Victor Champonnois
email: victor.champonnois@inrae.fr

Olivier Chanel
email: olivier.chanel@univ-amu.fr.

Abul Naga

Dominique Bureau

Katrin Erdlenbruch

Charles Figuières

Emmanuel Flachaire

Bengt Kriström

Justin Leroux

Pierre-Alexandre Mahieu

Michel Lubrano

Stéphane Luchini

Jürgen Meyerhoff

Philippe Quirion

Tina Rambonilaza

Emilie Sartre

Erik Schokkaert

Hubert Stahn

Jean-Christophe Vergnaud

Accounting for subsistence needs in non-market valuation: A simple proposal 0

Keywords: subsistence needs, adjustment factor, non-market valuation, value transfer, population's preferences D60, D70, Q51

Revealed and stated preference techniques are widely used to assess willingness to pay (WTP) for non-market goods as input to public and private decision-making. However, individuals first have to satisfy subsistence needs through market good consumption, which affects their ability to pay. We provide a methodological framework and derive a simple ex post adjustment factor to account for this effect. We quantify its impacts on the WTP for non-market goods and the ranking of projects theoretically, numerically and empirically. This confirms that non-adjusted WTP tends to be plutocratic: the views of the richest -whatever they are -are more likely to impact decision-making, potentially leading to ranking reversal between projects. We also suggest that the subsistence needs-based adjustment factor we propose has a role to play in value transfer procedures. The overall goal is a better representation of the entire population's preferences with regard to non-market goods.

Introduction

Over the past 50 years, non-market goods and services -like ecological services, improved recreation, visual amenities, odours, noise, loss of biodiversity, psychological factors, or the valuation of health -have made their entry into public and private decision-making.

With no marketplace to set economic prices for these goods, their values are often assessed by methods based on revealed or stated preferences (SP). These valuation methods elicit individuals' preferences for a given non-market good, either directly through surveys (stated) or indirectly through exploiting market data (revealed). They then derive shadow prices / willingness to pay (WTP) for the corresponding welfare change, and these fuel collective choices, more comprehensive economic assessments like cost-benefit analyses (CBA), or (international) value transfer from one site to another.

The standard project-assessment criterion in CBA is the Kaldor-Hicks compensation test, an extension of the Pareto test for projects involving losers. It states that if the net present value of a project (measured by the discounted sum of individual benefits and costs) is positive, then social welfare is increased and the gainers can compensate the losers with a monetary transfer [START_REF] Johansson | Cost-Benefit Analysis[END_REF]. The seminal rationale was that CBA targets efficiency (as given by the Lindahl-Samuelson condition for public goods) and not distributional issues, which are handled by the tax-transfer system. However, arguments against this rationale rapidly emerged because there is no guarantee that the transfer between gainers and losers will actually take place once the project is implemented. Equity issues (disadvantaged individuals deserve protection, and the losers should be compensated by the gainers) and distributional issues led to the current commonly accepted view that distributional weights are required, and should correspond to the social marginal utility of income, i.e. society's valuation of the individual marginal utility of income [START_REF] Brent | Applied Cost-Benefit Analysis[END_REF][START_REF] Fleurbaey | The Use of Distributional Weights in Benefit-Cost Analysis: Insights from Welfare Economics[END_REF][START_REF] Johansson | Cost-Benefit Analysis[END_REF].

Following [START_REF] Nyborg | Project Evaluation with Democratic Decision-Making: What Does Cost-Benefit Analysis Really Measure?[END_REF], we consider that while CBA is a tool that can inform decision-makers on the efficiency of projects involving non-market goods, it cannot be used to measure social welfare effects. We hence adopt a positive rather than normative interpretation of CBA by leaving subjective choices, both on how to aggregate gainers' and losers' individual choices and on the implementation of compensation mechanisms, in the hands of the decision-maker [START_REF] Hammitt | Accounting for the Distribution of Benefits and Costs in Benefit-Cost Analysis[END_REF]. S/he will then make choices based on what s/he considers the predominant view of fairness in the population [START_REF] Sager | The Comprehensiveness Dilemma of Cost-Benefit Analysis[END_REF][START_REF] Mouter | The Politics of Cost-Benefit Analysis[END_REF], or possibly by looking at how different fairness views affect the decision [START_REF] Van Wee | How Suitable is CBA for the Ex-Ante Evaluation of Transport Projects and Policies? A Discussion from the Perspective of Ethics[END_REF]. We believe that the major value of CBA lies in providing decision-makers with full and accurate information on individuals' preferences (in particular non-market-related) rather than a definitive final ranking among projects.

Another way in which non-market valuation plays a role in public decision-making is through value transfer (see [START_REF] Johnston | Guidance to Enhance the Validity and Credibility of Environmental Benefit Transfers[END_REF]; for a recent overview). Multiple studies on different populations and different non-market goods are costly and time-consuming, and require the expertise of specialists. Consequently, in Europe and the United States, governmental and non-governmental bodies often transfer values obtained from studies realized at a study site to a policy site of interest, in order to assess the impacts of regulations or inform policy-making. According to OECD (2018), "Value transfers are the bedrock of practical policy analysis" (p. 157). However, this raises the critical issue of how best to account for income differences between the study and the policy sites, especially in international or interregional value transfers.

These two processes -CBA and value transfer -appear very transparent and consistent with mainstream welfare economics, directly feeding the preferences of the whole population into decision-making. Nevertheless, willingness to exchange or receive money for non-market good provision, while acting as an indicator of public preferences, also depends on the ability to pay [START_REF] Brent | Applied Cost-Benefit Analysis[END_REF], with the consequence that the richer are likely to more greatly influence policy decisions [START_REF] Pearce | Cost-Benefit Analysis and the Environment: Recent Developments[END_REF][START_REF] Atherton | Capturing Public Views on Complex and Unfamiliar Goods: Chemical Water Pollution in England and Wales[END_REF]. There have been proposals to take this into account, ex ante by replacing money with a different numéraire (see [START_REF] Brekke | The Numéraire Matters in Cost-Benefit Analysis[END_REF][START_REF] Kassahun | Revisiting Money and Labor for Valuing Environmental Goods and Services in Developing Countries[END_REF]; for a recent review), or ex post, by weighting the WTP (often by a function of income, [START_REF] Donaldson | Valuing the Benefits of Publicly-Provided Health Care: Does 'Ability to Pay' Preclude the Use of 'Willingness to Pay[END_REF][START_REF] Treasury | The Green Book: Central Government Guidance on Appraisal and Evaluation[END_REF] or via a structural model; [START_REF] Lee | Income and Distance-Decay effects on Willingness to Pay Estimated by the Contingent Valuation Method[END_REF], or using a social welfare function (SWF, see [START_REF] Adler | Measuring Social Welfare: An Introduction[END_REF]. However, ex ante approaches call for specific designs, while ex post approaches rely on subjective choices in the weighting process or require additional data and complex procedures rarely used in practice.

We propose an alternative to existing approaches, simple to apply ex post on any existing data and limiting subjective choices. We start by considering that although many income-based corrections try to capture inequalities, they do not allow for the fact that the irreducible costs of meeting subsistence needs (often pre-incurred) limit individuals' ability to pay. The public economic literature contains some work that takes this into account by considering the effects of subsistence requirements when measuring minimum health conditions [START_REF] Russell | Ability to Pay for Health Care: Concepts and Evidence[END_REF] or minimum levels for ecosystem services [START_REF] Baumgärtner | Subsistence, Substitutability and Sustainability in Consumption[END_REF][START_REF] Drupp | Limits to Substitution Between Ecosystem Services and Manufactured Goods and Implications for Social Discounting[END_REF]. However, to our knowledge, the impact of individual subsistence needs on WTP for non-market goods has not been explored either theoretically or empirically.

We propose to fill this gap by investigating how individual subsistence needs affect WTP for non-market goods and then the collective choices that involve them. First, we consider how subsistence needs impact individual WTP, and look for a simple ex post individual adjustment factor. Second, we introduce heterogeneous preferences towards the non-market good, and examine how subsistence needs affect both the mean WTP for a given project and the likelihood of ranking reversal between two projects with different non-market goods. Finally, we provide both numerical and empirical illustrations for various non-market good preferences.

We find that the subsistence needs issue more strongly impacts the WTP of the poorest individuals than that of the richest, and decreases the monetary assessment of a project at the aggregate level. As a consequence, when a population's preferences are heterogeneous, the views of the richest -whatever they are -are more likely to impact decision-making, a standard result that can be considered a plutocratic partiality. We show how the adjustment factor we propose tackles this issue, and can be theoretically obtained with appropriate distributional weights. We find that ranking reversal between two projects can occur, depending on the preferences of the richest and the poorest. Finally, the empirical application estimates adjustment factors on real data for two countries, using both CBA-type and value transfer-type analyses.

Our contribution is to the methodology of policy choice in presence of non-market goods. We propose a framework for assessing the impact of subsistence needs on individual WTP elicited for non-market goods, and a simple and pragmatic way to adjust ex post for this impact. This adjustment factor can be applied to existing data based solely on respondent income and country-and good-specific data. It may precede the application of distributional weights in a CBA or be part of value transfer. This adjustment factor could help decision-makers better account for the preferences of the entire population with regard to non-market goods, which is particularly relevant because poorer households are more exposed to negative environmental externalities (air or water pollution, toxic wastes, noise, natural hazards). Moreover, poor households have disproportionately lower access to positive amenities provided by the natural environment (recreational and aesthetic resources) and it is harder for the poor to combat negative environmental externalities through costly behaviours, like prevention, avoidance or moving away.

The remainder of the paper proceeds as follows. Section 2 briefly sketches the existing approaches to the income-related equity issue relevant to non-market valuation, and introduces subsistence needs. Section 3 describes the relevant models and proposes a simple adjustment factor. Section 4 analyses the impacts of subsistence needs on the monetary assessment of non-market goods: a lower valuation, a plutocratic partiality and potential ranking reversal. Section 5 presents an empirical illustration from Canadian and French income data. The discussion and conclusion are in Section 6.

2. Accounting for the income-related equity issue: a literature review [START_REF] Pearce | Cost-Benefit Analysis and the Environment: Recent Developments[END_REF] remarked that WTP "is heavily influenced by ability to pay (income, wealth). The result is a cost-benefit rule for sanctioning or rejecting projects or policies that is biased in favour of those with higher incomes, raising issues of distributional fairness" (p. 31). Several approaches may help decision-makers tackle the ability to pay issue and better account for the non-market good preferences of the whole population.

Ability to pay

One strand of research attempts to capture inequalities in ability to pay through theoretical or empirical income-based corrections.

Instead of income, the use of discretionary income (i.e. the income above a level of committed expenditure on market goods) has been proposed in non-market valuation modelling. However, this is limited to theoretical models: [START_REF] Mcfadden | Issues in the Contingent Valuation of Environmental Goods: Methodologies for Data Collection and Analysis[END_REF] use discretionary income up to the compensating variation function, subsequently explicitly using income in the remainder of their paper, and [START_REF] Carson | The Discrete Choice Experiment Approach to Environmental Contingent Valuation[END_REF] quickly abandon discretionary income on the grounds that it carries considerable measurement error, which is likely to bias the coefficient estimates. The only noticeable exception we found is an empirical study exploring the effects of a mental accounts-type treatment. Li et al. (2005a,b) use additional reminders about the discretionary income of respondents and its use for environmental causes, and find significant budget constraint effects, although the joint additional reminders make disentangling the income effect difficult.

From an empirical perspective, a few authors tackle the ability-to-pay issue through ex ante or ex post methods. [START_REF] Donaldson | Valuing the Benefits of Publicly-Provided Health Care: Does 'Ability to Pay' Preclude the Use of 'Willingness to Pay[END_REF], for instance, proposes an ex post weighting of individual WTP defined as the ratio of the sample average of incomes to individual income at a given power, the elasticity of the marginal utility of income. This is assumed to help account for inequality aversion. Although the ranking did not change under no or different weightings, he concludes that WTP reflects not only strength of preferences but also ability to pay, which is problematic when preferences are correlated with income.

In SP surveys, [START_REF] Chanel | Décision en Présence d'Incertitude et d' Émotions Face à des Risques de Catastrophes Naturelles (RISKEMOTION)[END_REF] use an ex ante approach with normalised scenarios involving a given (hypothetical) income assumed equal for everyone, and compare them to standard scenarios. They exploit the differences to adjust WTP, which leads to a 20% increase in standard WTP on average. [START_REF] Shono | Willingness to Pay for Public Health Services in Rural Central Java, Indonesia: Methodological Considerations When Using the Contingent Valuation Method[END_REF] explore whether individuals are actually able to pay the amount they declare. They use an ex ante approach to assess two WTPs: "standard" WTP as well as the maximum price respondents can pay without resorting to debt (referred to as "payable"). In their empirical study on three health services, they find a higher demand curve for standard WTP than for payable WTP (from 15.4% to 70.8%). In addition, the gap is negatively affected by income and larger for the poorest for one of these health services. [START_REF] Breffle | Understanding How Income Influences Willingness to Pay for Joint Programs: A More Equitable Value Measure for the Less Wealthy[END_REF] collect WTP ex ante through a specific design and derive an equity adjustment factor, applied ex post. They consider three programs, two independent and one combining the two others, and establish that income effects should make the WTP for the combined program lower than the sum of WTP for the two others. Because this income effect is expected to be larger for the poorest than for the richest, they exploit this difference on the combined program to build a partially equity-adjusted WTP. When applied to the combined program of the poorest, it leads to a WTP increase of about 13%.

Overall, the above approaches tackle the ability-to-pay issue either from a theoretical perspective, using an ex ante specific design with non-monetary contributions or purposely-collected WTP, or through subjective ex post corrections without consensus.

Distributional weights

A second strand of research, frequent in the normative interpretation of CBA, uses ex post distributional weights. It computes the change in social welfare associated with a project (potentially including non-market goods) by applying distributional weights, representing the social marginal utility of income to individual WTP (see [START_REF] Johansson | Cost-Benefit Analysis[END_REF][START_REF] Fleurbaey | Equivalent Income And Fair Evaluation Of Health Care[END_REF]. According to [START_REF] Fleurbaey | Equivalent Income And Fair Evaluation Of Health Care[END_REF], there are two main approaches available to estimate distributional weights: welfarist and non-welfarist.

The welfarist approach estimates the two components of the social marginal utility of income separately: the individual's marginal utility of income, and the weight attributed to every individual in the SWF. Whereas the former only depends on the characteristics of the individual utility function, the latter depends in addition on the choice of SWF, with a parameter that stands for aversion to inequality. Among the many, generally non-independent, sources of inequalities in a population, income and (to a lesser extent) health status are those most frequently taken into account. To avoid choosing an SWF, practitioners sometimes directly specify the social marginal utility of income, generally a function of income alone [START_REF] Donaldson | Valuing the Benefits of Publicly-Provided Health Care: Does 'Ability to Pay' Preclude the Use of 'Willingness to Pay[END_REF][START_REF] Samson | Fairness in Cost-Benefit Analysis: A Methodology for Health Technology Assessment[END_REF][START_REF] Treasury | The Green Book: Central Government Guidance on Appraisal and Evaluation[END_REF]. However, there is no consensus on how to set its parameters [START_REF] Brent | Applied Cost-Benefit Analysis[END_REF][START_REF] Johansson | Cost-Benefit Analysis[END_REF].

The non-welfarist approach directly estimates the social marginal utility of income in monetary terms, which requires tricky interpersonal comparison of utilities [START_REF] Adler | Benefit-Cost Analysis and Distributional Weights: An Overview[END_REF][START_REF] Fleurbaey | The Use of Distributional Weights in Benefit-Cost Analysis: Insights from Welfare Economics[END_REF]. This can be achieved through the equivalent income approach based on the fairness principle: survey respondents are asked to give their preferences on different combinations of resources [START_REF] Fleurbaey | Equivalent Income And Fair Evaluation Of Health Care[END_REF][START_REF] Samson | Fairness in Cost-Benefit Analysis: A Methodology for Health Technology Assessment[END_REF]. The subjective well-being approach can also be used to compare individuals' emotions, feelings or life satisfaction and derive distributional weights (see [START_REF] Fleurbaey | The Use of Distributional Weights in Benefit-Cost Analysis: Insights from Welfare Economics[END_REF][START_REF] Bronsteen | Well-Being Analysis vs. Cost-Benefit Analysis[END_REF]; for a discussion). Although non-welfarist approaches are truly based on individual preferences, decision-makers almost never implement them in practice due to their complexity and the additional data required: they are good-and country-dependent, and require specific surveys.

Overall, the above approaches tackle the income-related equity issue by requiring specific surveys to directly elicit individual preferences, or explicit subjective judgments on the interpersonal comparison of utilities. As pointed out by [START_REF] Hammitt | Accounting for the Distribution of Benefits and Costs in Benefit-Cost Analysis[END_REF], all approaches "depend on normative choices that are fundamentally equivalent judgments about how to evaluate improvements to some people and harms to others" (p. 16). We propose below an approach that offers an ex post alternative to account for the impact of differences in income on non-market preference revelation, simple to implement, and that relies on subsistence needs.

Subsistence needs

The concept of subsistence needs is based on the works of the psychologist [START_REF] Maslow | A Theory of Human Motivation[END_REF] and the economist [START_REF] Georgescu-Roegen | Choice, Expectations and Measurability[END_REF]. It relies on the following hierarchy of needs (or wants), from the bottom upwards: physiological, safety, love and belonging, esteem, and self-actualisation. [START_REF] Strasnick | Neo-Utilitarian Ethics and the Ordinal Representation Assumption[END_REF] noted two interesting points based on Georgescu-Roegen (1954)'s approach. First, because each of the needs must be fulfilled before considering satisfying the next one, this "subordination of wants and satiable wants" leads to the principle of diminishing marginal utility. Second, the "irreducibility of wants" limits substitutability not only between needs, but also between goods for a given type of need [START_REF] Stern | Limits to Substitution and Irreversibility in Production and Consumption: A Neoclassical Interpretation of Ecological Economics[END_REF].

Drawing on this framework, we consider that individuals start by satisfying their basic needs (referred to as subsistence needs) thanks to the minimum expenditure on food, water, energy, housing, clothes, transportation, etc. required to live in a given country.

It is only when these subsistence needs are satisfied that individuals can consider more secondary needs (including non-market goods) by moving up in the hierarchy. This minimum level of subsistence needs is country-dependent, due to differences both in standard of living and in cultural construction [START_REF] Sen | The Standard of Living[END_REF]. It is thus related to the recent concept of societal poverty (World Bank, 2018) accounting for the fact that needs increase with the wealth of a society to allow participation in that society with dignity. It also speaks to the long-standing debate on the impact of universal provision of subsistence (or basic) goods [START_REF] Reinert | No Small Hope: Towards the Universal Provision of Basic Goods[END_REF], for instance through universal basic income [START_REF] Van Parijs | Basic Income: A Radical Proposal, for a Free Society and a Sane Economy[END_REF], currently revitalised by the COVID-19 pandemic.

Consequently, when individuals state their WTP for non-market goods, in revealed or SP methods, they rely on substitutability between market goods and non-market goods depending on their preferences, but consider that there is a minimum level of market goods corresponding to the fulfillment of subsistence needs. This differs from the approaches based on discretionary income or ability to pay, which already embed preferences for market goods leading to various levels of consumption.

As far as we know, no study to date has explored how individual subsistence needs impact WTP for non-market goods. Yet economists have long applied the concept of subsistence requirements, in ecological economics for natural resources [START_REF] Shyamsundar | Tropical Forest Protection: An Empirical Analysis of the Costs Borne by Local People[END_REF][START_REF] Thompson | Costs of Lost Opportunities: Applying Non-Market Valuation Techniques to Potential REDD+ Participants in Cameroon[END_REF][START_REF] Shrestha | Estimating the Local Cost of Protecting Koshi Tappu Wildlife Reserve, Nepal: A Contingent Valuation Approach[END_REF] or ecosystem services [START_REF] Baumgärtner | Subsistence, Substitutability and Sustainability in Consumption[END_REF][START_REF] Drupp | Limits to Substitution Between Ecosystem Services and Manufactured Goods and Implications for Social Discounting[END_REF]. In non-market valuation, subsistence requirements have been applied to lexicographic preferences between market and non-market goods [START_REF] Stevens | Measuring the Existence Value of Wildlife: What Do CVM Estimates Really Show[END_REF][START_REF] Veisten | Lexicographic Preference in Biodiversity Valuation: Tests of Inconsistencies and Willingness to Pay[END_REF][START_REF] Rekola | Lexicographic Preferences in Contingent Valuation: A Theoretical Framework with Illustrations[END_REF] or used to discuss the limits to substitution between them (cf. a thorough albeit old presentation in [START_REF] Stern | Limits to Substitution and Irreversibility in Production and Consumption: A Neoclassical Interpretation of Ecological Economics[END_REF] Let us consider that this preference relation is represented by a utility function u i (x i , q i,j ), where x i represents the quantity of a composite market good and q i,j the quantity of non-market goods, j = 1, ..., J, associated with a project. u i (x i , q i,j ) is assumed to be twice continuously differentiable, strictly increasing and strictly quasi-concave in x i and q i,j , with x i , q i,j ≥ 0. The individual budget constraint is px i = y i , i.e. all his/her income y i is spent on the composite market good at price p,1 and q i,j is considered exogenous to the individual (see [START_REF] Horowitz | Behavioral Foundations of Environmental Economics and Valuation[END_REF][START_REF] Dupoux | Can the Environment be an Inferior Good? A Theory with Context-Dependent Substitutability and Needs[END_REF].

Models

We are interested in the relation between the WTP for the non-market goods and the individual's income. We follow the main trend in the literature on non-market valuation [START_REF] Hanemann | Willingness to Pay and Willingness to Accept: How Much Can They Differ?[END_REF][START_REF] Lankford | Measuring Welfare Changes in Settings with Imposed Quantities[END_REF][START_REF] Ebert | Environmental Goods and the Distribution of Income[END_REF] by defining the marginal WTP as the Lindahl or virtual price for q i,j : W T P i,j (p, q i,j , y i ) = ∂v i (p, q i,j , y i )/∂q i,j ∂v i (p, q i,j , y i )/∂y i (1)

where v i (p, q i,j , y i ) is the indirect utility function obtained from the standard maximization problem. W T P i,j represents the change in income that compensates for the change in the non-market good j. It only depends on the individual's preferences represented by the parameters characterising v i (.), quantities of non-market goods q i,j , p and income y i .

Since we consider that an individual spends all his/her income on market goods, we set

x i ≡ y i /p and p ≡ 1 (without loss of generality in a static framework) in the following.

Thus, composite market good x i can be seen as the numéraire representing the individual's income.

Standard model under a CES utility function

To determine the explicit relationships between the standard and the subsistence needs frameworks, we need to start from a functional form that is as flexible as possible regarding preferences. A relevant, easy to interpret, tractable and well-known specification of the utility function in consumer theory is the CES function first proposed by [START_REF] Arrow | Capital-Labor Substitution and Economic Efficiency[END_REF] and extensively used since then in environmental economics (see for instance [START_REF] Ebert | Environmental Goods and the Distribution of Income[END_REF][START_REF] Sterner | An Even Sterner Review: Introducing Relative Prices into the Discounting Debate[END_REF][START_REF] Baumgärtner | Subsistence, Substitutability and Sustainability in Consumption[END_REF][START_REF] Drupp | Limits to Substitution Between Ecosystem Services and Manufactured Goods and Implications for Social Discounting[END_REF][START_REF] Dupoux | Can the Environment be an Inferior Good? A Theory with Context-Dependent Substitutability and Needs[END_REF][START_REF] Meya | Environmental Inequality and Economic Valuation[END_REF]. For J + 1 goods and a given individual i it is:

u i (x i,k ) = [ k α i,k x θ i i,k ] 1 θ i for θ i ∈]-∞; 1] ; 0 < α i,k < 1 ; k α i,k ≡ 1 ; k = 0, ..., J; ∀i (2)
where x i,k is the quantity of good k, α i,k its share parameter and 1/(1 -θ i ) the elasticity of substitution. Note that the CES function covers a range from perfect complement (θ i → -∞) to perfect substitute (θ i → 1), as well as the Cobb Douglas function (θ i → 0).2

WTP are defined as in Eq.( 1), but based on u i (x i,k ) = u i (x i , q i,j ), where

x i ≡ x i,0
stands for the quantity of composite good / income, and q i,j ≡ x i,j , j = 1, ..., J stands for the quantities of non-market goods.

Model with subsistence needs under a CES function

Let us consider that individuals face minimum subsistence needs defined by level of consumption x s of the composite good. Below the minimum subsistence needs, nobody is willing to trade the composite good for non-market goods, because basic needs must be fulfilled first. This implies that W T P i,j is set at 0. Above the minimum subsistence needs, W T P i,j is defined as in the standard CES utility model but based on the u s i (x i -x s , q i,j ) function that accounts for these subsistence needs.3 3.2. Defining the WTPs under a CES utility function

Case of one non-market good (J=1)

The preferences over x i and q i,1 are expressed in a CES as follows:

u i (x i , q i,1 ) = [α i x θ i i + (1 -α i )q θ i i,1 ] 1 θ i for θ i ∈] -∞; 1] ; 0 < α i < 1; ∀i (3)
where α i represents the preference for market good x i relative to the preference for non-market good q i,1 .

At equilibrium, the WTP for the non-market good in the standard CES model is (from Eq. ( 1) and Eq. ( 3)):

W T P i,1 = ∂u i (.)/∂q i,1 ∂u i (.)/∂x i = (1 -α i )q θ i -1 i,1 α i x θ i -1 i (4)
We extend the CES function to account for minimum subsistence needs as follows:

u s i (x i -x s , q i,1 ) = [α i (x i -x s ) θ i + (1 -α i )q θ i i,1 ] 1 θ i for x i > x s ; θ i ∈] -∞; 1]; 0 < α i < 1; ∀i (5)
The WTP for q i,1 in the CES model with subsistence needs is (from Eq.( 1) and Eq.( 5)):

W T P s i,1 = ∂u s i (.)/∂q i,1 ∂u s i (.)/∂x i = (1 -α i )q θ i -1 i,1 α i (x i -x s ) θ i -1 (6)
It is clear that observed W T P s i,1 , when individuals face minimum subsistence needs, are always lower than W T P i,1 , except when x s = 0, in which case W T P s i,1 ≡ W T P i,1 .

Case of two non-market goods (J=2)

We extend the individual CES function in Eq. ( 3) to the case of two non-market goods, with quantity q i,1 and q i,2 :

u i (x i , q i,1 , q i,2 ) = α i,0 x θ i + α i,1 q θ i i,1 + α i,2 q θ i i,2 1/θ i (7)
with α i,0 the preference for the composite market good, α i,1 and α i,2 respectively the preferences for the first and second non-market goods, and α i,0 + α i,1 + α i,2 ≡ 1 ∀i. The WTPs for the two non-market goods are respectively:

W T P i,1 = ∂u i (.)/∂q i,1 ∂u i (.)/∂x i = α i,1 α i,0 q i,1 x i θ i -1 and W T P i,2 = ∂u i (.)/∂q i,2 ∂u i (.)/∂x i = α i,2 α i,0 q i,2 x i θ i -1 (8)
Extending the CES function similarly to Eq. ( 5) leads to:

W T P s i,1 = α i,1 α i,0 q i,1 x i -x s θ i -1 and W T P s i,2 = α i,2 α i,0 q i,2 x i -x s θ i -1 (9)
As with one non-market good, observed W T P s i,. , when facing minimum subsistence needs, are always lower than W T P i,. , except when x s = 0.

Deriving a subsistence-needs adjustment factor

What we are looking for is the (unobserved) WTP that an individual endowed with the same preferences and the same income would have if her ability to pay equalled her entire income. That is, the practical individual subsistence-needs adjustment factor Z i that makes the observed W T P s i (when facing minimum subsistence needs) equal to W T P i (i.e., Z i W T P s i = W T P i ):

Z i = W T P i W T P s i = (1-α i )q θ i -1 α i x θ i -1 i (1-α i )q θ i -1 α i (x i -xs) θ i -1 = x i -x s x i θ i -1 (10)
Note that Z i does not depend on preferences for the market good α i and is proportionally larger for those who have a smaller income (due to the homothety of the CES). In the case of two non-market goods, it is clear from Eq. ( 8) and ( 9) that Z i is also defined as above for each non-market good.

Z i relies on a country-specific minimum level of subsistence needs and a very flexible utility function, which are indeed normative choices, but is characterized by parameters θ (a non-market-good-specific substitutability) and x s , exogenous to both the individual and the decision-maker. It also relies on a country-specific distribution of income. Consequently, in a value transfer procedure, transferring mean observed WTPs from a study site (indexed by S) to a policy site (indexed by P) may account for differences between the sites, as follows:

E(W T P s,P ) = E(W T P s,S ) E(x P -x P s ) E(x S -x S s ) η ( 11
)
where η is the income elasticity of WTP, which, in a CES, is equal to 1-θ (cf. [START_REF] Meya | Testing Structural Benefit Transfer: The Role of Income Inequality[END_REF].

Overall, we propose a simple and practical way to account for the impact of differences in ability to pay on WTP elicitation. This adjustment factor Z i is only meant to account for the impact of subsistence needs on non-market valuation and is to be separated from the approaches sometimes used under a normative interpretation of CBA to account for health, economic or social inequalities. Consequently, it does not preclude additional equity-based adjustments using distributional weights or an SWF.4

Impacts of subsistence needs on decision-making

We explore how the subsistence needs issue impacts the WTPs of non-market goods (defined in section 3.2) as well as the outcomes of decision-making when income changes.

The closer Z i is to 1, the smaller the adjustment required to account for subsistence needs. We consider first how the average WTP assessed for a given project is affected when preferences are homogeneous over individuals (i.e. same α) and characterise the plutocratic partiality when they are heterogeneous between income groups (i.e. different α). Then we consider how relative project rankings are affected when preferences are heterogeneous.

Homogeneous preferences for one non-market good

When preferences are homogeneous over the population, accounting for minimum subsistence level leads to increased WTP. The size of this increase will depend on the actual distribution of income in the population (see applications to Canada and France in section 5)

Figure 1 illustrates the magnitude of adjustment factor Z i for different combinations of θ and income (represented in terms of x/x s ). It can be seen that the lower the income, the higher Z i for any given value of θ, due to the fact that W T P s i tends towards zero when income tends towards x s . For an income seven times larger than x s , for instance, the adjustment factor is about 1.26 (i.e. a 26% increase in WTP) when θ exhibits complementarity (θ = -0.5), but only about 1.08 for substitutability (θ = 0.5). This means that, at the aggregate level, the monetary assessment of projects including this non-market good will be increased ceteris paribus when adjustment factor Z i is applied to account for subsistence needs.

Heterogeneous preferences for one non-market good

When preferences regarding the non-market good are heterogeneous (i.e. vary over income groups), accounting for subsistence needs also increases the WTP, but the adjustment factor Z i has a greater upward impact on WTP for the poorest fraction of the population than for the richest. This implies that without adjustment, the preferences of the richest will be better represented than those of the poorest whatever they are, a kind of plutocratic partiality.

As an illustration, imagine a population with a bi-modal income distribution (for the sake of simplicity): M individuals have a low income (x L = 1.5 times subsistence needs), and N individuals have a high income (x H = 10 times subsistence needs). 5 Let us consider that the preferences of the two subpopulations regarding the non-market good are respectively measured by α L for the poorest and α H for the richest, varying by stepsize We compute and represent [E(W T P ) -E(W T P s )]/E(W T P s ), the relative change in mean WTP when subsistence needs are accounted for, for three values of substitutability (θ = 0.5, 0, -0.5) in Figure 2, for M = N . The closer to 0, the lower the impact of subsistence needs on the population's non-market monetary assessment.

Whatever the substitutability value θ, we have the following results. For homogeneous preferences (represented by the diagonal black line segment on the three figures), the adjustment factor is clearly constant, with a relative change of about 20%. Provided the preferences of the richest are more non-market oriented than those of the poorest (to the left of the diagonal), the relative change is smaller than in the homogeneous case. The preferences of the richest (for the non-market good) are favoured, because the WTP for the non-market good requires less adjustment to account for subsistence needs. Provided the preferences of the richest are less non-market oriented than those of the poorest (to the right of the diagonal), the relative change is larger than in the homogeneous case. The preferences of the richest (now for the market good) are favoured again, because more adjustment is required. Note that when the number of the poorest differs from the number of the richest, the previous results still hold, the average adjustment factor being higher when M > N and lower when N > M , ceteris paribus.

Overall, whatever the preferences of the richest, they are always better represented in the monetary assessment of a project involving a non-market good than those of the poorest, a kind of plutocratic partiality. In particular, the non-market preferences of the poorest appear never to be properly accounted for unless shared by the richest (i.e. the homogenous case), whereas the non-market preferences of the richest are unfailingly better accounted for, for two reasons. First, their WTPs are higher. Second, their WTPs are also less affected by the subsistence needs: the parts of Figure 2 to the left of the diagonal are always closer to 0 than those to the right. This second fact explains why applying the adjustment factor Z i accounts for the plutocratic partiality.

Heterogeneous preferences for two non-market goods

We will now consider how the issue of subsistence needs may affect the ranking of two projects with different (levels of) non-market goods. If preferences are homogeneous among income groups, there cannot be ranking reversal by definition, because everyone will prefer the same project. However, in the heterogeneous case, there may be ranking reversal between projects depending on whether or not the monetary assessment includes the subsistence-needs adjustment factor. We consider two projects (A and B)6 and introduce heterogeneity in preferences for non-market goods as before, by considering a population composed of N individuals with a high income (with preferences α H,A and α H,B ) and M individuals with a low income (α L,A and α L,B , with

α 0 + α H,A + α H,B ≡ 1 and α 0 + α L,A + α L,B ≡ 1).
Ranking reversal only occurs if the following condition is fulfilled (see proof in Appendix B):

1-α 0 - N M x H -x s x L -x s 1-θ (1-α 0 -2α H,A ) > 2α L,B > 1-α 0 - N M x H x L 1-θ (1-α 0 -2α H,A )
Figure 3 (and C1 and C2 in Appendix C) represents this condition in terms of α H,A and α L,B for three values of θ, and as a function of α 0 . For convenience and ease of comparison with previous results, we set as previously x L at 1.5 times subsistence needs, and x H at 10 areas of the poorest individuals' preferred project grow and cross the 45 • line: the number effect makes it more likely that their preferred project will be chosen, although the subsistence-needs effect still favours the richest. There is still a ranking reversal area, which grows.

Finally, when there are three times more high incomes than low incomes (N = 3M , Figure 3(c)), the number effect reinforces the dominance of the richest individuals' preferences so that there is almost no room for the preferences of the poorest, and ranking reversal areas, albeit limited, are still observed.

The cases where θ = -0.5 (complementarity) and θ = 0 are shown in Appendix C. All previous results hold. A decrease in θ -the substitutability between the composite market good and the non-market goods -leads to decreased likelihood of the poorest individuals' preferences dominating, as well as to smaller ranking reversal areas. The preferences of the richest become increasingly likely to dominate as substitutability decreases and/or their proportion in the population increases.

Overall, we find that the subsistence-needs issue when a population's preferences are heterogeneous creates the conditions for ranking reversal between two projects, always with a bias towards the richest individuals' preferences, whatever they are.

Empirical illustrations

Data

We use real data to examine the extent to which the subsistence needs issue might affect the monetary assessment of non-market goods and value transfer procedures. We rely both on country-specific data for income and the cost of meeting subsistence needs (in Canada and France) expressed in 2016 euros, and on empirical studies eliciting elasticities of substitution for various non-market goods.

Regarding the distribution of income, we compute the distribution of annual (disposable) income by unit of consumption 7 for Canada (Statistics Canada, 2019) and France (Institut National de la Statistique et des Etudes Economiques, 2018), see the first part 7 We use the OECD-modified scale to calculate equivalised disposable income per unit of consumption.

This scale assigns a value of 1 to the household head, of 0.5 to each additional adult member and of 0.3 to each child below 14.

of Table 1. The average income by unit of consumption unit is e27,307 for Canada and e25,030 for France. We then have to set the cost of meeting subsistence needs x s . For Canada, we rely on income supports covering basic expenses for individuals and families in the province of Alberta (AlbertaWorks, 2016), including food, clothing, household and personal needs, transportation and private housing expenses. The monthly core benefits for one single adult expected to work, living in private housing, was $CA627 in 2016 (e439). A French survey estimates the cost of subsistence needs to be about e600 per month for one adult in 2016 (Carrefour des Solidarités, 2011), which is comparable to the active solidarity revenue (RSA) paid by the French government to a single individual with no resources (e545 per month in 2017, in addition to aid for housing, public transport and a free health care scheme). We therefore adopt as a reasonable benchmark an annual cost of meeting subsistence needs per individual of e439x12 = e5,268 for Canada, and e600x12 = e7,200 for France. The distributions of annual income by unit of consumption are given in the first part of Table 1.

Regarding the substitutability of market goods for non-market goods, we merge data from [START_REF] Drupp | Limits to Substitution Between Ecosystem Services and Manufactured Goods and Implications for Social Discounting[END_REF] and [START_REF] Drupp | Relative Prices and Climate Policy: How the Scarcity of Nonmarket Goods Drives Policy Evaluation[END_REF], who gather θ estimates for various environmental non-market goods (air or water quality improvements, forest or marine services, landscape or recreational amenities, biodiversity, etc.) in different countries.

We obtain 28 values in the range [-.42; .90], with a mean empirical estimate of θ = .48 and a standard deviation of .34. This means that, on average, individuals exhibit substitutability between market goods and non-market goods. According to our results in section 4, the subsistence-needs adjustment factor would be lower ceteris paribus than for complementarity, although there would be room for ranking reversal between projects.

Results in Table 1 are presented for three values of θ: mean (0.48), and -/+ 1 standard deviation around the mean, i.e. .14 and .82.

Comparing monetary assessments of a non-market good

We assume that preferences regarding the non-market good are homogeneous over income groups, since we lack relevant data on the population's actual distribution of preferences for the non-market good w.r.t. income. The second part of Table 1 represents the subsistence-needs adjustment factor Z by country and values of θ, and for various levels of income (remember from section 3, that Z does not depend on α in the homogeneous case).

Within a given country, the adjustment factor decreases with income and decreases with the substitutability parameter θ, as expected. Between countries, we find larger adjustment factors for France than for Canada at any given income level, due to the difference In rows (4-5), W T P s are based on Eq. ( 6), mid-values of income classes, q=1 and α=.5. In row (6), results on changes in mean W T P s do not depend on q nor on α. In rows (7-9), the policy site is by convention the other country. In row (7), the true value transfer factors are computed as the ratio of the mean W T P s for the policy site over the mean for the study site. In row (8), the value transfer factors are based on Eq. ( 12), and in row (9), on Eq. ( 11).

in the cost of meeting subsistence needs. We then compute the mean income-weighted WTP over the population without and with subsistence needs adjustment in rows (4) and

(5) as well as the corresponding relative change in row (6). When θ = .48 (respectively .14 and .82), the change in mean WTP is found to be 14.9% (respectively 6.1% and 20.8%) for Canada, and larger for France: 22.3% (respectively 8.3% and 33.5%). This is due to the additional effect of country differences in income distribution.

Comparing value transfer procedures

The subsistence needs-based adjustment factor we propose may have a role to play in value transfer procedures. We start from the commonly used formula for estimating the value transfer factor, which relies on the mean observed WTP from the study site, the mean income levels at both sites and the income elasticity of WTP (see [START_REF] Czajkowski | Choosing a Functional Form for an International Benefit Transfer: Evidence from a Nine-Country Valuation Experiment[END_REF][START_REF] Meya | Testing Structural Benefit Transfer: The Role of Income Inequality[END_REF]:

E(W T P s,P ) = E(W T P s,S ) E(x P ) E(x S ) η ( 12
)
where η is the income elasticity of WTP and equal to 1 -θ.

In Table 1 row (7), we compute the true ratio of study site observed WTPs to those of the other (policy) site (the latter being computed thanks to Eq. ( 6) but unobserved during real value transfers). These values are higher (respectively lower) than 1 when the study site has a lower (respectively higher) mean income level than the policy site, and approach 1 when θ increases. In row (8), we compute the corresponding factor based on Eq (12)

and observed WTP when θ = .48 (respectively .14 and .82). We obtain .956 (respectively .984 and 928) when the transfer is from Canada to France, and 1.046 (respectively 1.016 and 1.078) when the transfer is from France to Canada. We can check that these factors are reasonably close to the figures in row ( 7), but bias towards 1.

Finally, in row (9), we compute the value transfer factors based on Eq. ( 11), i.e.

accounting for the cost of meeting subsistence needs at the study and the policy sites.

These factors differ from the commonly-used factors, but are much closer to the figures in row (8). Note that accounting for the subsistence-needs issue in value transfer can be done ex post, based on the Z distribution in the policy site.

Overall, we find that the value transfer factor accounting for subsistence needs performs better in predicting observed WTP at the policy site than the commonly-used factor, while requiring no additional data other than the cost of meeting subsistence needs in both sites.

Discussion

The monetary assessment of a project containing a non-market good is always driven by the preferences of the richest unless income-related equity is allowed for. This is true not only in absolute terms, but also in relative terms, when the population's preferences differ.

Our findings show that incorporating a subsistence-needs adjustment factor is a simple and practical way of better accounting for the preferences of the poorest, without precluding the additional use of distributional weighting to tackle the equity and distributional issues.

In many economic analyses, differences in the non-market values chosen to assess welfare change may lead to divergent conclusions (see for instance [START_REF] Sterner | An Even Sterner Review: Introducing Relative Prices into the Discounting Debate[END_REF]; on the economic impact of climate change).

Our work is subject to limitations. First, for the sake of interpretation and tractability, we chose to derive our subsistence-needs adjustment factor from one specific utility function. The CES was the best candidate: an absolutely standard and flexible function widely used in consumer theory that fits very different patterns of preferences. Second, what we propose is a way to better account for the non-market preferences of the whole population when comparing several projects under a positive interpretation of CBA.

However, we lack a definitive normative justification for our adjustment factor, like any other adjustment method [START_REF] Hammitt | Accounting for the Distribution of Benefits and Costs in Benefit-Cost Analysis[END_REF]. All we can claim is that ours has the advantage of being exogenously based on country-specific and good-specific parameters, and of being applicable ex post to data already collected. Finally, within CBA, we are aware that the question of whether a given project will indeed pass a cost-benefit test once implemented applies to any adjustment factor. Actually, if the project is to be funded through individual contributions, there is no guarantee that the poorest will be able to contribute as much as they indicate through WTP, regardless of how it is adjusted.

Our findings have implications for empirical research in economics, in addition to raising policy issues.

From an empirical perspective, our findings challenge the use of revealed and SP techniques in CBA involving preferences for a non-market good and measured through WTP. When these preferences are homogeneous, the average preference of the population is properly accounted for. When these preferences depend on income group (or any other socio-demographic characteristics correlated with income, like education, place of residence or age), the preferences of the poorest individuals may be under-represented and those of the richest over-represented. Decision-makers should be aware of the plutocratic partiality issue and the possibility of project ranking reversal. The simple ex post adjustment factor we propose offers an initial guide adaptable to country-specific minimum subsistence needs and to any substitutability value of non-market goods.

Our findings also contribute to the body of research on international value transfer.

Recent evidence suggests that transferring values through simple income adjustment [START_REF] Czajkowski | Choosing a Functional Form for an International Benefit Transfer: Evidence from a Nine-Country Valuation Experiment[END_REF][START_REF] Johnston | Guidance to Enhance the Validity and Credibility of Environmental Benefit Transfers[END_REF][START_REF] Meya | Testing Structural Benefit Transfer: The Role of Income Inequality[END_REF] or income inequality adjustment (Baumgärtner et al., 2017a;[START_REF] Meya | Testing Structural Benefit Transfer: The Role of Income Inequality[END_REF]) may be as efficient as more complex adjustment through benefit functions. The adjustment factor we propose constitutes a utility-based alternative approach that accounts for country differences in both income and levels of subsistence needs, and whose performance w.r.t. existing value / function transfers deserves investigation. So too does its potential to account for differences in the type of non-market good that is the object of the value transfer (through different values for elasticity of substitution / income elasticity of WTP).

In terms of policy implications, our findings contribute to the equity vs. equality debate around whether WTP elicited from the poorest should be adjusted when preferences for a non-market good are known to depend on income groups. Doing so means choosing equity (an as-fair-as-possible representation of preferences) over equality (a common representation of preferences). How would public priorities be affected (see [START_REF] Olsen | Helicopters, Hearts and Hips: Using Willingness to Pay to Set Priorities for Public Sector Health Care Programmes[END_REF]; for a discussion regarding health, where priorities depend on income or age)?

What impact would a change in income inequality have on the assessment of a project? Baumgärtner et al. (2017a) and [START_REF] Meya | Inequality and the Value of Public Natural Capital[END_REF] show that, depending on whether the non-market good is a substitute or a complement for manufactured goods, increased inequality can either decrease or increase mean WTP. Once non-market values are involved in decision-making, we need to be on the lookout for any potential plutocratic partiality or ranking reversal effect that may not be accounted for ex post by distributional weightings.

1 2 1 -α 0 - N M x H -x s x L -x s 1-θ (1 -α 0 -2α H,A ) > α L,B
When ranking is based on adjusted W T P , and by the same reasoning, condition (A2) leads to (from Eq. ( 8)):

1 2 1 -α 0 - N M x H x L 1-θ (1 -α 0 -2α H,A ) < α L,B
Consequently, conditions (A1) and (A2) taken together implies that:

1 2 1 -α 0 - N M x H -x s x L -x s 1-θ (1 -α 0 -2α H,A ) > α L,B > 1 2 1 -α 0 - N M x H x L 1-θ (1 -α 0 -2α H,A )
hence the ranking reversal condition:

1-α 0 - N M x H -x s x L -x s 1-θ (1-α 0 -2α H,A ) > 2α L,B > 1-α 0 - N M x H x L 1-θ (1-α 0 -2α H,A ) AII] Assume that α H,A > α H,B . AII-a] Assume that α L,A ≥ α L,B .
Ranking reversal is meaningless, as both income groups prefer project A.

A-IIb] Assume that α L,A < α L,B

By the same reasoning as in Ib], condition (A1) leads to:

1 2 1 -α 0 - N M x H -x s x L -x s 1-θ (1 -α 0 -2α H,A ) < α L,B
and condition (A2) leads to:

1 2 1 -α 0 - N M x H x L 1-θ (1 -α 0 -2α H,A ) > α L,B
Consequently, we have:

1 2 1 -α 0 - N M x H -x s x L -x s 1-θ (1 -α 0 -2α H,A ) < α L,B < 1 2 1 -α 0 - N M x H x L 1-θ (1 -α 0 -2α H,A )
This condition cannot be met since (1 -α 0 -2α H,A ) < 0 and x H -xs

x L -xs 1-θ > x H x L 1-θ
∀x H , x L , x s , θ in their respective previously-defined domains of definition.

  Below, we detail the standard model and the model incorporating subsistence needs based on a Constant Elasticity of Substitution (CES) utility function, determine the WTPs and propose a subsistence-needs adjustment factor. 3.1. Defining the two utility models under a CES function 3.1.1. Standard model under a general utility function Consider an individual i whose preference relation is continuous, monotonic and convex.

Figure 1 :

 1 Figure 1: Adjustment factor Z i when preferences are homogeneous (by θ and income relative to x s )

Figure 2 :

 2 Figure 2: Average adjustment factor when preferences are heterogeneous (upper panel: θ = .5, middle panel: θ = 0, lower panel: θ = -.5)

Figure 3 :

 3 Figure 3: Pattern of preferences leading to ranking reversal between two projects when θ = .5 (upper panel: N = M , middle panel: M = 3N , lower panel: N = 3M )

Table 1 :

 1 Subsistence-needs adjustment factor Z in the French population, by θ

	Income classes by unit Distribution of income (2)	Subsistence-needs adjustment factor Z (3)
	of consumption (1)	Canada	France	Study site: Canada	Study site: France
	(in e)	(in %)	(in %)	θ=.82 θ=.48 θ=.14 θ=.82 θ=.48	θ=.14
	Less than 5,268	5%	2.9%	-	-	-	-	-	-
	5,268 to 7,200	3.3%	4.2%	1.399 2.637	4.971	-	-	-
	7,200 to 10,000	6.9%	3.4%	1.186 1.637	2.260	1.386	2.570	4.764
	10 to 15,000	13.5%	12.3%	1.104 1.329	1.601	1.167	1.562	2.092
	15 to 20,000	14.2%	25.1%	1.067 1.205	1.361	1.100	1.317	1.578
	20 to 25,000	13.2%	18.3%	1.049 1.149	1.258	1.072	1.222	1.393
	25 to 30,000	11.4%	12.1%	1.039 1.117	1.201	1.056	1.171	1.298
	30 to 35,000	9.0%	5.3%	1.032 1.096	1.164	1.046	1.139	1.240
	35 to 40,000	6.6%	3.6%	1.028 1.082	1.139	1.039	1.117	1.201
	40 to 45,000	4.3%	3.1%	1.024 1.071	1.121	1.034	1.101	1.173
	45 to 50,000	2.6%	1.9%	1.021 1.063	1.106	1.030	1.089	1.152
	50 to 55,000	1.4%	1.4%	1.019 1.057	1.095	1.027	1.080	1.135
	55 to 60,000	0.8%	0.6%	1.017 1.051	1.086	1.024	1.072	1.122
	60 to 65,000	0.8%	0.8%	1.016 1.047	1.079	1.022	1.066	1.111
	65 to 70,000	1.2%	0.8%	1.015 1.043	1.072	1.021	1.060	1.102
	70 to 75,000	1.8%	2.8%	1.014 1.040	1.067	1.019	1.056	1.094
	75 to 80,000	2.3%	0.5%	1.013 1.037	1.062	1.018	1.052	1.087
	80,000 plus	1.8%	1.0%	1.008 1.024	1.039	1.011	1.033	1.055
	(4) Mean W T P s (e): (2)xW T P s		5.5	163	5,213	5.3	146	4,359
	(5) Mean W T P (e): (2)x(3)xW T P s		5.8	187	6,297	5.7	179	5,818
	(6) Change in Mean WTP (%): [(5)-(4)]/(4)	6.1	14.9	20.8	8.3	22.3	33.5
	(7) True value transfer factor on mean W T P s	.955	.897	.836 1.047 1.115	1.196
	(8) Commonly-used value transfer factor for W T P s	.984	.956	.928 1.016 1.046	1.078
	(9) Adjusted value transfer factor for mean W T P s	.963	.896	.833 1.038 1.116	1.200
	Notes:

We restrict to small projects unable to markedly change relative prices of goods or real income, to avoid inconsistencies(Brent,

[START_REF] Brent | Applied Cost-Benefit Analysis[END_REF][START_REF] Boadway | The Welfare Foundations of Cost-Benefit Analysis[END_REF][START_REF] Blackorby | A Review Article: The Case against the Use of the Sum of Compensating Variations in Cost-Benefit Analysis[END_REF].

Indeed, u i (x i,k ) → k x α i,k i,k when θ i → 0.

The rationale can be found in the discretionary income (see section 2.1) or in models that take into account minimum levels of consumption (known as "Stone-Geary" functions, after[START_REF] Geary | A Note on 'A Constant-Utility Index of the Cost of Living[END_REF][START_REF] Stone | Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand[END_REF].

Note that W T P i can also be theoretically obtained with appropriate distribution weights based on a utilitarian SWF (see Appendix A).

The generalisation to more income groups in a discrete or continuous way is straightforward but would make the graphic representation less intuitive. See for instanceBaumgärtner et al. (2017a) or[START_REF] Meya | Environmental Inequality and Economic Valuation[END_REF], who use a log-normally distributed income with a CES function in a continuous framework.

To avoid adding complexity, we assume that the non-market goods of the two projects are different.Otherwise, a function accounting for the proportion of the two goods in each project would be required.

anonymous reviewers for their numerous and valuable comments and suggestions, which helped improve the paper. This work was supported by the French National Research Agency under Grants ANR-17-EURE-0020 ANR-08-RISKNAT-007-01 (Riskemotion) and ANR-16-CE03-0005 (GREEN-Econ), and by the Excellence Initiative of Aix-Marseille University -A*MIDEX.

times subsistence needs. On the X-axis, we measure α H,A , the preference for project A of the high-income individuals: the closer to (1 -α 0 ), the stronger this preference, whereas the closer to 0, the stronger the preference for project B, while (1 -α 0 )/2 indicates indifference between the two projects (i.e. α H,A = α H,B ). On the Y-axis, we measure α L,B , the preference for project B of the low-income individuals: the closer to (1 -α 0 ), the stronger this preference, whereas the closer to 0, the stronger the preference for project A, We observe that when M = N (Figure 3(a)), the area of ranking reversal is below the 45 • line in quadrant 3 (and above it in quadrant 2), which confirms the previous finding that high-income individuals' preferences (for project B in quadrant 3 and project A in quadrant 2) dominate those of low-income individuals (for project A in quadrant 3 and project B in quadrant 2) when WTP is not adjusted for subsistence needs, i.e. there is a Appendix A Deriving W T P i from appropriate ex post distributional weights Let us first consider whether an ex post weight based on the marginal utility of income can properly account for the effect of subsistence needs. For an individual i with preferences (α i , θ i ) and one non-market good q i,1 , the marginal utility of income V s i is equal to:

If we weight the W T P s i in the model with subsistence needs (Eq. ( 6)) by the marginal utility of income, we obtain:

The resulting W T P s w i still depends on the level of subsistence needs x s : accounting for the marginal utility of income does not fully account for the effect of subsistence needs.

Theoretically, we can find a "social weight", denoted SW i , and obtain the same W T P i as that obtained with the subsistence-needs adjustment but after weighting by the marginal utility of income and a utilitarian SWF. This social weight would be equal to:

The implied SWF is defined by the primitive of this social weight with respect to W T P s i . The W T P s w i weighted by the marginal utility of income and by SW i would then be equal to:

In practice, the SW i is almost impossible to elicit without specific surveys asking for individual preferences on different combinations of income and non-market-good levels [START_REF] Fleurbaey | Equivalent Income And Fair Evaluation Of Health Care[END_REF][START_REF] Samson | Fairness in Cost-Benefit Analysis: A Methodology for Health Technology Assessment[END_REF].

Appendix B Condition for ranking reversal

Ranking reversal occurs when the relative ranking of 2 projects (A and B) depends on the way they are evaluated (via observed W T P s or subsistence-needs adjusted WTP). We use the notations previously introduced.

A] Consider that project A is ranked first based on observed W T P s (condition A1) but ranked second based on adjusted WTP (condition A2), i.e.:

(A1) :

Ranking reversal is meaningless, as both income groups prefer project B.

When ranking is based on observed W T P s , condition (A1) leads to (from Eq. ( 9)):

We know that α L,A = 1 -α 0 -α L,B and α H,B = 1 -α 0 -α H,A , hence:

Then, because α H,A < α H,B and α L,A > α L,B , we have 1 -α 0 -2α H A > 0 and 1 -α 0 -2α L,B > 0. Easy manipulations lead to:

Ranking reversal is meaningless: Equation ( 13) cannot be met since We use the symmetry argument to obtain the same valid ranking reversal condition as in A].

Ranking reversal is meaningless, as both income groups prefer project A.


Emilie Luczka-Majérus

Arnaud Bonnomet

Adeline Germain

Nathalie Lalun

Claire Kileztky

Jeanne-Marie Perotin

Gaëtan Deslée

Gonzague Delepine

Myriam Polette

Valérian Dormoy

Christelle Coraux
email: christelle.coraux@univ-reims.fr

Ciliogenesis is intrinsically altered in COPD small airways

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

To the Editor, Chronic obstructive pulmonary disease (COPD) is characterised by a progressive and irreversible airflow limitation due to airway obstruction and emphysema [START_REF] Rabe | Chronic obstructive pulmonary disease[END_REF]. We and others showed that bronchial epithelial remodelling in COPD is characterised by alteration of ciliogenesis and cilia function [START_REF] Gohy | Altered generation of ciliated cells in chronic obstructive pulmonary disease[END_REF][START_REF] Ancel | Impaired ciliary beat frequency and ciliogenesis alteration during airway epithelial cell differentiation in COPD[END_REF], as well as a dysregulation of non-motile primary cilia (PC) [START_REF] Perotin | Alteration of primary cilia in COPD[END_REF]. In COPD, the main site of obstruction is located in small airways [START_REF] Hogg | The nature of small-airway obstruction in chronic obstructive pulmonary disease[END_REF]. Considering that COPD is foremost a small airway disease (SAD) [START_REF] Hogg | Site and nature of airway obstruction in chronic obstructive lung disease[END_REF][START_REF] Yanai | Site of airway obstruction in pulmonary disease: direct measurement of intrabronchial pressure[END_REF][START_REF] Bonini | The role of the small airways in the pathophysiology of asthma and chronic obstructive pulmonary disease[END_REF], we investigated the differentiation of bronchiolar epithelium in COPD, focusing on motile and primary ciliogenesis.

Bronchioles, defined and selected as small airways (maximum diameter ≈ 2 mm) devoid of any microscopically observable cartilage, were obtained from surgical resections of non-COPD (n=7, 100% men, mean age (interquartile range (IQR)) 70.6 years (63-87), FEV1 (IQR) 87% (71-105)) and mild/moderate COPD (n=9, 88.9% men, mean age (IQR) 67.1 years (54-84), FEV1 (IQR) 74% (68-82)) lungs. Bronchiolar epithelial cells were enzymatically dissociated from bronchioles flipped to expose inside-out, and used to establish air-liquid interface (ALI) cultures using a modified BEGM (Lonza, Walskerville, MD) medium [START_REF] Adam | Cystic Fibrosis airway epithelium remodelling: involvement of inflammation[END_REF]. All patients were exsmokers (smoking cessation for more than 6 months) or current smokers, with no difference in smoking history between the groups (non-COPD: 6/7 ex-smokers, mean pack-years (IQR) 46 (35-60); COPD: 6/9 ex-smokers, mean pack-years (IQR) 43 (20-65)). Use of human tissues was authorized with the written consent of patients (Biological Collection DC-2012-1583, IRB 00003888 Inserm 21-775). Immunofluorescence staining was performed on ALI day (D) 25 cultures (methanol-fixed and formalin-fixed paraffin-embedded cultures), and lung tissues (non-COPD: n=8, 62.5% men, mean age (IQR) 72.9 (62-83); COPD: n=6, 83.3% men, mean age (IQR) 65.8 (56-80)) with antibodies anti-Arl13b [START_REF] Perotin | Alteration of primary cilia in COPD[END_REF], anti-β-tubulin [START_REF] Adam | Cystic Fibrosis airway epithelium remodelling: involvement of inflammation[END_REF], anti-MUC-5AC [START_REF] Adam | Cystic Fibrosis airway epithelium remodelling: involvement of inflammation[END_REF], anti-CK13 [START_REF] Adam | Cystic Fibrosis airway epithelium remodelling: involvement of inflammation[END_REF] and anti-SCGB1A1 (R&D Systems, Minneapolis, MN). Images were acquired using AxioImager Z1 microscope (Carl Zeiss, Oberkochen, Germany) or VS120 automated slide scanner (Olympus, Rungis, France). Cell proliferation was assessed using TOX8 kit (Sigma, St Louis, MO). Expression of ciliogenesis effectors in cultures (ALI D0, D7, D15 and D25) was assessed by RT-qPCR as previously described [START_REF] Ancel | Impaired ciliary beat frequency and ciliogenesis alteration during airway epithelial cell differentiation in COPD[END_REF]. Specific primers (Eurogentec, Seraing, Belgium) were P63 (forward-5'-CGCCATGCCTGTCTACAA-3', reverse-5'-TGACTAGGAGGGGCAATCTG-3'), E2F4 (forward-5'-ATCAAGGCAGACCCCACA-3', reverse-5'-GGGCAAACACTTCTGAGGAC-3'), GMNC (forward-5'-ACGGAGACTTGGGTCTCTTTC-3', reverse-5'-TCCGGAAGAGGAAAATTTGA-3'), (forward-5'-CTTTACCTGGGACGTGAATGA-3', reverse-5'-GGAAGTCCTTTCACCCCTTT-3'), RFX3 (forward-5'-ACCTCAACCGTGTCGACTTT-3', reverse-5'-GCTGCTGAAGCATCTTGAAGT-3'), SCGB1A1, FOXJ1, MUC-5AC, HEATR2, MCIDAS and RFX2, all previously described [START_REF] Ancel | Impaired ciliary beat frequency and ciliogenesis alteration during airway epithelial cell differentiation in COPD[END_REF][START_REF] Belgacemi | Primary ciliogenesis is a crucial step for multicilated cell determinism in the respiratory epithelium[END_REF]. Results were normalized to the housekeeping gene GAPDH expression [START_REF] Ancel | Impaired ciliary beat frequency and ciliogenesis alteration during airway epithelial cell differentiation in COPD[END_REF][START_REF] Belgacemi | Primary ciliogenesis is a crucial step for multicilated cell determinism in the respiratory epithelium[END_REF]. Relative expression (ΔΔCt) was expressed as fold change from ALI D0 values of each gene in each group. Results were expressed as mean±SEM. Data were analysed using the Mann-Whitney test. Statistical significance was determined as p<0.05.

To decipher cellular mechanisms involved in SAD and airway remodelling in COPD, we studied the bronchiolar epithelium differentiation in ALI cultures. In the fully differentiated COPD epithelia, computer-assisted quantification (10 images/culture covering ≈ 80% of the total surface) showed a two-fold decrease in the number of -tubulin-positive multiciliated cells (MCC) (1306±282 MCC/mm 2 vs 634±57 MCC/mm 2 , COPD vs non-COPD) (Figure 1a).

Although a slight increase in the number of CK13-positive basal cells, MUC-5AC-positive goblet cells and cells co-expressing MUC-5AC and SCGB1A1, as well as a small decrease in SCGB1A1-positive Club cells were detected in COPD cultures, these values did not differ significantly between non-COPD and COPD cultures, as previously reported in comparison between ex/current smokers with and without COPD [11]. Cell proliferation was not different between groups (not shown).

We therefore explored further the expression of ciliogenesis regulators [START_REF] Lewis | Transcriptional regulation of multiciliated cell differentiation[END_REF] (Figure 1b) which was not significantly different at ALI D0 between non-COPD and COPD cultures. MCC differentiate from basal cells under the control of GMNC, master regulator of ciliated cell fate whose expression was found lower in COPD than in non-COPD differentiated cultures at ALI D25 (5.6±2. GMNC, E2F4, FOXJ1, RFX2, RFX3 and HEATR2, showed expression that plateaued after ALI D15 in COPD cultures, unlike their expression in non-COPD cultures. MCC originate from primary ciliated cells (PCC) [START_REF] Belgacemi | Primary ciliogenesis is a crucial step for multicilated cell determinism in the respiratory epithelium[END_REF][START_REF] Jain | Temporal relationship between primary and motile ciliogenesis in airway epithelial cells[END_REF] and we previously reported a dysregulation of PC in COPD bronchial epithelium [START_REF] Ancel | Impaired ciliary beat frequency and ciliogenesis alteration during airway epithelial cell differentiation in COPD[END_REF][START_REF] Perotin | Alteration of primary cilia in COPD[END_REF]. We therefore analysed primary ciliogenesis in bronchiolar epithelium. As in bronchi, PC were localised on undifferentiated cells at the basal part of the differentiated epithelia in cultures (Figure 1c) and tissues (Figure 1d). Double-blind manual counting (3 to 6 random fields per culture) revealed that the PCC number was decreased in COPD when compared to non-COPD cultures (5.5±0.7% vs 11±0.5% of total cells), reflecting observations in tissues (10.7±1.6 vs 17.7±2.9 PC/mm of epithelium).

Despite the crucial contribution of small airways to COPD pathogenesis [START_REF] Hogg | Site and nature of airway obstruction in chronic obstructive lung disease[END_REF], investigations on the bronchiolar epithelium biology remain sparse because of the complex isolation and culture of non-previously amplified primary cells. We circumvented this difficulty with the microdissection of small airways. This allowed us to harvest several million epithelial cells, thus avoiding prior amplification before ALI culture which leads to the loss of the primary characteristics of cells, in particular in terms of MCC differentiation capacity [START_REF] Adam | Cystic Fibrosis airway epithelium remodelling: involvement of inflammation[END_REF]. We were thus able to highlight for the first time an intrinsic impairment of the bronchiolar MCC differentiation in COPD. Our in vitro model being inflammation-free, and all patients being exor current smokers with no difference in smoking history, we demonstrated environment and tobacco-independent alterations of multiciliogenesis in small airways in mild/moderate COPD.

This MCC defect was accompanied by downregulation of key multiciliogenesis regulators acting throughout cilia construction and by a decrease in the number of PCC. A correlation between the decreased number of PCC and that of MCC in COPD small airway epithelium could be expected. Indeed, it was previously reported that PC removal of airway undifferentiated cells led to impairment of multiciliogenesis [START_REF] Belgacemi | Primary ciliogenesis is a crucial step for multicilated cell determinism in the respiratory epithelium[END_REF] and that murine tracheal MCC originated from PCC [START_REF] Jain | Temporal relationship between primary and motile ciliogenesis in airway epithelial cells[END_REF]. However, in COPD bronchial epithelium, the number of PCC is markedly increased, especially in areas of epithelium remodelling, suggesting the involvement of PC in altered epithelial repair/regeneration processes in COPD [START_REF] Perotin | Alteration of primary cilia in COPD[END_REF]. It can be hypothesized that the small airway epithelium is less prone to environment-associated damage and consequently to regeneration than the large airway epithelium. The role of PC in the regulation of remodelling in small airways remains therefore to be elucidated. Based on our results, we can suggest different roles of the PC in the complex molecular mechanisms regulating cell fate, depending on epithelial location and environmental stimuli.

Some limitations of our study are that the potential impact of COPD treatments is not taken into account in the phenomenon, and the low number of patients at the origin of bronchiolar epithelial cells. However, this last weakness also represents a strength. Indeed, the bronchiolar primary and motile ciliogenesis defect in COPD is convincingly evidenced with a cohort of small size, suggesting the robustness of the reported phenomenon.

In conclusion, we have shown both motile and primary impaired ciliogenesis in the small airways of mild/moderate COPD patients. These alterations could impact the mucociliary clearance with a potential involvement in the initiation of remodelling mechanisms in airway epithelium and/or the development of emphysema [START_REF] Higham | The pathology of small airways disease in COPD: historical aspects and future directions[END_REF]. Data on severe COPD as well as longitudinal data could be needed in the future to provide the evidence that altered ciliogenesis represents an intrinsic abnormality of some smokers at-risk to develop COPD, or a feature seen in early disease and/or correlated to severity. The determinants and underlying mechanisms of this dysregulation of epithelial differentiation will have also to be determined to pave the way for the development of new therapeutic strategies for COPD patients. Relative mRNA expression

Figure 1 :

 1 Figure 1: Motile and primary ciliogenesis are altered in COPD bronchiolar epithelium. a) Immunodetection and quantification of β-tubulin-positive (red) multiciliated cells (MCC) in non-COPD (n=7) and COPD (n=9) human bronchiolar cultures at ALI D25. Nuclei are stained with DAPI (blue). Results show means ± SEM, *p<0.05. b) Histograms representing the RT-qPCR assessment of fold-change at ALI D7, D15 and D25 (compared to ALI day 0) in the GAPDH-normalized expression of the ciliogenesis effectors GMNC, MCIDAS, E2F4, FOXJ1, RFX2, RFX3, GRHL2 and HEATR2, in non-COPD (n=7) and COPD (n=9) cultures. Results show means ± SEM, *p<0.05, ***p<0.001. c) Representative fluorescence acquisitions from non-COPD and COPD ALI D25 culture sections showing the presence of motile cilia and primary cilia (PC) stained using antibodies directed against Arl13b (red). Nuclei are stained with DAPI (blue). Boxed areas are shown as magnifications of PC (arrowhead). Histogram represents the quantification of cells with PC (% of total population). Results show means ± SEM, ***p<0.001. n=7 non-COPD cultures and n=9 COPD cultures. d) Representative micrographs showing motile cilia and PC, stained using antibodies directed against Arl13b (red), on fluorescence acquisitions of non-COPD (n=8) and COPD (n=6) sections of small airway tissues . Nuclei are stained with DAPI (blue). Boxed areas are shown as magnifications of PC (arrowhead). Histogram represents the quantification of cells with PC per mm of epithelium. Results show means ± SEM.

  6±0.7 vs 7.5±2.2), as well as HEATR2, involved in the initiation of dynein complex assembly (1.3±0.1 vs 2.8±0.4). Importantly, most of these regulators of ciliogenesis, namely

	7 vs 24.1±13.4-fold change from ALI D0 values). GMNC activates MCIDAS
	forming the complex EDM containing E2F4 that activates genes required for centrioles
	biogenesis. Interestingly, we showed a lower expression of MCIDAS (93.2±59.1 vs 226.3±152)
	and E2F4 (1.5±0.1 vs 2.2±0.3) in COPD compared to non-COPD cultures at ALI D25. EDM
	also activates transcription factors implicated in multiciliogenesis later steps and required for
	the docking of basal bodies to the apical surface and the formation of motile cilia. Among them,
	FOXJ1, RFX2 and RFX3, that are believed to function together, were downregulated in ALI

D25 COPD cultures (2545±664 vs 7800±1956, 12.8±2.8 vs 42.7±14.3, 7.3±1.2 vs 30.7±6.2, COPD vs non-COPD, respectively). Moreover, GRHL2, known to modulate MCIDAS and RFX2, was two-fold less expressed in COPD than in non-COPD differentiated cultures at ALI D25

(3.

Funding: This work was supported by University of Reims Champagne-Ardenne (URCA), Région Champagne-Ardenne and the French National Institute for Health and Medical Research (Inserm).

Competing interests: None declared