domain: scco shs

text:
Amelia Rizzo
email: amrizzo@unime.it

Patrizia Marra
email: pmarra@unime.it

Marra Patrizia

Psychologist, PhD Cbt Psychotherapist

Temperament, Character and Organisational wellbeing among Obstetrics and Gynaecology Personnel

Keywords: Temperament, Character and Organisational wellbeing among Obstetrics and Gynaecology Personnel Obstetrics, Temperament, Bio-psycho-social Model, Organisational Wellbeing

HAL is

Introduction 1.1 Organisational well-being and health

The state of 'Organisational Wellbeing' or 'Organisational Health' is inseparable from the concept of 'Health', which has been defined by the World Health Organisation in a holistic sense. 'Health' comprehensively encompasses the mind-body unity of the individual within his or her socio-cultural context, it represents "a state of complete physical, mental and social well-being, and not merely the absence of disease or infirmity" (WHO, 1948).

Organisational well-being refers to the way in which people live in relation to several aspects of the organisation in which they work. Montgomery et al. (2020) describe wellbeing challenge as 'the ability of an organisation to promote and maintain the highest degree of physical, psychological and social wellbeing of workers in all types of employment'. Organisational malaise, on the contrary, represents the antithesis of what has been stated about organisational well-being, a condition of worker discomfort and suffering [START_REF] Torri | Organizational wellbeing: challenge and future foundation[END_REF]. The main components representing the macro dimensions that every organisation must refer to in order to achieve and maintain the wellbeing objective are: satisfaction with the organisation; desire to be committed to the organisation; feeling of being part of a team; desire to go to work; high involvement;

The bio-psycho-social model of Temperament and Character

Over the past twenty years, data has shown several studies related to Temperament and Character, conducted on specific groups such as military personnel [START_REF] Elsass | Susceptibility to maladaptive responses to stress in basic military training based on variants of temperament and character[END_REF][START_REF] Han | The temperament and character of korean male conscripts with military maladjustment-a preliminary study[END_REF] Sung-Bu, 2013; Jang et al. 2014), nurses [START_REF] Eley | Exploring temperament and character traits in nurses and nursing students in a large regional area of Australia[END_REF][START_REF] Yazici | The relationship between temperament and character traits and burnout among nurses[END_REF][START_REF] Mihailovic | The personality of newly graduated and employed nurses: Temperament and character profiles of Swedish nurses[END_REF], office workers (Hwang, 2020), phisicians [START_REF] Vaidya | Relationship between specialty choice and medical student temperament and character assessed with Cloninger Inventory[END_REF][START_REF] Sievert | The influence of temperament and character profiles on specialty choice and well-being in medical residents[END_REF], students [START_REF] Rizzo | How young adults imagine their future? The role of temperamental traits[END_REF] etc. and in international, rather than national, contexts, neglecting the obstetrical-gynaecological sphere.

Temperament is the result of biological evolution that conditions the individual from birth, and is determined by intrinsic factors in humans. Temperament, personality and character are independent concepts, although often misunderstood and interchanged.

They are the result of various factors, both innate and acquired, that influence each individual throughout his or her life history [START_REF] Cloninger | A psychobiological model of temperament and character[END_REF][START_REF] Rizzo | Temperament and generativity during the life span[END_REF].

Considering that each healthcare professional, before being considered as a 'worker' is an individual with unique personality, character and temperament, who more or less consciously influence and is influenced by the work context, the career choices and the care setting [START_REF] Mento | The Empathy in Young Students of Health Professions[END_REF].

The biosocial theory of Robert C. [START_REF] Cloninger | A psychobiological model of temperament and character[END_REF], a well-known American psychiatrist, argues that personality is a combination of neurobiologically inherited traits (temperamental dimension) and traits that reflect sociocultural influence (character dimension). Cloninger provides a systematic method of classifying personality types.

Originally, it was a three-dimensional model covering three facets, such as 'Novelty seeking', 'Harm Avoidance' and 'Reward dependence'. Cloninger later added to the three basic dimensions four more scales, believing that temperament and character would be better explained by a seven-dimensional structure: four for temperamental traits (selfdirectedness, cooperativeness and self-transcendence and persistence) and three for character traits. In summary the dimensions for temperament are: (1) Novelty Seeking.

This dimension implies a continuous search for stimulation that leads to an intense state of 'excitement' and a tendency to avoid monotony and punishment; (2) Harm Avoidance.

This is a behavioral mode characterized by a peculiar tendency to avoid any situation that is followed by punishment or frustration resulting from a lack of reward and an inability to expose oneself to new stimuli considered as potentially dangerous; [START_REF] Torri | Organizational wellbeing: challenge and future foundation[END_REF] Reward Dependence. The tendency to engage in behavior to respond promptly and appropriately to social demands in search of social approval.

Dimensions of character are: (1) Self-directedness, a sense of responsibility that can also lead the subject to take responsibility for others; (2) Cooperativeness, cooperation, a dimension that can lead to over-dependence on others; (3) Self-transcendence, a need for transcendence that can evolve into either mysticism or psychotic like experiences;

(4) Persistence, stubbornness and determination to pursue the achievement of the proposed goals.

The instrument that can be used to investigate temperament and character is the Temperament and Character Inventory (TCI). A validated self-administered test capable of detecting the levels of the dimensions considered, it is useful in the differential diagnosis and therapeutic planning of various psychiatric disorders. The temperament and character profile that emerges from the TCI can be useful for investigating the subject's personality in categorical diagnostic assessment [START_REF] Cloninger | The Temperament and Character Inventory (TCI): A guide to its development and use[END_REF].

Temperament in Healthcare

A study conducted in Norway by Kluger et In 2009, a study was conducted on nurses within the psychiatric department, assessing self-esteem and temperament, to determine which factor determines occupational stress.

The results showed a gender difference, women presented a higher self-esteem, furthermore, the study shows that the most prevalent subtype was Hyperthymic Temperament, observing an interaction between the subtypes of temperament, selfesteem and professional experience. This shows the importance of investigating in the healthcare field to detect those factors that indicate personality and temperament disorders to improve organisational well-being and customer satisfaction [START_REF] Cordeiro | Self-esteem and affective temperament of nurses in psychiatric and mental health services[END_REF].

Objective of the present study

Analysing the wellbeing process and all the related intrinsic and extrinsic factors, we hypothesize a correlation between the dimensions of the health professional's temperament (persistence, self-transcendence, cooperation, harm avoidance, selfdirectedness, reward dependency, novelty seeking) and the dimensions of organisational well-being perceived by the worker. There is much evidence in the literature of the interconnection between temperament and adaptation [START_REF] Vaughn | Attachment, temperament, and adaptation: One long argument[END_REF].

Adaptability is that characteristic which allows one to easily adapt to changes or to a new environment. Temperament can be assumed to be the basis on which perceptions of one's environment are built [START_REF] Rothbart | Temperament and the development of competence and motivation[END_REF].

At the same time, there is scientific evidence that events and the environment, due to their reciprocal interaction with the person, can create changes in traits, which from a clinical point of view constitute an attempt at adaptation, an accommodation reaction [START_REF] Quinn | Heterogeneous selection on a heritable temperament trait in a variable environment[END_REF]. Sometimes individuals' reactions to adverse events take on a psychopathological form (maladaptation or reactive anxious-depressive syndrome), and this becomes of clinical competence, as the subject manifests egodystonic symptoms that generate (or rather, represent) suffering [START_REF] Nigg | Temperament and developmental psychopathology[END_REF][START_REF] Miettunen | Predictive and discriminant validity of different psychopathology and temperament scales for major psychiatric disorders-23-year follow-up of the Northern Finland Birth Cohort 1966[END_REF].

Given these premises, it is easy to understand how both temperament, as a biological and genetic disposition, and character, as the result of reciprocal interactions between person and environment, can be closely related to organisational well-being. This certainly passes through objectifiable forms, as seen, but from the psychic point of view, it also passes through representations of a subjective nature.

METHODS

Sample

The sample used for the study consisted of 38 subjects; 89.5% were women, while the remaining 10.5% were men working in Obstetrics and Gynaecology Units. Of these, 21% had a fixed-term contract type, while the majority (78.9%) have a permanent

Procedure

The questionnaires were completed during the quarter August -October 2021.

Completion took between 20 and 40 minutes on average, in a single session. Only one of the questionnaires was not definitively completed and was therefore excluded from the analysis. Each subject was provided with all the introductory information regarding the research, with reference to the regulations requiring a compulsory periodic assessment by the health system of perceived organisational well-being. They were also provided with all the instructions concerning the compilation, a matrix with the questions and an answer sheet. Participants were guaranteed anonymity of the data and confidentiality of the information. Subjects were informed about the cognitive and non-diagnostic purposes of the research and signed a consent for participation in the observational study and data processing. No experimentation was planned in the study.

Instruments

Two instruments were used for the research, a description of which follows.

Temperament and Character Inventory (Cloninger, 1993)

The TCI, in its most comprehensive version (version 9) consists of 240 items: 89 are derived directly from the TPQ and, together with a further 27 items added ex novo to improve the reliability of the scales, explore temperamental traits (NS, HA, RD and P), As the item assessment is dichotomous (true/false), the score is 1/0 for positive items and 0/1 for negative items. The raw scores are transformed into standardised T-scores that allow a personality profile to be drawn up. For each temperamental and character trait and for the corresponding subscales, T-scores and percentile scores corresponding to the respective raw scores are prepared on the basis of a normative sample. For interpretation purposes, the following cutoff points are indicated for the percentile scores: very low 0-16.7% ; low 17-33% ; medium 34-66.7% ; high 67-83%

; very high 84-100% .

CIVIT Organisational Wellbeing Questionnaire (Independent Commission for the Evaluation, Transparency and Integrity of Public

Administrations)

The questionnaire data sheet

In the sections of the questionnaire, the respondent is asked to express his or her assessment by means of an always identical scale using 6 classes in ascending order.

The respondent for each question and/or statement expresses his/her rating in relation to how much he/she agrees or disagrees with the statement or how important or unimportant he/she considers it to be.

The sections are:

Organisational

Results

Statistical analysis

Considering the small size of the sample for the present study, it was not possible to calculate any differences between the groups determined by age variables, such as gender, age, length of service, role held, nor to study the different perceptions of the groups by means of Student's t-test for independent groups. At this stage of the work, however, the focus was on a rather descriptive statistic, which would give an account of the results obtained from the sample, in order to adequately describe the expression of the variables measured. Nevertheless, it was possible to explore an initial connection between Temperament, Character and Organisational Well-being through the calculation of Pearson's correlations.

Descriptive statistics

The first step of the analysis focused on the descriptive statistics of the sample. In particular, the results of the Temperament and Character Inventory will be presented in order of administration, followed by the Organisational Wellbeing assessment.

Temperament in the Obstetrics Units

Table 1 shows the overall statistics concerning the minimum and maximum scores obtained and the corresponding averages and standard deviations. Overall, it can be seen that the greatest differentiation is obtained between the scales relating to Character, while a higher standard deviation is observed in the temperament scales, indicative of antithetically expressed temperament types in the sample.

TCI Descriptive Statistics

The prevailing temperament

In order to obtain information on the prevailing temperament type in the group examined, after transforming the scores into percentages, it was possible to determine which temperament type was the most prevalent among the three temperament types.

Table 3 shows the distribution of the temperament types in the sample. As can be observed, the prevalent type is the reward-dependent type.

Temperament type

Type of prevailing character

Similarly, the same procedure was used to identify the prevailing character type for the sample examined, based on classes established from the percentage prevalence. Table 4 shows the distribution of the three types among the subjects assessed. Most of the subjects show a cooperative type of character, i.e. based on social acceptance.

Character type

Percent Self-directedness 36,8

Cooperativeness 47,4

Self-transcendence 15,8

Table 4 -Types of Character in the sample

Analysis of organisational well-being

For the analysis of organisational well-being, the sections indicated in the questionnaire were followed and a total score was also calculated from the sum of all raw scores (see table 15). In the scoring phase, those items that were formulated negatively were taken into account as reversed items, i.e. the scores were reversed in favour of the scale, which focused on the measure of satisfaction and thus indicated a positive outlook where it took the numerically highest values and vice versa. Table 5 shows the descriptive statistics obtained for the various sections of the organisational well-being questionnaire. Similarly, the same procedure used for temperament, of conversion into percentage scores, was used in order to make the scores comparable. As can be seen, many of the scales were 100% saturated, which would indicate the scores obtained by some subjects, who expressed the highest satisfaction with their organisation. In summary, subjects express medium satisfaction with fairness, and medium-high satisfaction with safety and performance, very high satisfaction with the absence of discrimination, the possibility of career advancement, colleagues, context, belonging and the image of the Unit. The answers are more ambivalent towards the boss, growth and equity. Most of the subjects express medium satisfaction and the remaining part is divided into low and high satisfaction. Towards work, on the other hand, it is medium to low. Overall, the sample's job satisfaction is medium-high.

Inferential statistics

Relationship between temperament and organisational well-being

In order to test whether there was a relationship between temperament, character and organisational well-being, and thus to answer the correlational hypothesis of the pilot research, Pearson's correlations were used. Only one negative relationship emerged between the type of novelty-seeking temperament and the aspect of fairness in the organisation: the more the subject is inclined to seek new stimuli, the less satisfactory he considers the level of fairness in his company to be. For the rest, however, it is possible to state that it is not temperament that characterizes the perception of wellbeing within an organisation.

Relationship between character and organisational well-being

Ultimately, the character scales were correlated with the dimensions of organisational well-being (see Table 6). From the results it would appear that temperament is the aspect of personality most closely related to the perception of well-being. In particular, significant associations emerged between novelty-seeking temperament and satisfaction with work and the work context: the greater the subject's disposition to new stimuli, the greater the perception of well-being in the work context (p< 0.05).

A negative association also emerged between the self-transcendent type and the perception of job security and discrimination. In fact, the result shows that the higher the dimension of Self-transcendence (see definition in the previous chapters), the lower the person perceives the safety of their work environment (p< 0.01). Moreover, the level of Self-transcendence is also negatively associated with the perception of discrimination (p< 0.05).

Conclusion

The aim of the present work was to identify the role of temperament and character, the founding components of personality according to Robert Cloninger's bio-psychosocial model, in the perception of organisational well-being in obstetrics.

Due to the smallness of the sample, it can at present be considered a pilot study; there are in fact a number of limitations that must be overcome if these results are to be considered generalisable. Firstly, the subjects are poorly represented; secondly, there is no gender balance, although it must be considered that obstetrics departments often have a clear predominance of female staff.

Despite this, the study presents some strong elements. First and foremost, it has pragmatically applied the indications of legislative decree 150/2009, which stipulates in Article 14(5) 'on optimising public work productivity and the efficiency and transparency of public administrations' an annual survey of organisational well-being.

The results that have emerged, although partial, have provided us with some research elements that may guide future studies. For example, we were able to observe that most of the subjects display a reward-dependent temperament type. This would imply that in the work context these subjects act on the basis of rewards and punishments from the environment. In fact, we have seen that the reward-dependent subject is generally oriented towards responding promptly and adequately to the demands of the social environment in order to obtain its approval: he appears particularly sensitive to the reactions of others and to social pressure, as well as dependent on rewards. He is therefore sociable, helpful and altruistic and, being highly emotional and sensitive, concerned with pleasing others.

It cannot be ruled out that this disposition influenced the choice of course of study, as shown by some research work linking temperamental traits to the choice of university [START_REF] Jaracz | Contributions of Affective Temperament Traits to Professional Choice: Evidence from the Study of Firefighters, Musicians, Athletes, Bank Managers, Nurses and Paramedics[END_REF]. Furthermore, this could also depend on the fact that predominantly women were evaluated: it is known that temperamental traits show gender differences, with a prevalence of Novelty Seeking among men and Reward Dependence and Harm Avoidance among women (Else-Quest et al., 2006).

We also observed a greater expression of character than temperament. In this respect, the subjects would appear to be divided into two subgroups: cooperative and selfdirected. Certainly, we have reason to think that this differentiation may also have an impact on the working environment. Indeed, there are studies that define the former as gregarious and the latter as leaders [START_REF] Kisling | Character for leadership: The role of personal characteristics in effective leadership behaviors[END_REF]. In this regard, the sample also obtained high levels of Persistence, which could indicate traits of stubbornness and perfectionism, tending to be associated with the self-directed character, i.e. based on the acceptance of the self as an autonomous and independent individual.

Another interesting aspect was being able to explore the perception of organisational well-being with respect to many dimensions of the working environment ranging from environmental and functional aspects to communication and relationship aspects. Overall, satisfaction with the sample's work well-being was medium to high.

The most ambivalent responses were those towards the boss: growth and fairness. The majority of the subjects in fact expressed medium satisfaction and the remainder divided into low and high satisfaction, with no half measures. This indicates that some subjects tend to perceive the boss as a figure who does not nurture the development and growth of his workers, or who may make unfair decisions towards different employees whom he perceives as more or less close. Undoubtedly, the relationship with one's boss is a dimension that involves a broader sphere concerning attitudes towards authority figures; so broad that it deserves an independent treatment [START_REF] Burwen | The generality of attitudes toward authority and nonauthority figures[END_REF]).

To answer and remain confined to the specific original research question, it would appear from the results that temperament is the aspect of personality most closely related to the perception of well-being. In particular, significant associations emerged between novelty-seeking temperament and satisfaction with work and the work context, i.e. the greater the subject's disposition to new stimuli, the greater the perception of well-being in the work context [START_REF] Rizzo | Burnout, decision-making and coping among healthcare workers: How the world was before the COVID-19 pandemic[END_REF][START_REF] Maggio | System usability, stress and mood among teachers using distance learning[END_REF].

The novelty-seeking type is in fact attracted to new stimuli and potentially more enterprising in initiatives and problem-solving, because it often also exhibits traits of creativity and a tendency to innovate [START_REF] Schweizer | The psychology of novelty-seeking, creativity and innovation: neurocognitive aspects within a work-psychological perspective[END_REF].

In addition, a negative association also emerged between the Self-transcendent type and the perception of job security and discrimination. In fact, the result shows that the higher the levels of Self-transcendence, the more negatively the person perceives the safety of their work environment and perceives discrimination. Self-transcendence is a personality trait that involves the expansion of personal boundaries and includes spiritual ideas, such as feeling part of the universe. It is possible that these individuals are more sensitive to aspects related to belonging, acceptance, feeling excluded or are more likely to notice attitudes of discrimination or threats to their sense of security, compared to others with characteristics of greater distractibility, extroversion or outward-oriented thinking.

In conclusion, the results obtained suggest that there is a relationship between temperament, character and organisational well-being, as hypothesised. In particular, it is not so much temperament, and thus the basic disposition of the individual (Yldirim et al., 2023), but character, formed from social interactions, that characterises the perception of organisational well-being in one's work environment.

However, in order to confirm and generalise this hypothesis, there is a clear need for future studies.

  feeling of self-efficacy; perception of success of the organisation; positive work-life relationship; satisfactory interpersonal relationships; recognition of organisational work; positive image of managers (De Simone, 2014; Wall et al. 2021). All public administrations must periodically carry out surveys to detect workers state of well-being. These surveys are aimed at a recognition of the 'health state' of the organisation itself, and aim to implement interventions to improve the workers wellbeing and consequently increase the productivity of the health authority (Carvajal-Arango et al., 2021).

  employment contract. With regard to the age groups represented, the distribution of subjects according to age group emerged as follows: 21.1 % up to 30 years; 15.8 % 41 to 50 years; 57.9 % 51 to 60 years; 5.3 % over 60 years. With regard to length of service, most of the subjects (68.4%) have worked for a minimum of 11 and a maximum of 20 years. The 26.3% have worked for less than 5 years and only 5.3% have worked for between 5 and 10 years. The position held in the organisation was also noted, resulting in 100% of the individuals holding a non-management role.

  119 assess character traits (SD, C and ST) and a further 5 serve as indicators of the presence of PD. The scale scores are still calculated on the 226 items of the previous version. There is also a reduced version of the TCI with 125 items, which is usually used as a screening instrument.

  Wellbeing A -Occupational Safety and Health and Work-related Stress B -Discrimination C -Fairness in my administration D -Career and professional development E -My work F -My colleagues G -The context of my work H -The sense of belonging I -The image of my administration Degree to which the assessment system is shared L -My organisation M -My performance N -The functioning of the system Evaluation of the Hierarchical Superior O -My boss and my growth P -My boss and equity Finally, the questionnaire allows the collection, for each employee involved, of following biographical and work-related data: gender; type of contract; age range; length of service; qualification.

Table 1 -

 1 Descriptive statistics for raw TCI scoresSince the scores for the various subscales are not comparable, as they do not have the same denominator, they were transformed into percentages to report the values on a scale with intervals from 0 to 100.

		Min	Max Mean	SD
	Novelty Seeking	12	25	17,63	4,258
	Harm Avoidance	6	32	18,53	7,09
	Reward Dependence	6	18	14,79	2,879
	Persistence	4	7	5,63	0,955
	Self-directedness	19	42	29,84	6,012

Table 2 -

 2 Descriptive statistics on TCI percentage scores

Table 3 -

 3 Prevalent Temperament Types

	Percent

Table 5 -Descriptive Statistics of row scores

 5

		Minimum Maximum	Mean	Std. Deviation	Mean %
	A. Security	24	54	38,63	8,578	65,85%
	B. Discrimination	31	53	39,47	6,363	67,72%
	C. Equity	6	24	16,53	5,015	46,11%
	D. Career	5	29	16,47	6,467	70,95%

C.I.V.I.T.

Table 6

 6

		-Correlations
		SD	C	ST
	A.Security	-0,07	-0,122	-,467 *
	B. Discrimination	0,025	0,162	,698**
	C. Equity	0,049	0,151	-0,175
	D. Career	0,151	-0,084	-0,09
	E. Work	,460 *	0,282	0,138
	F. Colleagues	0,014	0,047	-0,167
	G. Context	,567 *	0,214	0,101
	H. Membership	0,312	0,185	-0,215
	I. Image	0,203	-0,102	-0,097
	L. Organisation	-0,047	-0,052	-0,017
	M. Performance	0,084	0,04	-0,161
	N. Functioning	-0,026	-0,124	-0,319
	O. Boss and growth	0,005	0,015	-0,114
	P. Boss and equity	0,122	0,151	-0,142
	**. Correlation is significant at the 0.01 level (2-tailed).
	*. Correlation is significant at the 0.05 level (2-tailed).
	SD= Self-Directedness; C=Cooperativeness; ST=Self-Trascendence

Funding: This research has received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Conflicts of Interest:

The authors declare that there is no financial, general, and institutional conflict of interest regarding the publication of this article.


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Title : Experimental simulation and modeling by ion beams of alpha decay damage in apatite -Applications to thermochronology and to nuclear sciences for energy Keywords : apatite; alpha decay; radiation-induced damage; ion channeling; thermochronology; confinement matrix Abstract : Apatite is a compound with applications in the fields of thermochronology and nuclear energy. Its natural mineral form can be used to reconstruct possible thermal histories of rocks while a synthesized apatite ceramic form can serve as a waste confinement matrix to immobilize actinides contained in spent nuclear fuels. For both applications, the amount of radiation damage created in apatite due to alpha decay events needs to be modeled and quantified. This thesis aims to investigate in a fundamental manner the kinetics of the following competing processes that determine the net amount of alpha decay damage in apatite: (1) buildup of damage considering the separate ballistic effects of alpha recoil nuclei and alpha particles emanating from alpha decay events; and (2) the athermal, ionization-induced recovery of pre-existing defects attributed to the electronic energy loss of alpha particles. The main techniques utilized in this study are in situ and ex situ ion implantation, Rutherford Backscattering Spectrometry (RBS/C), McChasy code, and Transmission Electron Microscopy (TEM). Experimental and simulation results strongly suggest that the kinetics of damage buildup in apatite irradiated with alpha recoil nuclei or alpha particles at 293 and 333 K could be described as a two-step process. The first step is a transformation from a near perfect crystalline structure to a partially-damaged one, while the second step, which is triggered after a certain ion fluence, results in a further structural transformation that could lead to a highlydamaged state. Amorphization due to alpha recoil nucleus irradiation and helium bubble formation due to alpha particle irradiation are the two physical mechanisms that lead to rapid apatite crystal destabilization. With regard to ionization recovery, experimental results suggest that only certain types of defects such as amorphous clusters could be efficiently recovered by alpha particles and that point defects are likely less sensitive to this recovery effect. This means that alpha-particle induced recovery of defects does not occur or is likely insignificant for natural apatites with very low concentrations of uranium and thorium (few hundreds of ppm).

  Experimental simulation and modeling by ion beams of alpha decay damage in apatite -Applications to thermochronology and to nuclear sciences for energy Simulation expérimentale et modélisation par faisceux d'ions de l'endommagement induit par la désintégration alpha dans l'apatite -Applications en thermochronologie et en sciences nucléaires pour l'énergie Thèse de doctorat de l'université Paris-Saclay École doctorale n° 576, Particules, hadrons, énergie et noyau : instrumentation, imagerie, cosmos et simulation (PHENIICS) Spécialité de doctorat : Science des Matériaux Graduate School : Physique Référent : Faculté des sciences d'Orsay Thèse préparée dans l'unité de recherche IJCLab (Université Paris-Saclay, CNRS), sous la direction de Frédérico GARRIDO, professeur et la co-direction de Cécile GAUTHERON

  Simulation expérimentale et modélisation par faisceaux d'ions de l'endommagement induit par la désintégration alpha dans l'apatite -Applications en thermochronologie et en sciences nucléaires pour l'énergie Mots clés : apatite; désintegration alpha; dégâts d'irradiation; canalisation d'ions; thermochronologie; matrice de confinement Résumé : L'apatite est un minéral aux nombreuses applications dans les domaines de la thermochronologie et de l'énergie nucléaire. Le minéral peut être utilisé pour reconstruire l'histoire thermique de roches et les apatites de synthèse sont envisagées comme matrice de confinement des actinides présents dans les combustibles irradiés. Pour ces deux applications, il faut modéliser et quantifier l'endommagement causé par la désintégration alpha. Le but de cette thèse est l'étude fondamentale de la cinétique des processus concurrents qui déterminent la quantité nette de l'endommagement dans l'apatite: (1) l'accumulation de dégâts en considérant les effets balistiques séparés des noyaux de recul alpha et des particules alpha; et (2) l'effet du recuit athermique, induit par l'excitation électronique des particules alpha sur les défauts préexistants. Les principales techniques utilisées sont l'implantation ionique conduite in et hors situ, la spectrométrie de rétrodiffusion Rutherford en géométrie de canalisation, le code de simulation McChasy et la microscopie électronique en transmission. Les résultats de cette étude montrent que la cinétique d'endommagement par les noyaux de recul alpha ou les particules alpha à 293 et 333 K peut être décrite comme un processus en deux étapes et que l'amorphisation et la formation de bulles d'helium sont les deux mécanismes physiques qui conduisent à la déstabilisation rapide des cristaux d'apatite. Seuls certains types de défauts comme les régions amorphisées peuvent être recuit efficacement par l'excitation électronique des particules alpha alors que les défauts ponctuels y sont moins sensibles. Le recuit par ionisation est probablement insignifiant pour les apatites naturelles contenant de très faibles concentrations en uranium et thorium (quelques centaines de ppm).


Roberto Balado-Naves

Marián Garcia-Valiñas

David Roibas

Efficiency, perceived prices, and household water demand: A stochastic frontier analysis for the Spanish city of Gijón

In the current context of pressure on available water resources, sustainable patterns of water consumption emerge as an important matter of concern. In this sense, efficient consumption is usually understood as the optimal usage of the available resources. Thus, we study households' efficiency levels by considering a stochastic frontier analysis of the demand for water services using a representative sample of a northern city in Spain.

. These range from the deviations between perceived and real prices to social characteristics such as the average age of households or their degree of environmental awareness. We find strong evidence in favor of higher efficiency levels among more informed households which also commit themselves to the environment.

The relevance of this research to the current state of the empirical literature is twofold: first, it expands the number of scarce analyses on stochastic frontiers of residential water demand; second, it contributes to a better understanding of the importance of accurate information on optimal decisions of consumers. Moreover, we use a novel and exclusive database for a representative sample of households in the city of Gijón (Spain) between 2017 and 2021, where we combine real data on water prices and consumption with consumer perceptions obtained from a survey.

INTRODUCTION

Water resources are under pressure in several areas in the world, where scarcity and quality problems are progressively increasing (UNESCO, UN-Water, 2020). The Goals proposed by the 2030 Agenda for Sustainable Development (UN, 2015) are aimed at ensuring access and quality of water resources to the entire population, promoting an efficient water use. Moreover, the 2030 Agenda is fostering to take urgent action to fight against climate change and its impacts.

In this context, the development of strategies for an efficient management of water resources is required, especially in areas with high levels of water stress. In this respect, Spain is considered as a water stressed country according to its water use index [START_REF] Taušová | Evaluation of Water Resources through Efficiency Index and Water Productivity in EU[END_REF], since its water consumption is over the 20% of its long-term annual average of available water.

Several institutions are keen of improving the efficiency of existing water infrastructure but also promoting water resource use efficiency thought the implementation of several water-demand side policies [START_REF] Eea | Towards efficient use of water resources in Europe[END_REF]UN-Water, 2021). Pricing and non-pricing tools are proposed to get efficient water consumption levels. Nevertheless, a previous assessment of water demands efficiency is necessary, in order to identify the best policy instrument to rationalize water consumption.

Water tariffs are a significant tool for addressing an efficient water management. However, the complexity of those tariffs could dilute its potential impacts when it comes to reducing water consumption [START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF]Brent y Ward, 2019). This complexity is especially significant in Spain, where plenty of non-linear and special tariffs are applied [START_REF] García-Valiñas | Wastewater tariffs in Spain[END_REF]. Thus, water price and consumption perceptions could be far from the actual prices, generating some distortions when adopting consumption decisions.

Although households and economic activities put pressure on water resources, there are plenty of studies focused on the water use efficiency of economic activities but the literature assessing the efficiency of residential water consumption is still scarce (Pérez-Urdiales, 2015;[START_REF] Hung | Residential water demand and water waste in Taiwan[END_REF]. This research looks to deal this shortcoming, by evaluating the efficiency of households' water consumption using an original microdata base. Moreover, the determinants of residential water use efficiency will be assessed, by deepening in the role of information on water prices and consumption.

The outline of the paper is as follows. First section presents a brief literature review on previous studies analysing residential water use efficiency though frontier analysis. Next, the methodology proposed in this research is shown, with special attention to frontier demand functions. Data set and variables are described in the next section, while section 5 is displaying the main results. Finally, the paper concludes with a summary of the main findings and public policy implications.

LITERATURE REVIEW

Residential water demand

Since there already exists an important number of exhaustive surveys on empirical studies regarding households' water demand [START_REF] Espey | Price elasticity of residential demand for water: a meta-analysis[END_REF]Arbués et al., 2003;Worthington and Hoffman, 2008;Nauges and Whittington, 2010;[START_REF] Reynaud | Modelling household water demand in Europe. insights from a crosscountry econometric analysis of EU-28 countries[END_REF]Reynaud and Romano, 2018;[START_REF] García-Valiñas | Are Economic Tools Useful to Manage Residential Water Demand? A Review of Old Issues and Emerging Topics[END_REF], the present subsection will cover their major conclusions as well as the most recent studies focused on the use of frontier analysis in the residential water sector.

According to previous literature, the impact of household income on water consumption is expected to be positive, while a negative relationship between prices and water consumption has been estimated. However, both income and price elasticities of demand lower than one (Arbués et al., 2003;Worthington and Hoffman, 2008;Nauges and Whittington, 2010;[START_REF] Reynaud | Modelling household water demand in Europe. insights from a crosscountry econometric analysis of EU-28 countries[END_REF][START_REF] García-Valiñas | Are Economic Tools Useful to Manage Residential Water Demand? A Review of Old Issues and Emerging Topics[END_REF]. This will confirm water as a necessity good, with a diminishing relative weight on household expenditure as income increases, and a demand quite insensitive to changes in water prices. [START_REF] García-Valiñas | Are Economic Tools Useful to Manage Residential Water Demand? A Review of Old Issues and Emerging Topics[END_REF] indicate that there are several groups of variables that have an impact on residential water use. First of all, households' characteristics and housing equipment are significant determinants of residential water use. Among others, household size and composition, education or the type of dwelling are some of those outstanding features. Secondly, some environmental factors such as climatic variables or water quality are considered as key-drivers of water demand. Third, attitudinal and psychological issues are also significant determinants of residential water use. Finally, some policy tools have been deeply analyzed when modelling residential water demand, including both pricing and non-pricing instruments (water efficient technologies, educational campaigns, etc).

Although there is a very large number of studies estimating residential water demand, the literature focused on modelling residential water demand efficiency are still scarce. Pérez-Urdiales (2016) estimated a Smooth-Coefficient stochastic frontier model using a sample of households in the city of Granada (Spain). She found that those households equipped with water efficient technologies and having recently renovated the house pipelines were more efficient in the use of water. [START_REF] Hung | Residential water demand and water waste in Taiwan[END_REF], estimated several stochastic frontier models under different error distribution to analyse the potential water savings in Taiwan. They concluded that smaller and richer households, with higher proportion of aged members and living in big houses registered higher efficiency levels in the use of water.

To conclude this section, it has to be stressed that some papers have found that households have significant shortcomings related to both water consumption and prices information [START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF][START_REF] Brent | Price perceptions in water demand[END_REF]Ward, 2019, García-Valiñas et al., 2021). These information gaps could lead in the adoption of non-optimal decisions in terms of water consumption. However and as far as we know, no paper has tested the impact of information deficiencies on the residential water consumption efficiency.

METHODOLOGY

3.1.The Stone-Geary demand function with imperfect perception on water prices and consumption

Since it is a quite popular functional form in previous literature, we will focus on the Stone-Geary specification of households' water demand (e.g., [START_REF] Gaudin | Demand specification for municipal water management: evaluation of the Stone-Geary form[END_REF][START_REF] Martínez-Espiñeira | Is really all domestic water consumption sensitive to price control? An empirical analysis[END_REF][START_REF] Madhoo | Policy and nonpolicy determinants of progressivity of block residential water rates: a case study of Mauritius[END_REF]Garcia-Valiñas et al. 2010;[START_REF] Dharmaratna | Estimating residential water demand using the Stone-Geary functional form: the case of Sri Lanka[END_REF][START_REF] Clarke | Household water demand seasonal elasticities: a stone-geary model under an increasing block rate structure[END_REF][START_REF] Hung | Residential water demand and water waste in Taiwan[END_REF][START_REF] Roibás | Measuring the impact of water supply interruptions on household welfare[END_REF]. The advantages of this function are the following [START_REF] Dharmaratna | Estimating residential water demand using the Stone-Geary functional form: the case of Sri Lanka[END_REF]): i) it allows for positive consumption independent of prices and disposable income (that is, subsistence consumption); ii) it allows for nonconstant price and income elasticities. However, in the context of price and quantity misperceptions, an inefficiency term arises that must be considered in the standard Stone-Geary water demand of households.

To that end, assume the head of a household faces the collective utility function

𝑈(𝑥, 𝑤 ̃) = 𝑥 1-𝛼 (𝑤 ̃-𝛾) 𝛼 (1)
where, 0 < 𝛼 < 1 and 𝑥 ∈ 𝑅 + is a composite of other goods and services than water. Since we assume that inefficient water demand implies an excess in its consumption, we follow [START_REF] Wichman | Information provision and consumer behavior: A natural experiment in billing frequency[END_REF] and the quantity of perceived water consumption is 𝑤 ̃= 𝜙𝑤, with 𝜙 ∈ (0,1] as the "quantity underperception parameter", and 𝑤 > 𝛾/𝜙 as real water consumption, where 𝛾 ≥ 0 is the parameter of subsistence water demand.

Considering a three-block increasing rate schedule [START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF], the maximization problem of a perfectly rational and informed individual is subject to (assume that 𝑥 is the numeraire good)

𝐼 = 𝑥 + 𝐹 + 𝑝 1 𝑏 1 + 𝑝 2 𝑏 2 + 𝑝 3 (𝑤 -𝑏 1 -𝑏 2 ) (2)
where, 𝐼 ∈ 𝑅 + is the household's disposable income, 𝐹 ∈ 𝑅 + as the real fixed rate, and 𝑝 𝑠 ∈ 𝑅 + as the marginal price of consumption block "s", and 𝑏 𝑠 as the maximum threshold level of water consumption in block "s". The three-block increasing rate schedule implies 𝑝 3 > 𝑝 2 > 𝑝 1 > 0. Following [START_REF] Nordin | A proposed modification on Taylor's demand analysis: comment[END_REF], equation ( 2) can be rewritten into

𝐼 𝐷 = 𝑝𝑤 (3)
where 𝐼 𝐷 = 𝐼 -𝑥 -𝐹 + 𝐷 is the household income disposable for water consumption. The income effect captured in the Nordin's difference variable equals

𝐷 = { 0 𝑖𝑓 𝑤 ≤ 𝑏 1 (𝑝 2 -𝑝 1 )𝑏 1 𝑖𝑓 𝑏 1 < 𝑤 ≤ 𝑏 1 + 𝑏 2 (𝑝 3 -𝑝 1 )𝑏 1 + (𝑝 3 -𝑝 2 )𝑏 2 𝑖𝑓 𝑤 > 𝑏 1 + 𝑏 2 (4)
while marginal prices equal

𝑝 = { 𝑝 1 𝑖𝑓 𝑤 ≤ 𝑏 1 𝑝 2 𝑖𝑓 𝑏 1 < 𝑤 ≤ 𝑏 1 + 𝑏 2 𝑝 3 𝑖𝑓 𝑤 > 𝑏 1 + 𝑏 2 (5)
Similar to (3), the budgetary constraint with price and quantity misperceptions [START_REF] Sexton | Automatic bill payment and salience effects: Evidence from electricity consumption[END_REF]Whichman, 2017) can be read as

𝐼 ̃D = 𝑝 ̃𝑤 ̃ (6)
where 𝐼 ̃𝐷 = 𝐼 -𝑥 -𝐹 ̃+ 𝐷 ̃(𝑝 ̃𝑠, 𝑏 ̃𝑠, 𝑤 ̃) is the perceived disposable household income for water consumption, 𝐹 ̃= ρ𝐹 perceived fixed charges on water consumption, with ρ ∈ (0,1] as the "fixed rate underperception parameter", and 𝑝 ̃𝑠 = 𝜃 𝑠 𝑝 𝑠 is the perceived marginal price of the 𝑠 block of perceived water consumption 𝑏 ̃𝑠, with 𝜃 𝑠 ∈ (0,1] as the "price underperception parameter".

Maximizing (1), subject to (6), with respect to 𝑤 ̃, yields the following Stone-Geary demand function with price and quantity underperception biases

𝑤 = (1 -𝛼)𝛾 + 𝛼 𝐼 𝐷 𝑝 + (1 -𝛼) ( 1 -𝜙 𝜙 ) 𝛾 +𝛼 (𝐼 ̃D -𝜙θ𝐼 𝐷 ) 𝜙 𝑝 ̃ (7)
Hence, (7) provides a theoretical justification for the estimation of residential water demand considering the inclusion of an inefficiency term containing price and quantity underperception biases, (1 -𝛼) (

Stochastic frontier analysis of the Stone-Geary demand function with perception bias

For estimation purposes, (7) can be rearranged into a stochastic frontier model [START_REF] Aigner | Formulation and Estimation of Stochastic Frontier Production Function Models[END_REF][START_REF] Meeusen | Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error[END_REF] for water demand (Hung et al., [START_REF] Kumbhakar | A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms[END_REF][START_REF] Huang | Estimation of a Non-Neutral Stochastic Frontier Production Function[END_REF][START_REF] Battese | A model for technical inefficiency effects in a stochastic frontier production function for panel data[END_REF])

𝜇 𝑢 = 𝐸(𝑢) = 𝛿 0 + ∑ 𝛿 𝑠 𝑧 𝑠 𝐻 𝑠 (9)
where 𝑧 𝑠 seeks to capture the vector of price and quantity underperception parameters (𝜌, 𝜙, θ) of ( 7). Contrary to [START_REF] Hung | Residential water demand and water waste in Taiwan[END_REF], we do not restrict ourselves to the sole estimation of the inefficiency effects on the mean of 𝑢. As it is common in stochastic frontier analyses, we also study of the impact of these 𝐻 exogenous regressors on the variance term of 𝑢 [START_REF] Caudill | Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity[END_REF][START_REF] Hadri | Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function[END_REF], that is

𝜎 𝑢 2 = 𝑉𝑎𝑟(𝑢) = 𝑒𝑥𝑝 (𝜆 0 + ∑ 𝜆 𝑠 𝑧 𝑠 𝐻 𝑠 ) (10)
Due to likely problems of endogeneity associated with marginal prices, we consider the control function approach for the estimations [START_REF] Amsler | Endogeneity in stochastic frontier models[END_REF]. This method produces numerical results identical to those of 2SLS but produces a heteroskedasticity-robust Hausman test for exogeneity (Woolridge, 2015) and allows to estimate stochastic frontiers easily by including the predicted control function 𝑣 ̂ as an additional regressor. This method has been previously considered in the context of water demand estimations by Pérez-Urdiales et al. ( 2016).

To summarize, we consider five stochastic frontier specifications, corrected by potential endogeneity, which change according to the assumptions on the probability distribution function followed by the inefficiency term 𝑢: the classic half-normal zero-truncated stochastic frontier model with 𝑢~𝑖𝑖𝑑 𝑁 + (0, 𝜎 𝑢2 ) (SF_HN_CF, M1), the half-normal zero-truncated stochastic frontier with heteroskedastic inefficiency term, thus 𝑢~𝑖𝑖𝑑 𝑁 + (0, 𝜎 𝑢 2 (λz)) (SF_HN_CF_HK, M2), the random positive-truncated stochastic frontier model with 𝑢~𝑖𝑖𝑑 𝑁 + (𝜇 𝑢 , 𝜎 𝑢 2 ) (SF_TN_CF, M3), the positive-truncated stochastic frontier model with heteroskedastic inefficiency term, thus 𝑢~𝑖𝑖𝑑 𝑁 + (𝜇 𝑢 , 𝜎 𝑢 2 (𝜆z))

(SF_TN_CF_HK, M4), and the positive-truncated stochastic frontier model with exogenous regressors in the inefficiency term, thus 𝑢~𝑖𝑖𝑑 𝑁 + (𝜇 𝑢 (δz), 𝜎 𝑢 2 )

(SF_TN_CF_IE, M5). To do so, we consider the sfcross STATA package for estimation of stochastic frontiers of water demand.

DATA AND VARIABLES

The database used in this study is one of its main contributions (see Tables 1 and2 for a comprehensive description of variables and their summary statistics).

Information regarding real bimonthly water consumption and its marginal prices was obtained from the water supplier in Gijón (the public company of EMA). It spans 1068 different households1 with individual water meters, for 29 periods between 2017 and the first 8 months of 2021. However, not all households present the same number of observations across time due to contract start/ending date. Therefore, we have an unbalanced panel data of 24,402 observations. Meteorological data were provided by the State Meteorological Agency (AEMET). Household socioeconomic and home characteristics were obtained from a survey conducted in Gijón between December 2020 and April 2021. Due to the pandemics, the survey was conducted by a mixed collection system, sending a letter with a questionnaire to households. According to the latest municipal census 2 , Gijón counted with 26% of ageing population, then mail and online submissions were considered to avoid losing a representative share of Gijón's population.

Water consumption and household income are considered in daily terms to control for the effect of changes in the size of billing periods. Billing periods range between 58 and 61 days, with mean of 59.60 days. Water consumption ranges between 0 and 449 cubic meters, with mean of 17.29 cubic meters and standard deviation of 17.36 cubic meters. Daily water consumption (w) ranges between 0 and 7.483 cubic meters per day, with average consumption of 0.289 cubic meters (see Table 2).

Regarding net household income, respondents make a choice from six different intervals of monthly net household income, starting from 0-500€ to 2701-3700€.

To obtain a non-categorical variable of corrected household income (disposable income after fixed charges on water consumption and the Nordin's differencesee Subsection 3.1-), we consider the mean of each income interval. Household Fixed charges range between 7.52 and 33.50€, with mean 16.63€ and mode 16.92€. These are a combination of a service fee for the maintenance and reparation of the water supply network, increasing with the water meter size, and a constant water sanitation regional tax, aimed to foster efficient water consumption and fund the preservation of water resources in the Principality of Asturias (Garcia-Valiñas and Arbues, 2021). Marginal prices (Pw) follow a threeblock increasing structure, raising with cubic meters of water consumption. Average marginal prices equal 1.034€, and most households are located in the first block of consumption for the entire period (almost 90% of the observations).

Given the variable part of the water sanitation regional tax creates a super progressive structure, the Nordin's difference is more sensitive to changes between blocks of consumption, and price misperceptions penalize consumer's welfare to a larger extent. More precisely, the Nordin's difference ranges between 0 and 15.137€, with mean 0.894€ and standard deviation 2.904€. After considering billing days, fixed charges and the Nordin's difference, corrected daily household income (I) ranges between 7.91€ and 199.87€, with an average of 69€ per day and household (more than two minimum wages according to the Spanish legislation 3 ).

Average household size (hsize) is 2.4, and almost 60% of households have two or less members. Furthermore, only 35 households (largehsize) have five or six members (3% of the sample). The share of members over 65 years (p_65) presents an average value of 30.7% (see Table 2), which is close to the share of elder people in Gijón (25.9%) 4 . Additionally, the share of female members (p_fem) is also representative of the population of Gijón (54%), with an average of 53.9% females per household, and less than half of the members of each household (42.2%) tends to be employed or self-employed (p_work). Therefore, we have a sample composed of small households, not excessively aged (members under 18 years represent less than 11% of the sample), balanced in terms of gender, and with more than half of the members not working.

Considering housing characteristics, Table 2 shows that households reside, on average, in large houses (106.89 m 2 ), with minimum and maximum sizes (surf) of 30 and 711 m 2 . Moreover, half of the sample resides in old houses (old_house), with more than 40 years old, while less than a quarter owns a garden (gard), and less than 5% are equipped with a swimming pool (pool).

Since practically the entire sample owns a washing machine (99%), and almost two thirds of them a dishwasher (62.55%), we prefer to focus on quality, instead of quantity, of household capital stock. To summarize the available information on efficient household capital stock, and maintain the highest degrees of freedom, we construct two indices for water-saving appliances and water-saving devices.

The first one (eff_k) takes the values 0 when there are no water-saving/energyefficient 5 washing machines or dishwashers; 0.5 when there is just one watersaving/energy-efficient appliance; and 1 when both appliances are efficient. The second one (eff_devices) takes the values 0 when there are no water-saving devices installed in the house, and ∑ Dev i /4 where Dev i is a dummy variable which takes the value of 1 when the 𝑖 water-saving device is installed (𝑖: efficient taps, efficient showers, efficient toilets, water pressure reducer). When eff_devices equals 1, the household owns all types of water-saving devices. According to Table 2, we expect that a randomly chosen household will present at least one efficient household appliance (44% of households own an efficient dishwasher and 67% an efficient washing machine), and about one efficient device (the most frequent efficient device is the double-flush toilet, with 48% of the sample, while general water pressure reducers are the least frequent, with 6% of the sample). curfews and movement restrictions on water consumption. We expect that people spending more time at home will lead to increases in residential water consumption.

Regarding the inefficiency determinants, we construct a self-reported water habits index (wathabit) which equals ∑ Hab i /13, where Hab i is a dummy variable which takes the value of 1 when the 𝑖 water habit is implemented6 . According to data, most of the sample declare to have rather good water habits (75% of the surveyed households declare to adopt at least 7 out of 13 efficient water habits), where the most popular habits are (with more than 90% of households answering positively): defrosting food in advance without making use of water, loading completely up the washing machine and the dishwasher, turning off the tap while brushing the teeth, and taking showers instead of baths. On the contrary, the least frequent habits are water recycling and filling the sink before washing dishes, with less than 20% of households declaring these habits.

Looking at marginal prices, quantity and bill misperceptions (Pw_under, w_under, bill_under) we construct two dummy variables. These take the value of zero when the respondent chooses a numerical value equal or superior to the actual values registered in terms of marginal prices, paid bill and quantity consumed. That is, those who have perfect information or overestimate the aforementioned variables are expected to not increase inefficient water consumption constrained to other information and cognitive biases. According to our data, there is a low percentage of households underestimating marginal prices, consumption levels and water bills (19%, 11.6% and 11.1% respectively). While the first and last ones are a result of generally overestimated marginal prices (more than 74% and 62% of the selected sample respectively), the second one is a consequence of respondents not estimating their consumption levels of water (more than 67% households).

To enrich our analysis, we also consider the ignorance of respondents on marginal prices, water consumption and water bill (Pw_unk, w_unk, bill_unk). Contrary to the previous misperception variables, our theoretical framework cannot presume how the ignorance bias will work on household decisions. For instance, previous works have found that provision of better information for water consumers tends to raise water demand (Whichman, 2017;[START_REF] Brent | Price perceptions in water demand[END_REF]. Therefore, declaring lack of knowledge on information associated with water consumption does not necessarily imply that respondents do not have an unconscious bias towards under or overperception of their consumption levels or marginal prices, which leads to inefficient levels of demand. According to our data, while there is a significant number of respondents who do not dare to estimate their water bills and consumption levels, most households have provided an estimation of the marginal prices they have faced (more than 96% of the sample). These differences in the response rate are likely a consequence of the construction of the questionnaire and should not be attributed to a salience bias towards marginal prices: while bill payment and water consumption must be answered with a specific figure guessed by the respondent, marginal prices are chosen from six possible intervals ranging from less than 1€ to more than 2€, including the possibility of answering I don't know.

Since we only have an answer for each household for the entire span of time, we must assume these answers are rather constant throughout time. This assumption is not too strong, given that water bills represent a limited share on household income (1.2% for the average household in our sample). Therefore, the costs associated with collecting information may not overcome the expected gains in terms of efficient consumption, and rational inattention remains as the optimal strategy [START_REF] Sims | Implications of rational inattention[END_REF][START_REF] Dellavigna | Psychology and economics: Evidence from the field[END_REF][START_REF] Sexton | Automatic bill payment and salience effects: Evidence from electricity consumption[END_REF]. Furthermore, water bills are received two months after consumption decisions are taken, and estimation errors are likely to prevail since agents do not receive "timely and organized feedback" [START_REF] Thaler | The psychology and economics conference handbook: Comments on Simon, on Einhorn and Hogarth, and on Tversky and Kahneman[END_REF].

RESULTS

This section presents the estimations of models, the comparison between them, the likely determinants of inefficient water demand, as well as the estimated elasticities and water waste levels.

Estimation of residential water demand considering water waste

Table 3 shows the estimates of the Stone-Geary frontier demand function; Table 4 presents the estimated impacts of exogenous regressors on water waste, and Table 5 exhibits estimated average income and price elasticities, as well as subsistence, efficient and waste levels of water consumption. We control for the likely endogeneity associated with corrected daily income divided by marginal prices (I/Pw) by considering the control function procedure [START_REF] Amsler | Endogeneity in stochastic frontier models[END_REF]. Inspired in the "Hausman instruments" [START_REF] Hausman | The competitive effects of a new product introduction: a case study[END_REF][START_REF] Hausman | An econometric assessment of telecommunications prices and consumer surplus in Mexico using panel data[END_REF], the chosen instruments are the 2-year lag of average corrected daily income divided by marginal prices (mean_area_L12_Iday/Pw) and a time trend for each billing period (t) (see Table A1 in the Appendix).

Besides, LR tests are carried out to choose among the different nested specifications that we consider, as well as the Akaike's Information Criterion (AIC) for selection of non-nested models (Table A2 in the Appendix shows the estimates for all models). According to LR tests, stochastic frontier specifications M4 and M5, with a positive truncated-normal distribution of the inefficiency term Notes: t statistics in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001. and exogenous inefficiency determinants, are the best ones at fitting data 7 . Furthermore, since the AIC Difference of M5 with respect to M4 (Δ 5 = 𝐴𝐼𝐶 5 -𝐴𝐼𝐶 4 ) equals 18.6, the level of empirical support of model 5 is essentially none [START_REF] Burnham | Model Selection and Inference: A Practical Information-Theoretic Approach[END_REF]. Therefore, our further analysis will be focused on model M4.

According to the estimations for the SF_TN_CF_HK model (see Table 3), we observe that water demand increases with income and decreases with marginal prices, as the theory predicts. Continuing with other socio-economic determinants, the household size (hsize) seems to increase daily water demand as expected [START_REF] Schleich | Determinants of residential water demand in Germany[END_REF][START_REF] García-Valiñas | Affordability of residential water tariffs: Alternative measurement and explanatory factors in Southern Spain[END_REF][START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF][START_REF] Pérez-Urdiales | Responses to changes in domestic water tariff structures: A latent class analysis on household-level data from Granada, Spain[END_REF][START_REF] Hoyos | Regional differences in the price elasticity of residential water demand in Spain[END_REF][START_REF] Hung | Residential water demand and water waste in Taiwan[END_REF]Roibás et al., 2019).

Furthermore, gender (p_fem) and employment (p_work) status also prove to be relevant variables at explaining household water consumption patterns. More precisely, an increase in the percentage of female-declared members leads to increases in water demand, as in [START_REF] Mu | Modeling Village Water Demand Behavior: A Discrete Choice Approach[END_REF] and [START_REF] Reynaud | Modelling household water demand in Europe. insights from a crosscountry econometric analysis of EU-28 countries[END_REF], while households with more employed members tend to present lower figures of water consumption, as in [START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF]. Since this specification already controls for water waste, and the number and quality of home efficient devices are also considered, our results points towards women having higher preferences over water consumption on average. On the other hand, given that we also control the changes in work patterns through the COVID-19 dummy variable, the explanation behind lower consumption among employed people is that they spend less time at home on average [START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF].

Regarding housing characteristics, we find that houses with larger surfaces (surf) present higher levels of water consumption, as in [START_REF] Pint | Household responses to increased water rates during the California drought[END_REF], [START_REF] Renwick | Do Residential Water Demand Side Management Policies Measure Up? An Analysis of Eight California Water Agencies[END_REF], Hajispyrou et al. (2002), [START_REF] Grafton | Determinants of residential water consumption: Evidence and analysis from a 10-country household survey[END_REF] and [START_REF] Hung | Residential water demand and water waste in Taiwan[END_REF]. Due to more likely leakages [START_REF] Nauges | Privately Operated Water Utilities, Municipal Price Negotiation, and Estimation of Residential Water Demand: The Case of France[END_REF], we find that older houses (old_house) are also associated to higher water consumption. This result is found in [START_REF] Nauges | Privately Operated Water Utilities, Municipal Price Negotiation, and Estimation of Residential Water Demand: The Case of France[END_REF] and [START_REF] Garcia | Estimating the benefits of efficient water pricing in France[END_REF]. As it is common in previous works, the ownership of a garden (gard) is significant and leads to increases in domestic water demand [START_REF] Agthe | Equity, price elasticity, and household income under increasing block rates for water[END_REF][START_REF] Rizaiza | Residential Water Usage: A Case Study of the Major Cities of the Western Region of Saudi Arabia[END_REF][START_REF] García-Valiñas | Nondiscretionary residential water use: The impact of habits and water-efficient technologies[END_REF][START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF][START_REF] Jayarathna | A GIS based spatial decision support system for analysing residential water demand: A case study in Australia[END_REF]. Moreover, we find that specific water-saving equipment measured by the index of efficient dishwashers and water machines (eff_k), and the installment of efficient devices in taps or flushes (eff_devices), is significant and presents the expected negative sign as in previous works [START_REF] Renwick | Do Residential Water Demand Side Management Policies Measure Up? An Analysis of Eight California Water Agencies[END_REF][START_REF] García-Valiñas | Nondiscretionary residential water use: The impact of habits and water-efficient technologies[END_REF][START_REF] Pérez-Urdiales | Responses to changes in domestic water tariff structures: A latent class analysis on household-level data from Granada, Spain[END_REF][START_REF] Rathnayaka | Prediction of urban residential end-use water demands by integrating known and unknown water demand drivers at multiple scales I: Model development[END_REF]. Notes: t statistics in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.

Ending with environmental factors, we find that only average humidity levels (avhum) are significant at explaining differences in domestic water demand. More precisely, we observe that drier bimonthly periods lead to higher levels of water consumption, most likely due to more intensive garden-water needs, as in [START_REF] Rinaudo | Simulating the impact of pricing policies on residential water demand: A Southern France case study[END_REF]. Finally, the COVID-19 period (Covid) has significantly increased water demand across households on average, a consequence of people spending more time at home due to curfews and other mobility restrictions.

Table 4 shows the parameter estimates for the likely determinants of inefficient water demand or water waste. As commented in the methodology section, we argue that inefficient water demand responds to different sources such as coordination or "agency" problems due to households' size (similar to firms, as in Williamson ( 1967))8 , cognitive biases and imperfect information (Kahneman, Strong and Goemans, 2015;[START_REF] Brent | Price perceptions in water demand[END_REF][START_REF] García-Valiñas | Wastewater tariffs in Spain[END_REF].

We first find that households with higher per capita income (I/hsize) are more inefficient, then richer households seem to present a laxer attitude towards water saving, probably due to the small relative importance of water expenditure over their budgetary constraints. As in [START_REF] Hung | Residential water demand and water waste in Taiwan[END_REF], larger household sizes (largehsize) tend to present higher levels of water waste, probably due to coordination and control problems. As expected, the index of declared efficient habits of water consumption (wathabit) presents a negative impact on the inefficiency term. For instance, [START_REF] Rajapaksa | Do monetary and non-monetary incentives influence environmental attitudes and behavior? Evidence from an experimental analysis[END_REF] show that fostering proenvironmental behaviors leads to significant reductions in water consumption.

Underperception of marginal prices (Pw_under), the water bill (bill_under) and water consumption (w_under) are significant at the 1% level. More precisely, those households which underestimate the value of these variables tend to present higher levels of water waste uncertainty (see Table 4) and lower efficiency scores (see Table 5). Despite they do not explicitly consider the existence of an inefficiency term, [START_REF] Binet | Estimation of residential water demand with imperfect price perception[END_REF] also find that individuals tend to increase water consumption when they underestimate marginal prices, and [START_REF] Rajapaksa | Do monetary and non-monetary incentives influence environmental attitudes and behavior? Evidence from an experimental analysis[END_REF] detect that monetary incentives foster reductions in water consumption.

Moreover, it seems that those households which lack of knowledge on marginal prices (Pw_unk) and water bills (bill_unk) also increase their levels of water waste uncertainty (see Table 4). However, their efficiency scores are superior to their counterpart. Therefore, providing better information only to those individuals who already underestimate economic information regarding residential water supply will likely increase consumer's surplus as well as reduce average water waste levels, as in Whichman ( 2017) and [START_REF] Brent | Price perceptions in water demand[END_REF]. On the other hand, a broad provision of information to the entire sample may lead to sustained reductions in average water waste at the expense of consumer's surplus losses due to less efficient residential water consumption.

Regarding water waste, we find that average levels of efficiency are not too high (for the entire sample, efficient water consumption represents more than 62% of total water consumption). These scores are higher for the subsample with good water habits and information. Moreover, we find the most significant changes in these scores can be found associated to underperception of water consumption and the overall charge in water bills. For instance, we observe that those who do not underestimate their bills present an increase superior to 30% in their efficiency scores.

Moreover, the estimated quantity of wasted water among those declaring a water bill charge inferior to the real one exceeds the 278 liters per household and day. This figure surpasses any other quantity of water waste and represents an increase of more than 105% of wasted water with respect to those who did not underestimate their water bills, while those who underestimate their consumption levels raise their water waste levels by more than 43%. Tackling other information biases, or water habits, seems to only reduce water waste by figures between 8% to 14%. Therefore, our results point towards driving efforts on improving the perception and understanding of residential consumers on their water bills and consumption levels. Notes: Water consumption is measured in liters. Worst habits limit is defined by the first quartile of households with the lowest indexes of water habits (wathabit<0.61). Best habits are defined by those habits above the third quartile of worst performers (wathabit>0.77).

The estimated average income and price elasticities 9 in absolute terms (Elast) equals 0.532 for the entire sample (see Table 5). Therefore, residential water demand in Gijón tends to be inelastic with respect to both income and price, implying that water is a necessary service whose share on household aggregate expenditure decreases with income levels and is rather insensitive to changes in marginal prices. This result is standard in previous literature (Arbués et al., 2003;Worthington and Hoffman, 2008;Nauges and Whittington, 2010;[START_REF] Reynaud | Modelling household water demand in Europe. insights from a crosscountry econometric analysis of EU-28 countries[END_REF][START_REF] García-Valiñas | Are Economic Tools Useful to Manage Residential Water Demand? A Review of Old Issues and Emerging Topics[END_REF].

Additionally, we also detect a pattern of lower average elasticities in those households who declare to have bad water habits, as well as underperceive information on prices, consumption and billing of their water demand (see Table 5). More precisely, we observe reductions ranging between 2.9% for marginal prices underperception, and 33.2% for water bill underperception. Therefore, ) is the mean of corrected household income divided by water consumption and marginal prices.

better information and water habits, a proxy for environmental awareness, seem to increase sensitivity of households towards increasing price structures.

Furthermore, as in [START_REF] García-Valiñas | Nondiscretionary residential water use: The impact of habits and water-efficient technologies[END_REF], we also detect that minimum threshold levels of water consumption are also sensitive to changes in determinants of efficient water consumption (third column in Table 5). In this sense, we find that those who do not underestimate economic information regarding water supply and provide an answer to marginal prices, water consumption and bill charges present lower levels of non-discretionary water use. Moreover, those households who declare having better water habits present lower levels of discretionary water consumption than those who state having worse habits).

CONCLUSIONS

In a context of scarcity and sustainable growth, efficient patterns of residential water consumption should be promoted. In this sense, the evaluation of water waste levels of target groups or areas must be considered in the design of accurate and effective public policies. Furthermore, nudging policies require of further evidence on the importance of information biases or ignorance regarding water demand and usage.

This work provides new evidence on inefficient water demand and its determinants by considering microdata from a sample of 1068 households from the city of Gijón (Spain) between 2017 and 2021. We first expand the standard Stone-Geary demand model for water consumption with determinants for water waste. Secondly, we analyze the efficient residential water demand of households by considering a stochastic frontier analysis, allowing for different specifications of the inefficiency term. Finally, we analyze the impact of several information and socio-economic variables on the inefficiency term, and measure the optimal and waste levels of water consumption.

Our findings show that efficient water consumption is significantly associated to standard regressors in the literature, such as the number of members in a given household, the share of elder people or the efficiency of installed appliances and water-saving devices. Moreover, we find the stochastic frontier demand with a positive-truncated and heteroskedastic inefficiency term is the best specification for this context. Regarding the determinants of water waste, underestimation or ignorance of marginal prices, the bill and consumption levels of water lead to higher waste levels. On the contrary, when households declare better water habits or lower levels of income per member, they present higher levels of water consumption. Finally, we find that providing better information on the water invoice may lead to the largest average reduction of water waste (more than 140 daily liters per household), while fostering better water habits show the lowest reduction (around 15 daily liters per household).

APPENDIX

Table 1

 1 Description of variables

	Variable	Name	Definition
	w	Daily water consumption	Bimonthly water consumption divided by the number of days at each billing period (m 3 /day)
	Pw	Marginal price	Marginal price of the last block of water consumption reached (€/m 3 )
	I	Corrected daily household income	Bimonthly household income discounted from water fixed charges, corrected by Nordin's difference and divided by the number of days at each billing period (€/day)
	hsize	Household size	Number of individuals residing in the surveyed household
	largehsize	Large household size	Dummy variable: 1 if household size is larger than 4
	p_65	Share of seniors	Proportion of household members older than 65 (%)
	p_fem	Share of females	Proportion of household female members (%)
	p_work	Share of employed	Proportion of household employed and self-employed members (%)
	surf	Residence surface	Residence surface area (m2)
	old_house	Old house	Dummy variable: 1 if residence is over 40 years old
	gard	Garden ownership	Dummy variable: 1 if residence has a garden
	pool	Swimming pool ownership	Dummy variable: 1 if residence has a swimming pool
	eff_k	Efficient appliances index	Index: 0.5 if residence has a water/energy-efficient dishwasher or washing machine / 1 if residence has both
	eff_devices	Water-saving devices index	Index: average number of affirmative answers on the ownership of water-saving devices (taps, shower, toilet, water pressure)
	avt	Average temperature	Mean of average daily temperatures registered at each billing period (ºC)
	avhum	Average humidity levels	Mean of average daily relative humidity registered at each billing period (%)
	avrain	Average rainfall	Mean of accumulated daily rainfall registered at each billing period (dm)
	Covid	Covid period	Dummy variable: 1 if billing period is between the second billing period of 2020 and the third billing period of 2021
	wathabit	Self-reported water use habits index	Index: average number of affirmative answers on the adoption of water-saving habits (see text)
	Pw_under	Underperception bias on marginal prices	Dummy variable: 1 if respondent declares a marginal price lower with respect to the real marginal price
	w_under	Underperception bias on water consumption	Dummy variable: 1 if respondent declares a water consumption lower with respect to the real consumption
	bill_under	Underperception bias on water bill	Dummy variable: 1 if respondent declares a water bill lower with respect to the real bill
	Pw_unk	Ignorance of marginal prices	Dummy variable: 1 if respondent does not estimate a marginal price
	w_unk	Ignorance of water consumption	Dummy variable: 1 if respondent does not estimate a level of water consumption

bill_unk Ignorance of water bill Dummy variable: 1 if respondent does not estimate a water bill

Table 2

 2 Main statistics

	Variable	Mean	SD	Min	Max
	w	0.289	0.29	0	7.483
	Pw	1.034	0.173	0.415	1.599
	I	69.015	39.937	7.91	199.87
	hsize	2.414	1.076	1	6
	largehsize	0.032	0.178	0	1
	p_65	0.307	0.42	0	1
	p_fem	0.539	0.287	0	1
	p_work	0.422	0.374	0	1
	surf	106.896	75.928	30	711
	old_house	0.5	0.5	0	1
	gard	0.226	0.418	0	1
	pool	0.042	0.201	0	1
	eff_k	0.535	0.424	0	1
	eff_devices	0.203	0.246	0	1
	avt	15.262	3.419	9.217	21.071
	avhum	75.918	2.661	71.369	85.214
	avrain	30.096	19.692	1.143	103.197
	Covid	0.34	0.474	0	1
	wathabit	0.656	0.135	0	1
	Pw_under	0.190	0.392	0	1
	w_under	0.116	0.321	0	1
	bill_under	0.111	0.314	0	1
	Pw_unk	0.039	0.194	0	1
	w_unk	0.670	0.470	0	1
	bill_unk	0.261	0.439	0	1
	income ranges between 250 and 5800€, with mean of 2073.31€ and standard
	deviation of 1194.57€.

  Since the COVID-19 pandemic captures one third of the sample (see the mean of Covid in Table2), we include a dummy variable to control for the effect of

https://www.lamoncloa.gob.es/lang/en/gobierno/councilministers/Paginas/2022/20220222_council.aspx Demographics of Gijón are available on https://observa.gijon.es/pages/inicio/ A, A+, A++, A+++ rating.

Table 3

 3 Parameter estimates of daily water stochastic frontier demand

	Variable / Model	SF_TN_CF_HK
		(M4)
	Intercept	0.0352
		(0.80)
	I/Pw	0.00133***
		(6.10)
	hsize	0.0347***
		(13.45)
	p_65	-0.00105
		(-0.25)
	p_fem	0.0203***
		(5.03)
	p_work	-0.0503***
		(-7.11)
	surf	0.000275***
		(8.44)
	old_house	0.0528***
		(20.46)
	gard	0.0206***
		(4.76)
	pool	0.0100
		(1.30)
	eff_k	-0.00923**
		(-2.94)
	eff_devices	-0.0351***
		(-6.25)
	avt	0.000821
		(1.93)
	avhum	-0.00177**
		(-2.79)
	avrain	0.0000357
		(0.83)
	Covid	0.0125***
		(5.77)
	𝑣 ̂	-0.00158***
		(-7.20)
	𝜆
	𝜎 𝑢 2
	𝜎 𝑣 2	0.07139***
		(68.17)
	𝜇	-127.024***
		(-10.56)
	Observations	14441
	Log likelihood	7424.4

Table 4

 4 Estimates on determinants of water waste

	Variable / Model	SF_TN_CF_HK
		(M4)
		𝑽𝒂𝒓(𝒖)
	Intercept	2.820***
		(25.73)
	I/hsize	0.0000795***
		(8.34)
	largehsize	0.427***
		(8.14)
	wathabit	-0.433***
		(-6.54)
	Pw_under	0.0606*
		(2.36)
	w_under	0.156***
		(4.79)
	bill_under	0.770***
		(27.00)
	Pw_unk	0.169**
		(3.22)
	w_unk	0.0315
		(1.24)
	bill_unk	0.294***
		(12.71)

Table 5

 5 Mean values of income and price elasticities (Elast), basic consumption levels or minimum threshold (𝛾), efficient water consumption (𝑤 * ), observed water consumption (𝑤 ̅), water waste (𝐸(𝑢/𝜀)), and efficiency scores (𝐸𝐹𝐹 = 𝐸(𝑤 * /𝑤))

	Sample	Elast	γ	w *	𝑤 ̅	𝐸(𝑢/𝜀)	EFF
	All	0.532	41.035	134.124	289.003	153.554	0.626
	Water Habits
	Best habits 0.527	41.161	130.885	291.414	155.533	0.622
	Worst habits 0.488	38.106	129.995	311.516	170.267	0.601
	Information on Pw
	No underestimation 0.535	39.533	131.462	285.001	150.963	0.631
	Underestimation 0.519	46.947	144.599	306.044	163.749	0.608
		Info 0.531	40.838	134.284	288.722	152.741	0.624
	No info 0.558	47.135	129.172	295.872	178.716	0.671
	Information on w
	No underestimation 0.547	40.283	131.287	277.971	145.359	0.646
	Underestimation 0.424	46.026	152.963	372.455	207.974	0.495
		Info 0.553	36.790	145.074	305.353	162.294	0.609
	No info 0.521	43.414	127.988	280.971	148.656	0.635
	Information on Bill
	No underestimation 0.553	38.222	130.839	266.615	135.726	0.650
	Underestimation 0.369	60.687	157.079	467.534	278.123	0.457
		Info 0.530	39.574	133.564	284.920	148.224	0.614
	No info 0.539	45.591	135.872	300.569	170.176	0.664

Table A1 .

 A1 Estimation of Control Function p < 0.05, ** p < 0.01, *** p < 0.001.Table A.2. Parameter estimates of daily water stochastic frontier demand Table 8 Estimates on determinants of water waste

			7.1.Appendix C
	Variable / Model	SF_HN_CF	SF_HN_CF_HK	SF_TN_CF	SF_TN_CF_HK	SF_TN_CF_IE
			(M1)	(M2)	(M3)	(M4)	(M5)
	Intercept I/Pw Log likelihood Observations 𝜇 𝜎 𝑣 𝜎 𝑢 𝜆 𝑣 ̂ Covid avrain avhum avt eff_devices hsize p_65 p_fem p_work surf old_house gard pool eff_k	Variables Intercept -0.0350 Variable / (-0.60) Model 0.00123*** SF_HN_CF_HK -0.00228 (-0.04) (M2) 0.000683** 𝑽𝒂𝒓(𝒖) mean_area_L12_Iday/Pw t hsize p_65 p_fem p_work surf old_house gard pool eff_k eff_devices avt avhum avrain Covid Observations Durbin χ 2 (1) Wu-Hausman F(1,14424) F(2,14424) Sargan-Hansen 𝜒 2 (1) 3842.2 5364.5 (overidentifying restrictions) 14441 14441 H0: instruments are exogenous 0 0 H0: instruments are weak (47.88) (50.75) 0.06322*** 0.06510*** (135.16) H0: Iday/Pw is exogenous 0.32194*** (1650.04) 5.0922*** (-5.67) (-4.91) -0.00159*** -0.00125*** (4.92) (4.23) 0.0142*** 0.0108*** (2.44) (1.68) 0.000142* 0.0000850 (-2.61) (-2.23) -0.00219** -0.00167* (4.55) (2.10) 0.00258*** 0.00105* (-4.76) (-5.75) -0.0349*** -0.0382*** (4.42) (2.70) Intercept -3.426*** 0.0309*** 0.0410*** (-42.66) (9.33) (13.67) I/hsize 0.000395*** 0.0108 -0.00611 (28.03) (1.89) (-1.25) largehsize 0.887*** 0.0172** 0.0187*** (12.01) (3.18) (3.88) wathabit -0.461*** -0.0410*** -0.0517*** (-4.97) (-4.38) (-6.21) Pw_under 0.283*** 0.000504*** 0.000380*** (7.82) (13.36) (10.49) w_under -0.0311 0.0403*** 0.0477*** (-0.68) (11.71) (15.66) bill_under 1.261*** 0.00662 0.0268*** (31.49) (1.20) (5.42) Pw_unk 0.507*** 0.0401*** 0.0238** (6.84) (4.45) (2.73) w_unk -0.0656 -0.0102* -0.00718 (-1.80) (-2.47) (-1.95) bill_unk 0.731*** (22.46)	Iday/Pw -34.01 * SF_TN_CF_HK 0.0228 (0.51) (M4) 0.00149*** 𝑽𝒂𝒓(𝒖) (-2.21) 0.530 *** (13.62) -0.144 (-0.99) 10.58 *** (29.12) 9.175 *** (7.46) -10.45 *** (-8.84) 27.06 *** (21.41) 0.0752 *** (11.81) -8.338 *** (-10.91) 10.01 *** (8.98) 0.004 (p=0.9484) 0.0352 SF_TN_CF_IE (0.80) (M5) 0.00133*** 𝑬(𝒖) 6778.1 7424.4 14441 14441 (-6.03) (-10.56) 92.891 *** (p=0.000) -214.5*** -127.024*** (66.66) (68.17) 38.524 *** (p=0.000) 0.069132*** 0.07139*** 38.467 *** (p=0.000) (12.05) 5.8840*** 14441 (174.32) (-1.36) 85.1119*** -1.810 (-7.59) (-7.20) (0.51) -0.00170*** -0.00158*** 0.00807 (6.45) (5.77) (1.56) 0.0143*** 0.0125*** 0.342 (1.07) (0.83) (-1.89) 0.0000471 0.0000357 -0.259 (-2.96) (-2.79) (11.30) -0.00192** -0.00177** 15.85 *** (2.78) (1.93) (8.64) 0.00121** 0.000821 7.501 *** (-6.18) (-6.25) (11.36) -0.0353*** -0.0351*** 21.10 *** (6.71) (6.10) 2.820*** -109.6*** 0.0321*** 0.0347*** (25.73) (-6.67) (12.31) (13.45) 0.0000795*** 0.00518*** 0.00338 -0.00105 (8.34) (5.58) (0.77) (-0.25) 0.427*** 27.58*** 0.0198*** 0.0203*** (8.14) (5.54) (4.80) (5.03) -0.433*** -37.14*** -0.0473*** -0.0503*** (-6.54) (-4.87) (-6.50) (-7.11) 0.0606* 3.512 0.000317*** 0.000275*** (2.36) (1.63) (9.76) (8.44) 0.156*** 11.62*** 0.0499*** 0.0528*** (4.79) (3.77) (18.83) (20.46) 0.770*** 60.85*** 0.0148*** 0.0206*** (27.00) (6.78) (3.35) (4.76) 0.169** 15.83*** 0.0133 0.0100 (3.22) (3.48) (1.72) (1.30) 0.0315 6.134* -0.0103** -0.00923** (1.24) (2.37) (-3.22) (-2.94) 0.294*** 29.01*** (12.71) (6.14)	0.0337 (0.77) 0.00136*** 7409.3 14441 (68.67) 0.07097*** (10.64) 3.8638*** (149.83) 54.4365*** (-7.22) -0.00158*** (5.81) 0.0125*** (0.82) 0.0000351 (-2.82) -0.00179** (2.01) 0.000851* (-6.04) -0.0337*** (6.26) 0.0341*** (13.37) 0.000293 (0.07) 0.0203*** (5.04) -0.0489*** (-6.92) 0.000274*** (8.44) 0.0520*** (20.21) 0.0202*** (4.69) 0.00912 (1.19) -0.00926** (-2.96)

t statistics in parentheses. * Notes: t statistics in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001. Notes: t statistics in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.

6,800 households were contacted, but the response rate was lower than 30%. Moreover, some households were purged due to excessive missing values or strange consumption levels (these were consulted with the EMA before taking a final decision).

For further information, check https://observa.gijon.es/pages/inicio

Water habits are: water recycling, cooling water by keeping it bottled in the fridge, turning the tap off while soaping hands, defrosting food in advance without making use of water, filling the sink before washing dishes, loading completely up the washing machine and the dishwasher, reducing the water volume by partially closing the shut-off valve, not using the toilet for waste disposal, making use of the partial-flush system on the toilet tank, turning off the tap while brushing the teeth, taking showers instead of baths, turning off the shower while soaping themselves up, not washing cars with residential water.

According to[START_REF] Diaz | Firm size and productivity in Spain: a stochastic frontier analysis[END_REF] andSchiersch (2012), there seems to exist an optimal size for firms which maximizes efficiency levels. This is explained due to "bureaucratic frictions, lack of motivation of workers, and difficulty in monitoring"[START_REF] Diaz | Firm size and productivity in Spain: a stochastic frontier analysis[END_REF], that can be easily matched by the functioning of a household.