Jonathan Sicsic
email: jonathan.sicsic@u-paris.fr

Thomas Rapp

Frailty transitions and healthcare use in Europe 1

Objective. There is relative consensus that chronic conditions, disability and time-to-death are key drivers of age-related health care expenditures. In this paper, we analyse the specific impact of frailty transitions on a wide range of health care outcomes comprising hospital, ambulatory care, and dental care use. Data source. Five regular waves of the SHARE survey collected between 2004 and 2015. Study design. We estimate dynamic panel data models on the balanced panel (N=6,078; NT= 30,390 observations). Our models account for various sources of selection into frailty, i.e. observed and unobserved time-varying and time-invariant characteristics. Principal Findings. We confirm previous evidence showing that frailty transitions have a statistically significant and positive impact on hospital use. We find new evidence on ambulatory and dental care use. Becoming frail has greater impact on specialist compared to GP visit, and frail elderly are less likely to access dental care. Conclusions. By preventing transitions towards frailty policy planners could prevent hospital and ambulatory care uses. Further research is needed to investigate the relationship between frailty and dental care by controlling for reverse causation.

INTRODUCTION

The growth of population aging in developed countries has raised interest in its associated costs. Understanding the drivers of medical care utilization and spending is crucial for the efficient organization (and allocation) of health care services (and resources). However, the relationship between ageing and health care expenditures has been the subject of much debate in the literature. [1][2][3] Initially, Zweifel et al (1999) showed that age per se did not have a significant impact on health expenditures after controlling for proximity to death. 2 Then, it has been suggested that comorbidities, chronic diseases and mental health issues, whose prevalence increases with age, actually mediate the relationship between age and increased health care expenditures. [4][5][6][7][8] In Canada, it has been shown that differences in pre-existing chronic conditions contribute to health differences in health care expenditures. 6 Furthermore, comorbidities, impairments, and proximity to death were found to be key mediators of agerelated expenditures in the UK. 7 Other results from cross-sectional data in Germany found that multimorbidity and mental health were consistently associated with total, inpatient, outpatient, and nursing costs. 8 Recently, it has been advocated that frailty could be a key variable to consider when exploring the relationship between ageing and increase in health care expenditures. 9 Frailty has been a well established concept in the medical literature. [10][11][12] It is considered as a distinct health dimension besides disability, chronic diseases, and functional limitations. 13 Frailty is defined as a "clinically recognizable state of increased vulnerability resulting from agingassociated decline in reserve and function across multiple physiologic systems". 12 Frailty is associated with loss of muscle mass and muscle quality referred to as sarcopenia, resulting from anatomic and biochemical changes in aging muscle. [START_REF] Marcell | Sarcopenia: Causes, consequences, and preventions[END_REF] As such, it is highly correlated with ageing. The estimated prevalence of frailty in Europe in 2004 was 4.1% among individuals aged 50-64 years and 17.0% among 65 years and older subjects. [START_REF] Santos-Eggimann | Prevalence of frailty in middleaged and older community-dwelling Europeans living in 10 countries[END_REF] The specific contribution of frailty to ambulatory care expenditures was calculated using French administrative data, peaking at about €1,500 for frail individuals. 9 From an economic point of view, the theoretical model underpinning the analysis of frailty in relation with health care utilization is the health deficit accumulation model. [START_REF] Dalgaard | Optimal Aging and Death: Understanding the Preston Curve[END_REF][START_REF] Strulik | Frailty, mortality, and the demand for medical care[END_REF] This model posits that ageing is associated with a loss of physical functions (e.g. depreciation of health capital), and ability to cope with stressing factors. This should increase the demand for healthcare when people become frail, a prediction that is consistent with Grossman healthcare demand model. [START_REF] Grossman | On the Concept of Health Capital and the Demand for Health[END_REF] A growing body of the empirical literature has explored the specific impact of frailty on health care utilization. [START_REF] Hoeck | Health-care and home-care utilization among frail elderly persons in Belgium[END_REF][START_REF] Ilinca | The Patterns of Health Care Utilization by Elderly Europeans: Frailty and Its Implications for Health Systems[END_REF][START_REF] Sirven | The Dynamics of Hospital Use among Older People Evidence for Europe Using SHARE Data[END_REF] Using cross-sectional data in Belgium, it has been shown that frail and prefrail individuals were more likely than robust elders to contact a GP, a specialist, or an emergency department. [START_REF] Hoeck | Health-care and home-care utilization among frail elderly persons in Belgium[END_REF] Using panel data in 10 European countries, two studies showed that frailty was significantly associated with hospital and ambulatory care use, after controlling for both socioeconomic and health status. [START_REF] Ilinca | The Patterns of Health Care Utilization by Elderly Europeans: Frailty and Its Implications for Health Systems[END_REF][START_REF] Sirven | The Dynamics of Hospital Use among Older People Evidence for Europe Using SHARE Data[END_REF] However, less is known about the correlation between frailty and dental care. Previous research underlined the importance of considering dental care access issues among the frail elderly population, [START_REF] Chen | Dental treatment intensity in frail older adults in the last year of life[END_REF][START_REF] Ettinger | Dental implants in frail elderly adults: A benefit or a liability?[END_REF][START_REF] Kikutani | Relationship between nutrition status and dental occlusion in community-dwelling frail elderly people[END_REF][START_REF] Nitschke | Dental care of frail older people and those caring for them[END_REF] but the evidence on the impact of (pre-) frailty on dental care use is scarce. The subject is important because by failing to consult for dental problems, pre-frail individuals may increase their chances to loose weight and become frail because of lower nutritional intake. [START_REF] Kikutani | Relationship between nutrition status and dental occlusion in community-dwelling frail elderly people[END_REF][START_REF] Stein | Dental Care in the Frail Older Adult: Special Considerations and Recommendations[END_REF] Our aim in this paper is to provide new and more robust evidence on the impact of frailty transitions on health care use. Our contribution to the literature is threefold. First, we use more recent and exhaustive data from the five regular waves of the Survey of Health, Ageing, and Retirement in Europe (SHARE) thus providing more insights for the analysis of frailty transitions and more robust conclusions. Second, we analyse the impact of frailty on a wider range of health care use outcomes, namely probability of hospital admission, probability of ambulatory care visits (by distinguishing GP and specialist visits), and for the first time exploring its correlation with dental care use in a longitudinal setting. Third, from a methodological point of view, we estimate empirical models that are less prone to endogeneity as they account for various sources of selection into frailty: (a) unobserved timeinvariant characteristics through inclusion of individual fixed effects, (b) time-varying observed variables and (c) time-varying unobserved shocks through the specification of a dynamic model with lagged dependent variable. [START_REF] Ravesteijn | The wear and tear on health: What is the role of occupation?[END_REF] Specifically, we formalize and discuss for the first time the conditions under which our estimates can be considered as causal.

DATA

Source and sample

We used data from the five regular waves of the Survey of Health, Ageing, and Retirement in Europe (SHARE) collected at different time points in 2004/05 (wave 1), 2006/07 (wave 2), 2011/12 (wave 4 1 ), 2013 (wave 5) and 2015 (wave 6). In these waves, SHARE provides information on socioeconomics, health and health-care use variables from representative samples of non-institutionalised individuals over the age of 50 in eleven countries. [START_REF] Börsch-Supan | Data Resource Profile: The Survey of Health, Ageing and Retirement in Europe (SHARE)[END_REF] The countries represent northern Europe (Denmark and Sweden), central Europe (Austria, France, Germany, Switzerland, Belgium, the Netherlands), and southern Europe (Spain, Italy and Greece). We restricted the sample to the nine countries participating in all regular waves (thus excluding Greece and the Netherlands) and to individuals who participated in the first wave of the panel.

Dependent variables

Three types of health care utilization indicators were used as dependent variables in our models: (1) hospital admission, (2) ambulatory care use, and (3) dental care use. Hospital admission was included as a dichotomous variable measuring whether, during the last 12 months, the respondent had been in a hospital overnight (HOSP = 1/0). We used three indicators of ambulatory care use. First, having 1+ visit to a medical doctor (including emergency room or outpatient clinic visits) in the last 12 months (DOC = 1/0). In the first three regular waves of SHARE, it was also possible to distinguish between GP visit (GP = 1/0) and specialist visit (SPE = 1/0). Finally, we used an indicator of whether the respondent had at least one visit with a dentist in the last 12 months (DENT = 1/0). Note that this information was not collected in wave 4.

Independent variables

Our explanatory variable of interest was Fried's frailty scale, which defines frailty according to five dimensions: 10,13 low energy, slowed walking speed, diminished appetite, low grip strength, and low physical activity. We followed prior work to compute the frailty scale: [START_REF] Santos-Eggimann | Prevalence of frailty in middleaged and older community-dwelling Europeans living in 10 countries[END_REF][START_REF] Ilinca | The Patterns of Health Care Utilization by Elderly Europeans: Frailty and Its Implications for Health Systems[END_REF][START_REF] Sirven | The Dynamics of Hospital Use among Older People Evidence for Europe Using SHARE Data[END_REF] one point was allocated for each fulfilled criterion and a frailty score was computed by summing each criterion which contributed equally to the score (theoretical bounds: 0-5). We set cut-off points in order to define three profiles: 0 for robust, 1-2 for pre-frail, and 3-5 for frail. 12,[START_REF] Ilinca | The Patterns of Health Care Utilization by Elderly Europeans: Frailty and Its Implications for Health Systems[END_REF] We controlled for several socioeconomics and health status indicators identified as predictors of health care demand in previous work 4,[START_REF] Andersen | Revisiting the Behavioral Model and Access to Medical Care: Does it Matter?[END_REF] and / or as potential correlates of frailty. [START_REF] Ilinca | The Patterns of Health Care Utilization by Elderly Europeans: Frailty and Its Implications for Health Systems[END_REF] Predisposing or enabling factors (according to Andersen' behavioural model) [START_REF] Andersen | Revisiting the Behavioral Model and Access to Medical Care: Does it Matter?[END_REF] included age, gender, education, living with a spouse or having a partner, and a dichotomous measure of income adequacy based on a 4-point scale indicating whether the household was able to make ends meet: with great difficulty / with difficulty (coded 1) versus fairly easily / easily (coded 0). This subjective indicator of economic deprivation that has been found to be well correlated with material deprivation items in SHARE data [START_REF] Börsch-Supan | Ageing in Europe -Supporting Policies for an Inclusive Society[END_REF] . In addition, we used a dichotomous variable of self-rated health being fair or poor (poor SRH), having two or more chronic diseases (chronic 2+), having two or more limitations in activities of daily living (ADL 2+), having two or more limitations in instrumental activities of daily living (IADL 2+), and having three or more depressive symptoms according to the Euro-D measure. [START_REF] Prince | Development of the EURO-D scaleâA European, Union initiative to compare symptoms of depression in 14 European centres[END_REF]

Sample attrition

Similarly to most panels focusing on elderly people, SHARE is characterized by an important attrition. In our sample, 52% of interviewees who participated in the first wave participated in all waves. In this situation, an important question arises, namely whether to use the balanced (i.e. with no missing data) or the unbalanced dataset. Fixed effects (FE) estimates on the unbalanced panel are consistent only in the presence of exogenous attrition, i.e. only if the determinants of attrition are uncorrelated with the time-varying regressors. [START_REF] Wooldridge | Econometric Analysis of Cross Section and Panel Data[END_REF] However, since individuals remaining in the panel are often healthier than attriters, sample selection is unlikely to be exogenous.

An overview of sample size, dropouts, and attrition rate by wave and according to respondents' characteristics is presented in Appendix A (Table A.1). Individuals with poor health and in particular, frail elders are more likely to be attriters. These results are confirmed by running Nijman and Verbeek' (1992) variable addition tests in order to test for exogenous attrition. [START_REF] Nijman | Nonresponse in panel data: The impact on estimates of a life cycle consumption function[END_REF][START_REF] Contoyannis | The dynamics of health in the British Household Panel Survey[END_REF] Rejection of one of the tests was interpreted as indicating non-exogenous selection, which was the case for nearly all models (see Table A.2). To be consistent, we estimated our FE models using the balanced sample, comprising 6,078 individuals and 30,390 person-wave observations. Results of models estimated on the unbalanced sample are provided in supplementary Tables A. 4 and A.5 (Appendix A). two endogeneity issues cannot be completely removed in the absence of a well-specified instrument. However, the source of bias can be partly reduced by using a correct dynamic specification of Eq (1).

ECONOMETRIC MODELS

General specification

Let

Dynamic correlated random effects (CRE) model

A generalization of the static FE model to the dynamic case is presented in Eq (2):

In the CRE specification, is treated as a random effect, and is replaced by its linear projection onto the means of the time-varying regressors (see technical Appendix B for additional information). As shown in the seminal work of Mundlak (1978) [START_REF] Mundlak | On the Pooling of Time Series and Cross Section Data[END_REF] , results of FE and CRE models estimated on a balanced panel collapse (see Table A.3 for empirical comparison using Hausman test). In the dynamic CRE model in Eq (2), is an autoregressive oneperiod lag of the dependent variable k and denotes the associated coefficient, which reflects persistence or state-dependence in health care utilization [START_REF] Kohn | The dynamics of medical care use in the British household panel survey[END_REF] . In addition, captures all timevarying unobserved shocks that may simultaneously affect frailty and health care use, thus reducing the correlation between frailty and residual unobserved heterogeneity. Following previous research, [START_REF] Sirven | The Dynamics of Hospital Use among Older People Evidence for Europe Using SHARE Data[END_REF] we used information contained in the third retrospective wave of SHARE -namely an indicator variable of whether individuals had health problems in adult life -as the initial value of the dependent variable. [START_REF] Wooldridge | Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity[END_REF] The models were estimated by feasible generalized least square (GLS) with standard errors accounting for clustering at the individual level.

Dealing with the endogeneity of time-varying controls

Our model accounts for all time-invariant and some time-varying characteristics that could be associated with both frailty and health care use. Two types of time-varying characteristics are included in : (1) exogenous variables (i.e., age and wave dummies) and

(2) potentially endogenous variables (e.g., living with partner, chronic diseases, ADL / IADL limitations) for which it is theoretically not possible to assert whether they are causes or consequences of frailty. On the one hand, including endogenous control variables that are consequences of frailty may block the causal pathway and lead to biased estimates of both the total and direct effect of frailty. [START_REF] Angrist | Mostly Harmless Econometrics: An Empiricist's Companion[END_REF] In particular, if these endogenous variables are positively correlated with frailty, they will capture part of the correlation between frailty and health care use such that controlling for these variables is likely bias downward the effect of frailty (assumption 1). On the other hand, if these variables are exogenous and exert a causal impact on frailty, then excluding them from the model would lead to an omitted variable bias, which likely will bias upward the effect of frailty (assumption 2). As it is not possible to determine with certainty which scenario is most plausible (most likely, there is a dynamic relationship between frailty and the included time-varying endogenous variables) two models have been considered: (1) excluding and (2) including these variables. Results of model ( 1) are interpreted as the total effect of frailty, and results of model ( 2) are interpreted as the partial effect of frailty.

Robustness analyses

We test the robustness of our main analyses by comparing the results of models ( 1) and ( 2)

across different model specifications and estimation strategies: fixed effects OLS, conditional maximum likelihood (fixed effects logit) and random effects GLS, in the balanced and unbalanced samples. We also replicate FE analyses using SHARE weights designed to obtain a representative population of each country. These weights are calibrated to precisely reflect each country's age and gender proportions. [START_REF]The SHARE sampling procedures and calibrated design weights. In: The Survey of Health, Aging, and Retirement in Europe-Methodology. Mannheim Research Institute for the Economics of Aging (MEA): Börsch-Supan A[END_REF] All results are provided in Tables A. 4 to A.7 .

RESULTS

Descriptive statistics

Table 1 provides an overview of the distribution of the independent variables at different points in time in the balanced sample. Not surprisingly, the proportion of frail individuals is increasing in time as a result of ageing of the population (+ 146% increase between wave 1 and wave 6). There is a similar increase over time in the levels of functional limitations (e.g., +174% increase in prevalence of 2+ ADL limitations), chronic conditions (+134% increase)

and to a lesser extent, depressive symptoms (+15% increase). The socio-economic indicators are stable over time.

[insert Table 1] Age and sex-standardized rates of health care use according to the frailty status are provided in Table 2. There is a strong positive correlation between frailty and hospital admission: 30.1% of frail individuals had at least one hospitalization in the past 12 months versus 9.7% among robust elders (of similar age and sex). Similarly, there is a strong positive correlation between frailty and ambulatory care: 97.5% of frail individuals had at least one doctor visit in the past 12 months versus 87.9% among robust elders. These differences seem to be more important concerning access to specialist versus primary care practitioner: there is a 20.9 percentage points difference in the probability of specialist visit among frail (versus robust) elders, as compared to a 14.0 percentage points difference in the probability of GP visit. On the contrary, there is a negative correlation between frailty and dental care use:

41.4% of frail elders had at least one visit to the dentist in the past 12 months versus 63.6% among robust elders.

[insert Table 2]

Results of econometric models

The results of the static FE and dynamic CRE models of health care use estimated on the balanced sample are presented in Table 3 (hospital admission and ambulatory care), Table 4 (GP and specialist visit) and Table 5 (dentist visit). In all models except dental care, the sign and statistical significance of frailty are stable across the two econometric specifications. For parsimony, we only detail the estimates of the dynamic CRE models.

In the model of hospital use, becoming frail is associated with a total effect of 14.4

percentage point (pp., hereafter) increase in the probability of hospital use, and a 9.7 pp.

increase once the effect of potentially endogenous controls has been netted out (partial effect displayed in model 2). As expected, in model 2, poor self-rated health, having 2+ ADL / IADL limitations and 2+ chronic diseases is further associated with increased hospital admission, but the marginal impact is lower compared to frailty. We find evidence of persistence in hospital admission. As expected, the initial conditions have a positive and statistically significant impact on contemporaneous hospitalization. Among the time-invariant socio-economic characteristics, only gender is significantly associated with hospital use: in model 2, being a female is associated with a 2.1 pp. decrease in the probability of hospital admission.

[insert Table 3]

The magnitude and statistical significance of the impact of frailty transitions on ambulatory care use vary in the models (1) excluding or (2) including potentially endogenous (total effect = 1.8 pp. increase and partial effect = 1.2 pp. increase). Becoming frail is associated with a significant effect on ambulatory care use only in model 1, with a total effect of 2.1 pp. increase (see Table 3). We find evidence of persistence in ambulatory care use.

Table 4 reports the results of the analyses according to the type of medical practitioner (i.e., GP or specialist). The impact of frailty transitions on care use is stronger for specialist compared to GP. Becoming pre-frail or frail are significantly associated with an increased probability of GP visit, though with limited magnitude (2.1 pp. and 2.9 pp. increase, respectively) and only in model 1 (not controlling for potentially endogenous covariates).

However, becoming frail is associated with a total effect of 7.7 pp. increaseand a partial effect of 5.7 pp. increasein the probability of specialist visit.

Among the time-varying health controls variables, poor self-rated health and 2+ chronic conditions are associated with increased ambulatory care use (either GP or specialist).

Moreover, transition into material deprivation (within-subject variability) is associated with higher likelihood of GP visit but no specialist visit. On the contrary, between-subject variability in socio-economic characteristics are significantly associated with specialist visit: having a tertiary education is associated with a 10.5 pp. increase in the probability of specialist visit, and material deprivation is associated with a 6.9 pp. decrease in the probability of specialist visit.

[insert Table 4] The results of the models of dental care use are displayed in [insert Table 5]

Results of robustness analyses

Our results are robust to competing econometric specifications: (i) estimations on the unbalanced panel, (ii) use of logit link function in a conditional maximum likelihood estimation framework, and (iii) and weighted FE estimation using SHARE sampling weights to ensure representativeness of the surveyed population. [START_REF]The SHARE sampling procedures and calibrated design weights. In: The Survey of Health, Aging, and Retirement in Europe-Methodology. Mannheim Research Institute for the Economics of Aging (MEA): Börsch-Supan A[END_REF] Interestingly, the estimates are higher in absolute terms in alternative specifications (i) and (ii) (see Tables A. 4 and A.5 for model comparisons). For instance, becoming frail is associated with a 23.0 pp. increase (total effect) in the probability of hospitalization in the conditional logit model on the unbalanced panel (versus a 14.4 pp. increase in the dynamic CRE on the balanced panel). This shows the results of our main analyses on the balanced panel may be conservative.

DISCUSSION

This study provides an empirical and methodological contribution to the literature on the determinants of health care utilization among older people. To our knowledge, this study is the first to have used the five regular waves of the SHARE survey to analyse the effect of frailty transitions on a wide range healthcare indicators using econometric specifications that account for various sources of selection into frailty and thus are less prone to endogeneity bias. In additions, we compare the results across different specifications, (1) excluding or (2) including potentially endogenous (health) controls, the results of which are interpreted respectively as (1) the total effect or (2) the partial effect of frailty. However, care is needed in interpreting these results, as both estimates may be biased: upward for the 'total effect' (because of omitted variable bias), downward for the 'partial effect' (because of endogenous controls capturing part of the relationship between frailty and the outcome). It is thus informative to present the results of both specifications, as they are likely to provide upper and lower bounds of the effect of frailty transitions on health care use. According to our preferred -though potentially conservative -estimates, transitions into frailty are associated with a marginal increase in the probability of hospitalization by about 9.7 to 14.4 percentage points. Concerning ambulatory care use, the impact of frailty transition is economically unsignificant for GP visit, but is associated with a 5.7 to 7.7 percentage points increase in the probability of specialist visit. On the contrary, becoming frail is associated with a 3.1 percentage point decrease in the probability of dental care visit. In all models, poor health, limitations in (instrumental) activities of daily living or chronic diseases were significant predictors of health care use.

The results on the impact of frailty on hospitalization and ambulatory care use confirm previous findings. Using the first three waves of SHARE, it was shown that progression by one point on the frailty scale [0;5] was associated with an additional risk of hospitalization of about 2.1 percentage point. [START_REF] Sirven | The Dynamics of Hospital Use among Older People Evidence for Europe Using SHARE Data[END_REF] In our study, frailty was defined as scoring three or more on the frailty scale, i.e. corresponding to an increase in three points (or more) on the frailty scale.

Using static models estimated from the first three waves of SHARE, it was found that frailty was significantly associated with doctor and GP visits. [START_REF] Ilinca | The Patterns of Health Care Utilization by Elderly Europeans: Frailty and Its Implications for Health Systems[END_REF] Using a dynamic specification controlling for time-invariant unobserved characteristics allowed us to provide more robust conclusions.

To our knowledge, our study is the first to assess the relationship between frailty and dental care use in a longitudinal setting. Previous work has underlined the importance of this subject, since frail elders suffer more from untreated dental issues than robust elders. [START_REF] Chen | Dental treatment intensity in frail older adults in the last year of life[END_REF][START_REF] Nitschke | Dental care of frail older people and those caring for them[END_REF] Nevertheless, our results should be interpreted with caution due to the problem of reverse causality, i.e. people may become frail precisely because they do not consult a dentist and are thus more exposed to malnutrition. [START_REF] Kikutani | Relationship between nutrition status and dental occlusion in community-dwelling frail elderly people[END_REF] In our model, the negative estimate of the impact of frailty on dental care use may capture both the 'pure' (causal) negative effect of frailty and also the negative 'selection effect' into frailty (i.e., the negative correlation between dentist care and frailty, see Table A .6). Yet, in the absence of a plausible instrument, we cannot disentangle the two effects and our results should not be interpreted in a causal way. Still, controlling for past dental care in the dynamic specification is an important contribution to the literature, as it should theoretically allow capturing some of the sources of reverse causality.

Despite this limitation, our results are consistent with the literature, showing for instance that functional limitations and poor oral health were associated with a lower probability of dental care among French institutionalized elders. [START_REF] Naouri | What are the determinants of dental care expenditures in institutions for adults with disabilities? Findings from a National Survey[END_REF] In any case, even in the hypothetical scenario where all of the negative correlation between frailty and dental care was driven only by a selection effect, our results underline the need to increase access to dental care for frail elders, and can be used to raise the awareness on that issue. The none significant effect of pre-frailty may either be explained by the fact that reverse causation (pre-frailty caused by absence of dental care) is lower or do not exist, or due to the fact that the 'pure' negative effect of prefrailty on dentist visit is less important. This seems a reasonable assumption, as pre-frails are less likely to suffer from mobility limitations associated with problems of access to dental care.

We found that socio-economic variables (i.e., living with a spouse, education, and subjective material deprivation) had little or non-significant impact on GP visit and hospital admission. These results are consistent with a previous analysis of health care use in the elderly German population. 5 However, these variables had significant impact on dental care use. In particular, the result that material deprivation is associated with lower dental care use strengthens the need to promote better access to dental care in the elderly, for instance by optimizing dental care insurance and / or increasing coverage. [START_REF] Calcoen | How can dental insurance be optimized?[END_REF] We found that only betweensubject differences in terms of material deprivation was associated with dental care use. This result could be partly explained by the low amount of within-subject variability in socioeconomic status across waves. Another interpretation of the result is that habits or 'predisposing' factors related to present or past economic conditions [START_REF] Andersen | Revisiting the Behavioral Model and Access to Medical Care: Does it Matter?[END_REF] have higher impacts on dental care use than transitive economic shocks. In any case, that lower economic resources are associated with less access to specialists is consistent with theoretical and empirical evidence. 4,[START_REF] Andersen | Revisiting the Behavioral Model and Access to Medical Care: Does it Matter?[END_REF] Our study faces several limitations. A well-known shortcoming of the linear probability model is that the predicted probabilities are unbounded thus making it unsuitable for making predictions. However, we were mainly interested in computing average marginal effects, and standard errors were adjusted for heteroskedasticity. We also checked the robustness of our results using non-linear logit specifications, but the conclusion remained unchanged (Tables A. 4 and A.5). Despite the richness of SHARE survey, the models were estimated only on a subset of the population being observed in all waves, which could create a selection bias. However, as our identification strategy relies on within-individual variability, our estimates are consistent in the presence of selection on observables or unobservables insofar as the non-ignorable non-response is due to time invariant characteristics. [START_REF] Nijman | Nonresponse in panel data: The impact on estimates of a life cycle consumption function[END_REF] Another way to deal with attrition would be either to apply inverse probability weighting (IPW) on the unbalanced panel, [START_REF] Contoyannis | The dynamics of health in the British Household Panel Survey[END_REF] or to use a competing-risk model treating attrition as an endogeneous variable. However, the conditional independence assumption underlying the IPW methodology could not be verified in our data (see technical Appendix B). Moreover, absence of information regarding the date of hospitalization, ambulatory care or dental care visit prevented joint modeling of health care use and attrition in a competing-risk framework. Yet, several influential studies reported that attrition does not lead to serious bias (i.e., affecting the magnitude of coefficients) even in the presence of large sample attrition. [START_REF] Jones | Panel Data Methods and Applications to Health Economics[END_REF][START_REF] Fitzgerald | An Analysis of Sample Attrition in Panel Data: The Michigan Panel Study of Income Dynamics[END_REF][START_REF] Cheng | Attrition Bias in Panel Data: A Sheep in Wolf's Clothing? A Case Study Based on the Mabel Survey[END_REF] risk of getting predicted probabilities out of the 0-1 range2 . Moreover, we estimated standard errors robust to heteroskedasticity using the Huber-White covariance matrix estimator. 2 1.2.Fixed effects (FE) specification FE estimation of Eq (1) is obtained by OLS estimation on the within-transformed data, i.e. on the initial variables net of their respective individual-specific means.

Identifying variation

Since our FE estimates are based only on frailty transitions, identification is secured only to the extent that there is sufficient within-subject variability in frailty states across waves. We tested this necessary condition by looking at the average transitions in frailty states (i.e., from robust to pre-frail and frail) from a period to the next (see Table 2). Within our sample, 4,020 out 6,078 individuals (66.1%) have switched from one frailty state to another during the study period. Applying OLS to the within-transformed data in Eq (2) would create endogeneity issues (leading to biased estimates of ) because of the correlation between and .

To overcome this difficulty, we estimated a correlated random effect (CRE) model 4 . In standard RE models, the random individual specific term is assumed normally distributed and uncorrelated with . This strong assumption was relaxed by replacing by its linear projection onto , the means of the regressors, and an intercept. Introducing in Eq (2)

allows netting out the effect of covariates arising from between-subject variability (e.g., differences in frailty status across individuals). This allows interpreting marginal effects as within estimates. 6 Based on the same rationale as that prevailing in the static FE models, we estimated two dynamic CRE models, one excluding and the other, including the potentially endogenous time-varying characteristics .

In dynamic CRE models, another issue is the problem of initial conditions 7 . Determining the initial condition of the dependent variable ( prevents inconsistent estimates of thus allowing for correct inference on the amount of state dependence in health care use.

Following previous research, 8 we used information contained in the third retrospective wave of SHARE -namely an indicator variable of whether individuals had health problems in adult life -as the initial value of the dependent variable. The models were estimated by feasible generalized least square (GLS) with standard errors accounting for clustering at the individual level.

Identifying variation

Under the assumption that after conditioning on unobserved time-invariant characteristics, lagged dependent variable, and some observed time-varying characteristics, all switches between frailty status are random, then our estimates reflect the causal 4 An alternative specification would be to consider the unobserved individual effects as being fixed and estimate dynamic first difference linear probability models using second and higher order lags of the dependent variables as instruments in a GMM estimation framework 5 . We tried to apply this framework to our data. However, the Sargan / Hansen test of overidentifying restrictions rejected the assumption of validity of the instruments in the models of hospital and ambulatory care use. The approach could not be applied in the models of GP and specialist visit because of insufficient number of time periods (with T=3, only one lag of the dependent variable could be used as an instrument).

effect of frailty transitions on health care use. We cannot rule out that unobserved shocks (e.g. accident, fall) occurring between two waves and thus not sufficiently captured by the lagged health care use variable simultaneously affect frailty transitions and health care use. For instance, Ravesteijn et al. (2018) encounter a similar issue when trying to estimate the causal effect of occupation on health using lagged health as control in a dynamic panel data model. 9 In this case, our estimate cannot literally be interpreted as the causal effect of frailty on health care use, but represent the best attempt to estimate such effect using observational data.

Dealing with attrition in the data

Similarly to most panels focusing on elderly people, SHARE is characterized by an important attrition. In our sample, 52% of interviewees who participated in the first wave participated in all waves. In this situation, an important question arises, namely whether to use the balanced in the presence of selection on observables or unobservables, as long as the non-ignorable non-response is due to time invariant characteristics. 10 The idea is that, with the initial sampling, the fact that some units are more likely to drop out of the survey is captured by the individual unobserved error term, which is allowed to be correlated with observed covariates in FE estimation thus 'removing' the selection bias associated with time-invariant characteristics.

An overview of sample size, dropouts, and attrition rate by wave and according to respondents' characteristics is presented in Appendix A (Table A.1). Individuals with poor health and in particular, frail elders are more likely to be attriters. These results are confirmed by running Nijman and Verbeek' (1992) variable addition tests in order to test for exogenous attrition. The following variables were included as covariates in the econometric models: (i)

whether the individual responded in the subsequent wave (NEXT WAVE), (ii) whether the individual responded to all waves (ALL WAVES) and (iii) a count of the number of waves that were observed for the individual (NUMBER of WAVES). 10,11 Rejection of one of the tests was interpreted as indicating non-exogenous selection. This was the case for all models except for ambulatory care use (see Table A.2, Appendix A). Consequently, we estimated our FE models using the balanced sample, comprising 6,078 individuals and 30,390 person-wave observations.

We investigated investigated the validity of a 'selection on observables' approach to correct for sample selection, by using inverse probability weighting (IPW) to adjust empirical estimates in the unbalanced panel. [11][12][13] This approach requires (i) a set of instruments Z t that are correlated with non-response and with the dependent variables Y t , and (ii) that attrition becomes uncorrelated with the dependent variables after controlling for Z t. We used the same instruments as in Arrighi et al (2017), 12 i.e., respondent's willingness to answer the questionnaire assessed by the interviewer and respondents' self-assessed understanding of the questions. However, assumption (ii) was rejected for all models (at the 5% statistical level), meaning that observations could not be considered as missing at random conditional on observed covariates. Therefore, using the IPW on the unbalanced panel would not allow removing the attrition bias.

  (i.e. with no missing data) or the unbalanced dataset. According toWooldridge (2002),1 fixed effects (FE) estimates on the unbalanced panel are consistent only in the presence of exogenous (un-informative) attrition, i.e. only if the determinants of attrition are uncorrelated with the time-varying regressors. However, since individuals remaining in the panel are often healthier than attriters, sample selection is likely to be informative. In particular, attrition may be associated with health through death, serious illness, or move to institutional care. A specific issue arising with the use of the unbalanced panel (contrarily to balanced panels where individuals are all observed the same number of times, i.e. T is fixed) is that individuals with more observations are given more weights in model estimation. This can result in inconsistent estimates if individuals with more observations do not constitute a random sample of the population. On the contrary, FE estimation on the balanced sample is consistent

Table 5 .

 5 Compared to previous results, the marginal impact of frailty transitions on dental care use (i) is negative, (ii) differ in the static FE versus dynamic CRE model, and (iii) is less impacted by the introduction of potentially endogeneous variables. First, pre-frailty transition is not significantly associated with dental care use in any of the models (at the 5% level). Second, becoming frail is significantly associated with lower dental care use only in the dynamic CRE specification. Third, the total and partial effect of frailty is of the same magnitude: frailty transition is associated with a 3.1 pp. decrease in the probability of dental care use in model 1 and model 2. Among the potentially endogenous time-varying characteristics included in model 2, having 2+ IADL limitations is negatively associated with dental care use, whereas depressive symptoms are positively correlated with dental care use. Moreover, there is significant persistence in dental care use: in model 2, past use increases the probability of contemporaneous use by 33.6 pp. Concerning the impact of the socio-demographic timeinvariant characteristics, being a female, having secondary or tertiary education, and living with a partner are all significantly associated with higher dental care use. On the contrary, material deprivation is negatively associated with dental care use, reflecting problems in access to dental care among economically less well-off populations.

TABLE 1 .

 1 Another data limitation is lack of information about the reasons for hospitalization (e.g., planned versus unplanned), which would be helpful distinguishing in empirical models. Finally, because of data limitations, we were not able to identify whether the use of hospital care and ambulatory care were adequate or not. Further studies should therefore explore whether frailty is correlated with unnecessary care use. Similarly, the decrease in dental care use associated with frailty may not necessarily indicate "inadequate" care/prevention, and this result should be therefore explored with caution. Sample means of the independent variables by wave

	Notes
	1 The third wave was a retrospective survey (SHARELIFE) conducted in 2008/09 and focusing on people's life
	histories.

CONCLUSION

Frailty is a multifactorial and dynamic concept. It is a non-absorbing state, which means it is possible to design interventions to delay, if not reverse, frailty transitions. Our results suggest that delaying transitions towards frailty (e.g., by promoting exercise and appropriate diet) may contribute to preventing hospital and ambulatory care uses. Further research is needed to investigate the relationship between frailty and dental care by controlling for reverse causation.

ADL: activities of daily living. IADL: instrumental activities of daily living Reading grid: mean age has increased by 17% between wave 1 and wave 6

TABLE 3 .

 3 Panel data linear probability models of hospital and ambulatory care visit(1) total effect of frailty : model without endogenous health controls b (2) partial effect of frailty : model including endogenous health controls † Mean of the time-varying characteristic (Mundlak device), interpreted as between-subject differences. Note that all the associated time varying regressors were mean-centered in order to achieve this interpretation.

			Hospital admission (1/0)		Ambulatory care visit (1/0)
		(1) Total effect of	(2) Partial effect of	(1) Total effect of	(2) Partial effect of
		frailty a	frailty b	frailty a	frailty b
	Model specification	Static FE	Dynamic CRE	Static FE	Dynamic CRE	Static FE	Dynamic CRE	Static FE	Dynamic CRE
	Fried's frailty
	Pre-frail	0.050*** 0.058*** 0.038*** 0.043*** 0.013*** 0.018*** 0.008*	0.012**
	Frail	0.134*** 0.144*** 0.090*** 0.097*** 0.016*** 0.021***	0.005	0.009
	Time-varying controls
	A. Exogenous controls
	Age dummies	yes	yes	yes	yes	yes	yes	yes	yes
	Time fixed effects	yes	yes	yes	yes	yes	yes	yes	yes
	Time*country	yes	yes	yes	yes	yes	yes	yes	yes
	B. Potentially
	endogenous controls
	Living with partner			0.004	0.007			-0.007	-0.008
	Material deprivation			0.004	0.003			0.007	0.006
	Poor SRH			0.084*** 0.094***			0.029*** 0.030***
	Limit. / ADL 2+			0.047**	0.042*			0.007	-0.003
	Limit. / IADL 2+			0.070*** 0.072***			-0.011	-0.008
	Chronic 2+			0.037*** 0.041***			0.041*** 0.047***
	Depressive symptoms			0.008	0.007			0.006	0.003
	C. Unobserved shocks							
	Lagged dep. variable		0.110***		0.097***		0.221***		0.197***
	Initial condition		0.046***		0.031***		0.026***		0.016***
	Time-invariant controls
	Female		-0.025***	-0.021***		0.007*		0.010**
	Secondary education		0.006		0.009		0.003		0.005
	Tertiary education		-0.008		0.001		0.009*		0.014***
	Avg(Prefrail) †		0.075***		0.022**		0.048***		0.006
	Avg(Frail) †		0.201***		0.066***		0.066***		-0.001
	Avg(Partner) †				-0.003				0.015***
	Avg(Deprivation) †				-0.018*				-0.017**
	Avg(SHR) †				0.094***				0.026***
	Avg(ADL2+) †				0.088**				-0.011
	Avg(IADL2+) †				-0.018				-0.018
	Avg(Chronic2+) †				0.047***				0.095***
	Avg(Depress) †				0.016*				0.022***
	Country fixed effects	yes	yes	yes	yes	yes	yes	yes	yes
	Obs.	30,390	24,312	30,390	24,312	30,390	24,312	30,390	24,312
	FE: Fixed effects. CRE : Correlated Random Effects
	Statistical significance: ***: <1% ; **:<5% ; *<10%

a

TABLE 4 .

 4 Panel data linear probability models of GP and specialist visit(1) total effect of frailty : model without endogenous health controls b (2) partial effect of frailty : model including endogenous health controls † Mean of the time-varying characteristic (Mundlak device), interpreted as between-subject differences. Note that all the associated time varying regressors were mean-centered in order to achieve this interpretation.

			GP visit (1/0)			Specialist visit (1/0)
		(1) Total effect of	(2) Partial effect of	(1) Total effect of	(2) Partial effect of
		frailty a	frailty b	frailty a	frailty b
	Model specification	Static FE	Dynamic CRE	Static FE	Dynamic CRE	Static FE	Dynamic CRE	Static FE	Dynamic CRE
	Fried's frailty
	Pre-frail	0.012** 0.021***	0.008	0.012	0.027*** 0.032*** 0.017**	0.023**
	Frail	0.021** 0.029**	0.010	0.004	0.073*** 0.077*** 0.046*** 0.057***
	Time-varying controls
	A. Exogenous controls
	Age dummies	yes	yes	yes	yes	yes	yes	yes	yes
	Time fixed effects	yes	yes	yes	yes	yes	yes	yes	yes
	Time*country	yes	yes	yes	yes	yes	yes	yes	yes
	B. Potentially endogenous
	controls
	Living with partner			-0.011	-0.008			-0.013	0.006
	Material deprivation			0.009	0.017**			0.011	0.005
	Poor SRH			0.037*** 0.052***			0.071*** 0.089***
	Limit. / ADL 2+			-0.011	-0.014			0.005	-0.037
	Limit. / IADL 2+			-0.002	-0.006			0.004	0.010
	Chronic 2+			0.031***	0.018*			0.085*** 0.064***
	Depressive symptoms			0.003	0.002			0.006	-0.001
	C. Unobserved shocks							
	Lagged dep. variable		0.225***		0.203***		0.206***		0.187***
	Initial condition		0.027***		0.012**		0.080***		0.060***
	Time-invariant controls
	Female		0.003		0.003		0.023***		0.031***
	Secondary education		-0.003		-0.000		0.045***		0.047***
	Tertiary education		-0.010		-0.004		0.097***		0.105***
	Avg(Prefrail) †		0.062***		0.024**		0.105***		0.027*
	Avg(Frail) †		0.073***		0.031**		0.158***		0.035
	Avg(Partner) †				0.017**				0.030***
	Avg(Deprivation) †				-0.007				-0.069***
	Avg(SHR) †				0.021**				0.112***
	Avg(ADL2+) †				-0.012				-0.051
	Avg(IADL2+) †				-0.052***				-0.037
	Avg(Chronic2+) †				0.119***				0.112***
	Avg(Depress) †				0.029***				0.044***
	Country fixed effects	yes	yes	yes	yes
	Obs.	27,480	18,320	27,480	18,320	27,480	18,320	27,480	18,320
	FE: Fixed effects. CRE : Correlated Random Effects
	Statistical significance: ***: <1% ; **:<5% ; *<10%

a

TABLE 5 .

 5 Panel data linear probability models of dental care use(2) partial effect of frailty : model including endogenous health controls † Mean of the time-varying characteristic (Mundlak device), interpreted as between-subject differences. Note that all the associated time varying regressors were mean-centered in order to achieve this interpretation.

			Dental care (1/0)
		(1) Total effect of	(2) Partial effect of
		frailty a	frailty b
	Model specification	Static FE	Dynamic CRE	Static FE	Dynamic CRE
	Fried's frailty
	Pre-frail	-0.005	-0.010	-0.011	-0.014*
	Frail	-0.012	-0.031**	-0.015	-0.031**
	Time-varying controls
	A. Exogenous controls
	Age dummies	yes	yes	yes	yes
	Time fixed effects	yes	yes	yes	yes
	Time*country	yes	yes	yes	yes
	B. Potentially endogenous
	controls
	Living with partner			0.006	0.008
	Material deprivation			0.009	0.021*
	Poor SRH			-0.016**	-0.018*
	Limit. / ADL 2+			0.015	0.002
	Limit. / IADL 2+			-0.044*** -0.039**
	Chronic 2+			0.009	0.002
	Depressive symptoms			0.027*** 0.024***
	C. Unobserved shocks			
	Lagged dep. variable		0.339***		0.336***
	Initial condition		0.001		0.004
	Time-invariant controls
	Female		0.027***		0.031***
	Secondary education		0.077***		0.071***
	Tertiary education		0.121***		0.111***
	Avg(Prefrail) †		-0.025**		-0.019
	Avg(Frail) †		-0.129***		-0.072***
	Avg(Partner) †				0.024**
	Avg(Deprivation) †				-0.073***
	Avg(SHR) †				-0.033**
	Avg(ADL2+) †				0.084**
	Avg(IADL2+) †				-0.130***
	Avg(Chronic2+) †				0.020**
	Avg(Depress) †				0.022*
	Country fixed effects		yes	yes
	Obs.	26,884	20,163	26,884	20,163
	FE: Fixed effects. CRE : Correlated Random Effects
	a (1) total effect of frailty : model without endogenous health controls
	Statistical significance: ***: <1% ; **:<5% ; *<10%

b

Table A . 3 .

 A3 Hausman test of fixed effects versus correlated random effects

		Balanced panel		Unbalanced panel
	Dependent variable	Chi-square	P-value	Obs.	Chi-square	P-value	Obs.
	Hospitalization	0	1	30,390	25.95	0.9925	64,437
	Ambulatory care	0	1	30,390	28.51	0.9799	64,437
	GP visit	0	1	27,480	18.8	0.9038	45,985
	Specialist visit	0	1	27,480	23.26	0.7198	45,985
	Dental care	0	1	26,884	59.15	0.0118	53,731

Table A . 6 .

 A6 Effect of dentist visit on frailty

		Pr (Frail)	Pr (Low appetite)
		FE	CRE	FE	CRE
	Dental care	-0.010**	-0.013***	0.002	0.001
		(0.004)	(0.004)	(0.004)	(0.004)
	Time-varying controls
	Age dummies	yes	yes	yes	yes
	Time fixed effects	yes	yes	yes	yes
	Time*country fixed effects	yes	yes	yes	yes
	Living with partner	-0.007	-0.012**	-0.019***	-0.022***
		(0.005)	(0.005)	(0.006)	(0.005)
	Material deprivation	0.015***	0.013**	0.002	0.000
		(0.005)	(0.005)	(0.005)	(0.005)
	Time-invariant controls
	Female		0.067***		0.031***
			(0.003)		(0.003)
	Secondary education		-0.036***		-0.014***
			(0.004)		(0.004)
	Tertiary education		-0.042***		-0.019***
			(0.005)		(0.004)
	Avg(Dentist care)		-0.043***		-0.018***
			(0.007)		(0.006)
	Avg(Partner)		0.004		-0.003
			(0.004)		(0.003)
	Avg(Deprivation)		0.103***		0.059***
			(0.007)		(0.005)
	Country fixed effects	no	yes	no	no
	Obs.		53,731
	FE: Fixed effects; CRE: Correlated Random Effects
	Low appetite: component of the frailty index, coded 1 if the appetite has diminished.
	Models estimated on SHARE waves 1,2,5,6 on the unbalanced panel
	Statistical significance: ***: <1% ; **:<5% ; *<10%

  Table2displays the transition matrix in frailty states across waves. which has a twofold interpretation. First, it reflects persistence or statedependence in health care utilization4 and thus it can be expected that . Second, it captures all time-varying unobserved shocks that may simultaneously affect frailty and health care use, thus reducing the correlation between frailty and residual unobserved heterogeneity.

	associated coefficient,
	within sample variability.
	1.3.Dynamic correlated random effects (CRE) specification
	A generalization of the static model presented in Eq (1) to the dynamic case if provided
	below:
	Where	denote a vector of within-transformed indicators
	of Frieds' frailty score 3 ,	denote the full rank matrix of within-transformed
	time-varying control variables,	is the full rank matrix of time-invariant controls. Finally,
	is an autoregressive one-period lag of the dependent variable k and	denotes the

None of the state is absorbing (the non-diagonal elements are significantly different from 0).

For instance, among pre-frails individuals in wave t-1, respectively 34.8% have back transitions to robust and 11.9% become frail in wave t. These findings attest for sufficient

Note that we also tested the robustness of the LPM specification by (i) computing the proportion of predicted probabilities either less than zero or greater than one and (ii) comparing the estimated AMEs with those of a probit model. The proportions of out-of-range probabilities were low and the conclusions did not change using the non-linear specification (see robustness checks results in Appendix A).

Note that within-transformation of time-varying covariates is not mandatory in standard correlated random effects models. Within-transformation allows more easily interpreting the effects of these variables arising from within or between-individual heterogeneity.3

The SHARE data collection has been primarily funded by the European Commission through FP5 (QLK6-CT-2001-00360), FP6 (SHARE-I3: RII-CT-2006-062193, COMPARE: CIT5-CT-2005-028857, SHARELIFE: CIT4-CT-2006-028812) and FP7 (SHARE-PREP: N°211909, SHARE-LEAP: N°227822, SHARE M4: N°261982). Additional funding from the German Ministry of Education and Research, the Max Planck Society for the Advancement of Science, the U.S. National Institute on Aging is gratefully acknowledged (see www.share-project.org). We would like to thank Nicolas Sirven, Eric Delattre, Julien Bergeot, and all participants to the MODAPA seminar (PSE, April 2018) for useful comments on previous versions of the paper. We also thank Charlotte de Bruyn for administrative support. The research leading to these results has received support from the SPRINTT project of the Innovative Medicines Initiative Joint Undertaking under grant Agreement number 115,621, resources of which are composed of financial contribution from the European Union's Seventh Framework Program (FP7/2007-2013) and EFPIA companies' "in kind contribution".

Appendix A -Additional analyses

Content description: additional or robustness analyses for the paper HSR-18-0703 "Frailty transitions and healthcare use in Europe." As is by definition a binary variable, the model we estimate is a linear probability model (LPM). In practice, it is difficult to assess which of a linear or non-linear specification is best (as noted by Angrist and Pischke, 2009, logit and probit models also rest on restrictive and un-testable assumptions concerning the distribution of the error terms and in practice, this choice may depend on the data and study objectives. Three considerations led us to the choice of a LPM over a non-linear specification: (1) we were mainly interested in computing average marginal effects (AMEs), which is not possible in the logit specification and necessitate a posteriori approximations and additional parametric assumptions in the probit model, (2) we had a large sample size thus the assumption of asymptotic normality for the idiosyncratic errors was reasonable 1 and (3) all independent variables were categorical thus putting less at


Diane Leblond

Martin Amis and 'the nature of the offence': from expressions of outrage to the experience of scandal

To a reader of contemporary English literature looking for a definition for outrage, Martin Amis's Time's Arrow, which tells the story of a Nazi doctor's life in reverse, may appear as a good starting point. The subtitle of the novel programmatically presents it as a meditation on 'the nature of the offence'. A quote from Primo Levi's The Truce, the phrase directly refers us to the worst transgression in human history: the Shoah.1 Within the conceptual and referential framework associated with this event, the words outrage and offence work as synonyms in that they both imply an attempt on another's integrity, the transgression of a boundary, be it legal, moral or physical. They are associated in their seriousness: both touch on a breach of sanctity, or of what appears as most sacred in a non-religious, humanist context-human life and freedom. And finally, both serve to designate the response to such acts as go beyond the bounds of what is acceptable, as we take offence or express outrage.

While its title lets us hope for a definition of the offence, the novel relies on aesthetic and structural choices that offend our very sense of meaning as historically determined and informed subjects. The narrator whose voice and perceptions we depend on experiences time backwards. In addition to subverting the founding principle of physical existence and perverting the order of logic, this inversion makes for what may be the most outrageous depiction of genocide: in the eyes of the narrator, mass murder is envisaged as a life-giving process. The Nazis conjure up a human race, gathering ashes from the heavens and moulding them into human figures whom they eventually send on their way across Europe.

Time's Arrow can be described as an emblematic piece of British contemporary writing: since its publication criticism has often turned to it, showing its adaptability to evolving approaches. Earlier studies tackled its experimental treatment of narrative and shed light on its nature as postmodern fiction. Michel Morel made a close reading of its narrative and linguistic make-up. Dermot McCarthy and Richard Menke explored its metatextual comments on the interaction between history and fiction. The subversion of aesthetic and narrative traditions was at the heart of Jean-Michel Ganteau's article on the novel's approach to literary and biological filiation. Similarly its complex inscription within literary tradition at a specific moment in history informed Brian Finney's piece on the 'postmodern sublime'. Later studies have tended to go beyond the issue of postmodernism per se, to find further meaning in the novel's experimentation. James Diedrick's monograph presents Time's Arrow in a section entitled 'Apocalypse Now', and indeed Amis's exploration of mankind's tendency to self-destruction, as 1 In this paper I will use the term Shoah, rather than Holocaust. Both are imperfect in their equation of genocide with a form of divine punishment. In making this choice, however, I have in mind Giorgio Agamben's reminder that the word Holocaust was used ironically in anti-Semitic contexts from the Middle-Ages onwards (Agamben, 31).

evidenced in the Shoah and the threat of a nuclear holocaust, made for possible interpretations within the thriving fields of holocaust and trauma studies. Valentina Adami read the novel as 'trauma fiction'; Maria Martinez-Alfaro connected its evocation of trauma with a specific treatment of ethics, and Jakob Winnberg explored its consequences in terms of commitment. All three emphasised the reader's response and responsibility in reading the novel.

While these approaches touch on vision and visuality, pointing to irony as a pattern of 'double vision' (Menke,965) or elaborating on the compulsion of repetition as a need to reenvision traumatic events in human history (Martinez-Alfaro), they do not make it their central concern. I propose to show how the novel deals with vision, starting from this crucial point where visual representation is presented as the ultimate offence to the memory of the Shoah.

As a fictional attempt at defining the ultimate offence, and in its outrageous revision of genocide as a process of generation, Time's Arrow finds its place within an ongoing critical debate surrounding the Shoah and its representation. This controversy finds its origins in the outrage felt once the extent of the Nazis' crimes was revealed, and expressions of outrage are still part and parcel of it. Outlining its aesthetic, political and ethical implications will help us understand the ambitions underlying the writing of Time's Arrow.

Since the 1950s, critical indictments of artistic accounts of the Shoah have been grounded in the sense that fictional or aesthetic constructs have no claim on the offence in its essence. Fiction cannot grasp the absolute horror and downfall of civilisation embodied in genocide: the idea of artistic and narrative reconfiguration is not permissible with such a historical object. This critical position draws its substance from multiple reinterpretations of Theodor Adorno's famous statement in Prisms: 'To write poetry after Auschwitz is barbaric' (Adorno 18). In the context of an unprecedented moral and ethical crisis, when the values that once made the core of Western civilisation seem to have been voided of all meaning, artistic representation proves hopelessly inadequate, and must therefore withdraw altogether. Visual representation, in particular, is doubly offensive in the context of the Shoah, in that it suggests a fascination for images that disregards Jewish aniconism, and its rejection of idolatry. This may explain some of the strong reactions elicited by the 2001 Paris exhibition Mémoire des camps, an event dedicated to four photographs snatched by one of the Sonderkommandos at Auschwitz while the process of mass killing was still under way. At the time, Georges Didi-Huberman's contribution to the catalogue, an essay entitled 'Images in Spite of All', attracted highly critical responses. Gérard Wacjman, a psychoanalyst and University lecturer, stated that when it came to the Shoah there was no such thing as visual archives; that considering the photographs as relevant was nothing short of fascist. He contrasted what he felt was an obscene fascination with images with the choices made by Claude Lanzmann in his film Shoah, which dismissed archive footage, and used only contemporary images of former camp sites and interviews with survivors. What appeared then was the fear that a transgression of the ban on visual representation should try and reinstate the image to the detriment of verbal testimony. By commenting on the photographs, Didi-Huberman seemed to have implied that the witnesses' voices were not proof enough. In the eyes of his detractors, this equated to adopting the Nazis' viewpoint regarding material proof, and insulting the victims. Similar arguments have been made in the field of literary criticism. In 2010, charges of collusion with the perpetrator's ideology were levelled by Charlotte Lacoste in her book Séductions du bourreau, as she set out to expose novelists who, by adopting the point of view of barbaric narrators, played on spectacular aesthetics and contributed to the 'nazification' (Lacoste 224) of their reader. Lacoste argues that such authors distort Hannah Arendt's thesis on the banality of evil,2 encouraging us to think of mass murderers as nothing more than fellow human beings, in a sweeping ontological assessment of mankind that collapses all ethical, moral and political boundaries between perpetrator and victim.

In contrast to the promotion of an iconoclastic aesthetics, which denies the hermeneutic validity of the perpetrator's perspective and rejects the ethical notion of a common measure, some thinkers have foregrounded the powerful ambiguity at work in visual representation. In Images malgré tout, for instance, Georges Didi-Huberman insists that images, in their very imperfection and 'in spite of all', may say something of the experience of absolute crisis associated with the Shoah. This seems to be the case in Time's Arrow, where the loss of logic and meaning implied by the reversal of time is approached through the prism of a visual crisis, namely: the adoption of a viewpoint that is 'wrong in time'. The inversion of the arrow of time cannot be considered outside the context of the novel's visual aesthetics. Indeed, this main structural choice entirely depends on the narrator's powerless and essentially visual perception of a Nazi doctor's life, from death to birth. The 'I' who speaks to us does not exist as anything other than a gaze, an intensity of visual apprehension. This explicitly visual take on the Shoah does not, however, transgress the rule of testimonial precedence, any more than it professes a deeper confidence in images than in words.

The term outrage implies a clear understanding of the lines that should not be crossed. This demand for clarity seems to extend to the discourse of outrage: indeed, the account of a transgression, or the indignant response to an offence, aim at the highest expressive transparency. But in Time's Arrow, fiction attempts to approach the Shoah as subject through a challenging, troubled experience of vision. It situates itself poles apart from the supposedly transparent voice of testimony. In its opacity, the narrative elicits not outrage, but scandal: it erects a stumbling block,3 in the form of a potential loss of faith in liberal humanist values, in time, and in language itself. Through a disquieting experience of blurred and restless vision, the novel repeatedly confronts us with the scandalous possibility that all meaning might be lost. In doing so, it touches on the offence in its more metaphysical acceptation. Yet it never anaesthetises us or transfixes us; rather, it encourages us to find in the gaze a common ground that highlights rather than negates our political and ethical responsibility as historical beings.

Tripping the reader up: the visual aesthetics of scandal

The visual paradigm adopted in Time's Arrow does not primarily rely on the feelings of outrage elicited by the disclosure of the perpetrator's viewpoint. The French origins4 of the term outrage indicate a deliberate step taken beyond the pale of what's acceptable. In contrast to that, the narrative effectively works to trip us up in our visual apprehension of the Nazi doctor's life. Far from revelling in the transgression of visual boundaries or turning us into complacent voyeurs, it challenges our perception in ways that give us pause and make for a deeply unsettled experience of reading. The ethical and metaphysical crisis inherent in the evocation of the Shoah constitutes a threat to sensual experience.

In Time's Arrow, the narrative agency finds itself confined to the role of focaliser. His position as 'passenger, or parasite' (Amis 16) inside the protagonist's body is explicitly envisaged with reference to the visual paradigm of film. The first mention of cinema is indeed one of the initial keys offered by a plainly confused narrator to an even more confused reader. After a few very disconcerting pages describing the heart attack, resuscitation and demise of the character in reverse with no previous warning, we start gathering clues pointing to the inversion of time-such as the regressive sequence of dates on newspapers. But the explicit formulation of this formal constraint is made through the metaphorical identification of the narrator to a spectator. In answering his own question: 'How do you figure that?' with this tentative explanation, 'It just seems to me that the film is running backwards' (Amis 16), the narrator retroactively motivates the dead metaphor that links understanding and visualising through 'figuring'. In emulation of the narrator, if we are to make sense of the way the plot unfolds, we will need to figure out what is being told, to apprehend it visually, as we would a series of images whose sequence runs contrary to our expectations. This piece of advice to the reader recurs throughout the novel, as the cinematographic paradigm resurfaces. In describing his own posture within the protagonist's perceptive system, the narrative voice identifies with your typical cinema-goer or tv-spectator: 'I just settle back, with some apprehension, admittedly, and give witness to the late show screened by Tom's head' (Amis 54). In the context of a traumatic nightmare which adds to our suspicions as to the ultimate truth of Tod Friendly's secret, the equation of cinema-goer and 'witness' verges on the outrageous. Indeed, those who bore witness to the event at the heart of the narrative are radically dissociated from the familiar, relaxed posture of the film spectator 'settling back' in his or her seat; and designating traumatic reminders of extermination as images in a 'late show' is seriously offensive. The dangers of a complacent spectator's point of view transpire in the narrator's failure to acknowledge signs of the character's guilt.

But as we readers have already realised by the time the narrator characterises his own position within the protagonist's visual world, reading things backwards is far more demanding than watching a film. Things do not unfold as we sit back and wait for them to appear on a screen. As active reader-viewers, we take a detour via a medium that constantly reminds us of another direction in which time's arrow points: our experience of vision is conflicted and blurs our sense of time. This is emphasised by the narrative voice's fascination for the written word, and his insistence on the peculiar status it holds for him: while Tod starts at the bottom of a page to read his way upwards, the focaliser finds in texts indications of a strangely familiar sense of direction. The written medium heralds the return of a repressed form of sequentiality. The few moments of access to this alternative understanding of time are significantly associated with reminders of Tod's past, for example as he peruses Hippocrates' oath or notes that observant Jews read the way he would, turning the pages from right to left (Amis 51). Much later at Auschwitz, the narrative order begins to work against the grain of the temporal inversion. In the evocation of Selection and the murder of children, a particular use of temporal adverbs justifies the depiction of images in the order in which a historical account of facts would present them. In the following sentences, 'Even the most skeletal patients thrust their chests out for medical inspection . . . a scant fifteen minutes earlier they were flat on the floor of the Inhalationsraum' (Amis 142), 'a child clinging to me after I held her down for "Uncle Pepi" ' (Amis 144), the succession of visual impressions contradicts the words 'earlier' and 'later'. This makes for an experience of double, palindromic5 vision, in which we are reminded of the ghost-like or negative persistence, within the narrator's backwards account, of Tod's life as it was first experienced.

The feeling we experience in this moment of suspension between two incompatible readings is scandal: when the written word works as a stumbling block, when the collision of its two timelines leaves us floundering, helplessly looking for a firm anchorage in chronology, in language or in meaning itself.6

Challenges to perceiving and understanding: making sense, from grand narratives to dissensus

The scandal of double vision constitutes an attempt on language itself.7 In the collision of inscription, visual apprehension, and narration, all meanings are subverted, and we are waiting for things to make sense just as much as the narrator. But while the Shoah brings full satisfaction to the focaliser's thirst for meaning, it insults ours. The narrative does begin to make sense, but in a way that is too grim for us to be at peace with it. Inversion leads us to put all of the central concepts and values we normally rely on 'under erasure'.8 In that sense, scandal signals what Lyotard describes in La Condition postmoderne as 'the end of grand narratives', and paves the way towards 'dissensus' or, the vertiginous coexistence of heterogeneous, radically non-reconcilable lines of discourse.

The fifth chapter, entitled 'Here there is no why', begins with the protagonist's arrival at Auschwitz under his final name, Odilo Unverdorben. Dramatically opening with the sentence: 'The world is going to start to make sense… / Now' (Amis 124), it erases all of the narrator's ontological doubts, as he enthusiastically adheres to what he perceives as a preternatural process of creation. But the unacceptable nature of this resolution brings into question the very concepts which serve as its foundation, and which constitute the basis of a liberal humanist frame of mind: rationality and freedom.

The development of a consensual focus, indicated by the sole use of the first-person pronoun, is associated with what may appear as a tyranny of absolute rationality. This is suggested by the ambivalence of the chapter title, 'Here there is no why'. In Primo Levi's If This Is a Man, the quotation encapsulated a world where logic had been engulfed in the absolute arbitrariness of the camp. But in the context of the narrator's inverted account, the sentence signals the opposite of absurdity. Its immediate contact with the first sentence delineates a world where everything makes so much sense and is so clearly determined that the adverb why has become redundant. In celebration of the meaning he has found at last, the narrator's voice 5 The word 'palindrome' makes an appearance quite early in the novel (Amis 16). 6 Spatial inversion is easier to deal with: neurological experiments have shown that subjects will quickly compensate the effect of mirrors swapping top and bottom: after a moment of unease they can see things upright again. But the vertigo created by Time's Arrow's two contradicting chronologies cannot be neurologically compensated: again and again, we run the risk of falling. 7 In that respect, it reminds us of the Nazi Sprachregelung, which prescribed the use of euphemisms such as 'special treatment' for extermination and 'resettlement' for deportation (see Arendt 86). 8 I borrow this phrase from Jacques Derrida, who uses it extensively, for instance in the second chapter of De la grammatologie (1967), 'Linguistique et grammatologie'.

harks back to one of Levi's persecutors: his diametrical reversal of the process does not turn out to make the Shoah more acceptable; it presents us with the risk of totalitarian rationality. Such a risk is again suggested by the narrator's use of the word 'enlightenment', when he asserts: 'Enlightenment was urged on me the day I saw the old Jew float to the surface of the deep latrine, how he splashed and struggled into life' (Amis 132). The association between the unbearable account of a death/birth and the ideological principle of liberal humanist thought again reminds us of Lyotard's thesis on the end of grand narratives. The development of postmodern dissensus can be read as a counterpoint to the failure of modern civilisations, whose consensual faith in the enlightenment of mankind eventually led to barbarity.

The sentence 'Here there is no why' refers us back to a book the title of which brought this ontological issue into focus: a question without a question-mark, hoping for no clear answer, Primo Levi's words 'if this is a man' presented humanity as one of the notions the Shoah most put to the test. In Time's Arrow, the unhinging of time says something of the nature of the offence: it negates humanity in that it replaces absolute contingency with absolute determinism.9 In that sense, it robs man of the right to die, as the narrator points out when he stresses the impossibility of suicide: 'Suicide isn't an option. Not in this world' (Amis 33). This final negation of freedom constitutes the ultimate challenge to humanity in the terms of liberal humanism: it renders all notions of free will and responsibility null and void.

Yet this crisis comes at a point when the reader desperately needs to rely on the notions of human agency and responsibility, just as the international community did in the aftermath of World War Two, so that the perpetrators might be brought to justice.10 In that sense, the experience of scandal does not paralyse us, but urges us to preserve and revisit, in all their imperfection, those values and concepts that may help us apprehend life in its contingency. The presence of dissensus does not leave us helplessly staring into the void. Ultimately, it makes for a process of seeing that includes our dynamic response: it encourages reading as a form of active dissent whereby we refuse to simply see eye to eye with the focaliser.

The gaze as common measure?

In Remnants of Auschwitz, Giorgio Agamben explores the challenge which the Shoah posed to the very idea of humanity. His interest in what Primo Levi terms the 'grey zone', a zone in which Auschwitz created 'brotherhood in abjection' (Levi 1997, 216;Agamben 17), conjures up a metaphor which apparently confirms some of the doubts expressed in critiques of visual representation. One of the main reasons for such critical iconoclasm when it comes to the Shoah is the fear that images should suggest the visual as a possible common ground, a sign of similitude between human beings. And indeed, the 'grey zone' visually breaks down the clear boundaries of good and evil; as it questions what it is to be human, it allows us to think of a common ground between perpetrators and victims.11 It is as if images erased all sense of 9 As the narrator remarks: 'people are free, then, they are generally free, then, are they? Well they don't look free. Tipping, staggering, with croaked or choking voices, blundering backwards along lines seemingly already crossed, already mapped out.' (Amis 51). 10 In Eichmann in Jerusalem, Arendt evokes the legal argument that called for the creation of a court whose scope of action would transcend national laws: the mass murder by the German State of its own nationals could only be tackled by the humanity court. 11 'the only thing that interests him is what makes judgement impossible: the gray zone in which victims become executioners and executioners become victims' (Agamben 17).

difference, and erected an ontological category oblivious to historical, political and moral responsibility. Visual representation must be banned, in short, because it ultimately aims at sideration, or a form of visual fascination culminating in paralysis.12 In response to such an understanding of the powers and dangers of the visual, I would argue that despite the challenge it poses, the need to think of humanity as a common measure presents itself, after World War Two, as a political and moral imperative.13 What Time's Arrow as well as Agamben's reading of Primo Levi show us, furthermore, is that this can be done in visual terms, and need not lead to sideration.

Remnants of Auschwitz begins with the assertion that the Shoah, as it is narrated by Primo Levi, saw the emergence of a new ethical territory, inaugurated by the figure we see in his poem 'If This Is a Man': the Muselmann. A liminal entity, this non-human man presents us with the insufficiency of the limits in which former theories of ethics previously defined humanity. Most urgently, he reminds us of the fundamental lack at the heart of any testimony. Those who do testify are not, in Primo Levi's words, the actual witnesses: as he asserts in The Drowned and the Saved, they who have seen the Gorgon haven't come back, or haven't been able to tell.14 Dwelling on the paradoxical motif of Medusa's face, which cannot be seen but cannot be escaped,15 Agamben defines the oxymoronic status of testimony as an impossible necessity to see shared by the witness who never spoke and the survivor speaking for him. On the new territory of ethics, a sign of similitude seems to be found in a complex commonality of the gaze-the visual call of that which cannot be seen. Agamben's reflection does not end with the silence of those whose existence and death question the notion of humanity: he sees in this silence the necessity to redefine the bounds of a common ground. Because not doing it would imply leaving the witness in silent sideration before the Medusa, and granting the Shoah the status of a deity.16

In its fundamentally paradoxical nature, the survivor's discourse is not to be saved by aesthetics: as Agamben reminds us, 'it is testimony, if anything, that founds the possibility of the poem' (Agamben 36). This is definitely the case for Time's Arrow, which asserts its debt to Primo Levi's voice from subtitle to Afterword. And in a homage to Levi's attempts at producing the Gorgon for us, Amis's novel conjures up its own Medusa. Through the recurrent motif of star-gazing, Time's Arrow presents us with a visual experience that dismisses sideration and insists on the historical and political nature of the human gaze.

12 The visual implications of sideration are mostly present in the French acceptation of the term, though the English does find its roots in the Latin for 'planet-struck', in a world-view where the stars influence human destinies. 13 Arendt repeatedly points to the presupposition, by the legal order, of a common ground between the accused and the court sitting in judgement of him/her, at one point referring to 'perpetrators, that is to say, human beings' (Arendt 290). This argument is taken up within the field of ethics in Didi-Huberman's reminder: '[C]'est en tant que semblable qu'un être humain devient le bourreau d'un autre . . . . La relation du bourreau à la victime se fonde sur leur commune 'espèce humaine", et c'est bien là que gît le problème éthique de la haine raciale, de l'humiliation, de la cruauté en général et du totalitarisme nazi en particulier' . 14 See The Drowned and the Saved, 'we, the survivors, are not the true witnesses . . . [we] did not touch bottom. Those who did so, those who saw the Gorgon, have not returned to tell about it or have returned mute, but they are the Muslims, the submerged, the complete witnesses' (Levi 1989: 83, Agamben 33). 15 As Agamben reminds us, the Gorgon has no prosopon, no face, and yet on Greek urns she is always represented full front. In her paradoxical invisibility she is the ultimate visual object: an image. 16 'To say that Auschwitz is "unsayable" or "incomprehensible" is equivalent to euphemein, to adoring in silence, as one does a god. … We, however, "are not ashamed of staring into the unsayable"' .

At the beginning of the novel, the narrator's wish to uncover the truth of Tod's secret is contradicted by his visual aversion for the stars, and the secret they seem to hold: 'I cannot bear to see the stars; even though I know they're there all right, and I do see them, because Tod looks upwards at night, as everybody does, and coos and points. . . . The stars, to me, are like pins and needles, are like the routemap of a nightmare. Don't join the dots...' (Amis 23). Physically speaking, the stars embody light in its historicity: because we only see a differed image of what they are, they bear witness to our past and, in the inverted sequence of the narrative, constitute harbingers of destruction and trauma. As the remotivation of their metaphorical description as pins suggests, they pose a threat to the narrator's integrity as an eye, just as trauma does to Tod's. In the evocation of his nightmares, 'full of figures who scatter in the wind like leaves, full of souls who form constellations like the stars I hate to see' (Amis 37), the order implied by the word 'constellation' is met with the same reluctance to 'join the dots'. What the narrator fears in the stars is the map they set for what he immediately anticipated as 'a terrible journey, towards a terrible secret' (Amis 12). Directing our gaze towards the past, the stars tell the message of our moral and political responsibility towards those 'souls' which the dream, according to a principle of condensation, metaphorically identifies with them. Keeping in mind this constellation of souls, we obey an imperative to join the dots, to look for a meaning, however nightmarish.

At Auschwitz, the star-lit sky and the 'storm of human souls' (Amis 16) are brought together again in apparent negation of the narrator's worst fears. Indeed, his description of the attitude of prisoners at the camp constitutes an occasion to affirm a sense of harmony: 'There's a thing they do, with their heads. They bend their heads right back until their faces are entirely open to the sky… I was puzzled at first but now I know why they do it, why they stretch their throats like that. They are looking for the souls of their mothers and their fathers, their women and their children, gathering in the heavens-awaiting human form, and union . . . the sky above the Vistula is full of stars. I can see them now. They no longer hurt my eyes' (Amis 131). In their juxtaposition, however, the two pictures of the sky once again conjure up for the reader the metaphor of Tod's nightmare. While the narrator happily replaces this memory with the assurance of reconciliation, we are reminded of the political implications of the image: the journey has brought us back to a time when a Jewish soul was summed up in the emblem of a star. For us, far from confirming the hope of union, the stars work as symbols of the Jews' branding and persecution.

Later appearances of the stars in the novel persist in this reminder of our common history. In a later mention, the stars, compared once more with the souls of those they will come to designate, become, like history, a shard in our eye: 'On Krystallnacht . . . the fizzy shards swirled like stars or souls' (Amis 165). Finally the narrator, although systematically critical of what he terms the 'human talent for forgetting' (Amis 89), proves completely oblivious to the metaphorical association. A few pages later the stars appear one last time, during a camping trip near Oświȩcim. But what the narrator describes then as their 'uncrackable code' and the 'innocence' (Amis 169) of a virgin landscape can only be seen by us through the double prism of collective and personal memory, as the names Auschwitz and Birkenau refer us both to history at large and to our own reading of the novel. In our eyes no image can be innocent, pre-political: the politics of visuality define the common ground on which we play our role as readers.

Writing an outrageous novel about the Shoah would have implied sustaining a clear awareness of the rules being transgressed, and thus preserving to an extent our epistemological and ethical bearings. But Time's Arrow, in its opacity, aims at a more radical form of unsettlement. Instead of bringing us across a clearly visible line, the narrative erects its principle of inversion as a stumbling block, and repeatedly forces on us the experience of scandal or, the loss of all bearings. It creates a feeling of vertigo, as we are made to question the concepts that normally regulate our relation to experience, knowledge and ethics.

Yet this experience of scandal does not simply turn us into anaesthetised spectators. When it addresses the ontological quandary which the Shoah brought to the fore, it does not leave us in silent fascination for the inhuman within man, but visually reminds us of our responsibility as political and historical beings. In that sense it revisits a paradigmatic motif of Enlightenment ethics: in Time's Arrow, the 'starry skies' above the Kantian subject compound the 'moral law'17 within him or her with images of a shared human history.

In Eichmann in Jerusalem, Arendt reads Eichmann's trial as 'the lesson of the fearsome, word-and-thoughtdefying banality of evil'(Arendt 252).

3 The word Amis borrowed from Primo Levi bridges the gap between outrage and scandal: 'offence' comprehends the judicial implications of outrage, but it can also refer to a stumbling block, 'a cause for spiritual or moral stumbling, an occasion of unbelief, doubt' (OED, 'offence, offense, n.'

). 4 The term dates back to the Anglo-Norman utrage, in which the French root ultr-outre-identifies a movement 'beyond' (OED, 'outrage, n.').