Vol. 11/1, pp. 1-49, https://doi.org/10.1177/1529100610387086.

[14] Gammon, K. (2021), “How the billionaire space race could be one giant leap for pollution”, The Guardian, 19 July, https://www.theguardian.com/science/2021/jul/19/billionaires-space-tourism-environment-emissions.

[9] Häggquist, E. and P. Söderholm (2015), “The economic value of geological information: Synthesis and directions for future research”, Resources Policy, Vol. 43, pp. 91-100, https://doi.org/10.1016/j.resourpol.2014.11.001.

[10] Hong, J. and Y. Eom (2011), “Estimating demand for public goods using survey methods: Issues and application to the valuation of environmental satellite project”, Journal of Korean Economic Analysis, Vol. 17/1, pp. 1-64.

[4] Kettley, S. (2020), “Space debris threatens satellites and we’re not paying attention, UK astronomers warn”, Express, 24 September, https://www.express.co.uk/news/science/1339612/Space-debris-threat-satellites-astronomy-space-news.

[7] Lemoine, B. (2016), “What is that?!’ Unidentified, unexplained large object damages man’s van on Milwaukee’s north side”, FOX6, 23 December, https://www.fox6now.com/news/what-is-that-unidentified-unexplained-large-object-damages-mans-van-on-milwaukees-north-side.

[6] Maley, P. (n.d.), “Space debris: 1960-1980”, Direct Travel website, https://eclipsetours.com/paul-maley/space-debris/space-debris-1960-1980.

[8] Murtaza, A. et al. (2020), “Orbital debris threat for space sustainability and way forward (review article)”, IEEE Access, Vol. 8, pp. 61000-61019, https://doi.org/10.1109/access.2020.2979505.

[1] Newman, C. and M. Williamson (2018), “Space sustainability: Reframing the debate”, Space Policy, Vol. 46, pp. 30-37, https://doi.org/10.1016/j.spacepol.2018.03.001.

[15] Rao, A., M. Burgess and D. Kaffine (2020), “Orbital-use fees could more than quadruple the value of the space industry”, Proceedings of the National Academy of Sciences, Vol. 117/23, pp. 12756-12762, https://doi.org/10.1073/pnas.1921260117.

[2] Undseth, M., C. Jolly and M. Olivari (2020), “Space sustainability: The economics of space debris in perspective”, OECD Science, Technology and Industry Policy Papers, No. 87, OECD Publishing, Paris, https://doi.org/10.1787/a339de43-en.

[13] Viscusi, W. and C. Masterman (2017), “Income elasticities and global values of a statistical life”, Journal of Benefit-Cost Analysis, Vol. 8/2, pp. 226-250, https://doi.org/10.1017/bca.2017.12.

Notes

← 1.  The case was filed under under the Convention on the International Liability for Damage Caused by Space Objects. For more information, see Aganaba (2021[16]).

← 2.  Throughout this report, an exchange rate of USD 1 ≒ KRW 1 166 was used. In the original study, the value converted to USD was USD 3.7. See also Hong and Eom (2011[10]) for a more comprehensive discussion on this topic (in Korean).