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## Econometric model

The equation of interest (Eq.1) estimates the effect of informal care (IC) and formal care hours (FCH) on mental health (MH). is a set of characteristics of the dependent elderly and her family. We control for activity restrictions and functional limitations (number of moderate restrictions in ADLs, number of severe restrictions in ADLs; number of moderate restrictions in IADLs, number of severe restrictions in IADLs; and motor, sensory and cognitive limitations), for demographic variables (age and gender), socioeconomic variables (education level – no diploma, Certificate of Primary Education15, higher diploma –; monthly income; urban area) and family characteristics (living with a partner, having children, recent widowhood, seeing the family less than once a month). We also take into account if individuals answer the survey for themselves or if a third party helps them answer or responds for them (in other words, we control for proxy respondents). All variables are described in Table 2 below. (Eq.1).

We estimate this equation first treating formal and informal care as exogenous. We use a linear probability model for depression16 and a standard linear regression for the mental health score. However, this naïve model may be biased due to the potential endogeneity of care variables. First, health measurement errors may exist. Second, poor mental health may increase the probability of receiving formal or informal care and the intensity of the help (reverse causality). The empirical literature has mainly highlighted the positive effect of activity restrictions on the probability of receiving formal care (Bonsang, 2009), informal care (Fontaine et al., 2007; Haberkern and Szydlik, 2010) and on informal care hours (Golberstein et al., 2009). Furthermore, some chronic diseases (hypertension, diabetes, stroke, dementia, cancer) increase the probability and the intensity of informal care (Golberstein et al., 2009). Moreover, a poor or very poor self-assessed health increases the use of informal care (Bonsang, 2007) and the probability of formal care (Stabile et al., 2006). Finally, some research has highlighted “significant influences of emotional and mental disabilities […] on long-term care utilization” (Portrait et al., 2000). Third, there exist unobserved factors influencing the elderly’s mental health that are correlated with formal and informal care. For example, children’s health plays a role in the provision of informal care and may impact parents’ mental health. Similarly, family history of mental health problems may change a dependent elderly person’s attitude; it also may increase awareness amongst potential informal caregivers. Furthermore, the medicalization of the health of the elderly facilitates the diagnosis of depression and may increase informal care due to information or guilt put on family members by medical institutions (Weber, 2010).

In order to address this potential endogeneity, we estimate instrumental variables models using two-stage least squares17. We estimate two models – one with a binary dependent variable (depression) and one with a continuous dependent variable (the mental health score) – with two endogenous regressors – one binary (informal care) and one continuous (formal care hours). We choose to consider depression and informal care as continuous variables and to estimate linear probability instrumental variables models for several reasons. First, the command to estimate IV-Probit models in Stata (Ivprobit) is appropriate only for use with continuous endogenous regressors. Since informal care is a binary variable, IV-probit models for depression could not be estimated. In addition, IV linear models need weaker assumptions, allow avoiding problems of convergence and the literature acknowledges that the linear probability model gives good estimates of marginal effects, particularly for mean values of the covariates (Angrist, 2009, p. 107; Wooldridge, 2002, p. 465). Since linear probability models violate the assumption of homoscedasticity, robust standard errors are used18. It is important to note that the instrument for formal home care is measured at the departmental level (see Subsection 3.4.). However, this chapter does no correct for the presence of within-department correlation, which may result in biased standard errors. An Erratum to this chapter is available after Appendices A and B. It allows the errors within each department to be correlated and replicate the analysis to study to what extent it changes the results.

### Descriptive statistics

Table 2 below provides descriptive statistics. They cover both the total sample (4,067 observations), used for estimating depression, and the subsample of individuals (2,117) that have completed the paper questionnaire, used for the estimations of the MHI-5. As far as our variables of interest are concerned, around 8% of individuals had suffered from depression in the twelve months prior to the survey in both samples. The MHI-5 is characterized by an average of 49 (out of 100) and a standard deviation of 21. In the total sample, 68% of individuals receive informal care (as compared to 66% in the subsample) and the average number of formal care hours received per week is 6 (as compared to 5 in the subsample). The large standard deviation of formal care hours (between 12 and 14 hours) underlines the significant dispersion of formal care intensity in both samples. These samples have similar demographic and socioeconomic characteristics: the mean age of dependent elderly individuals is 79 years old; a large majority are women (around 70%); three quarters of individuals have no diploma or a Certificate of Primary Education; most individuals (76%) live in an urban area; and the mean proportion of individuals aged 75 and older receiving the Personal Autonomy Allowance at the departmental level is around 15%. They are also comparable in terms of family characteristics: 45% of surveyed individuals live with a partner; 4-5% of elderly are recently widowed; 87% have at least one child; and 13% see their family less than once a month. The majority of individuals (66%) have at least one child who lives nearby; around 40% have one child who has no partner; and 30% have one child who has no child.

By contrast, the two samples are characterized by different levels of dependence. Indeed, in the subsample, the average number of severe restrictions in ADLs is 0.49 and the average number of severe restrictions in IADLs is 2.78, as compared to 0.68 and 3.36, respectively, for the total sample. They are also less frequently limited: 32% report sensory limitations and 31% report cognitive limitations, versus 37% and 38%, respectively, for the total sample. This better health status of individuals in the subsample probably explains why they receive less care and why proxy respondents are less present.

#### Replication of the subsample analysis with departmental clusters

When the sample is restricted to dependent elderly who receive formal support (Table 17), the *F*-statistics associated with formal care are higher than in the total sample (*F*=8.34 in the depression model and *F*=11.54 in the MHI-5 model). In addition, the exogeneity tests highlight that formal and informal care are endogenous in the MHI-5 model (*p*=0.069). The IV model for the MHI-5 shows that a one-unit increase in formal care hours significantly improves the mental health score by 1 point (or 0.05 standard deviations). On the other hand, informal care has no longer effect; it seems to be ineffective in reducing the risk of depression among highly dependent individuals. These results are in line with those obtained without clustering the errors. As in the Chapter 1, when we restrict the analysis of depression to the same subsample than for the MHI-5 (Table 18), the exogeneity of care variables cannot be rejected, indicating that OLS are preferred to instrumental variables. OLS results confirm that informal care significantly limits the risk of depression, though the magnitude of the effect is lower than for the total sample (-3.4%).

.Finally, when we focus on dependent elderly that did not use a proxy respondent (Table 19), the effects are similar to those of the main analysis. Indeed, informal care decreases the risk of depression by 64%, while formal care hours have no effect.

**Focus on children who provide care to a parent who has no spouse**

When the analysis is restricted to children providing care to a single parent (tables 27 and 28), the effect of formal care on health becomes insignificant. The number of informal caregivers decreases the probability of moral fatigue (-12.8% as compared to -8.2% in the main analysis) and palpitations (-6.8% vs. -5.8% in the main analysis). However, the exogeneity of informal support could not be rejected in the model for palpitations and tachycardia (p=0.146). Similarly, informal support limits the risk of sleep disorders and anxiety in IV models, but the exogeneity test cannot reject the hypothesis of exogeneity (p=0.112 for sleep disorders and p=0.124 for anxiety). These results may be explained by a lack of statistical power due to the smaller number of observations. Alternatively, it is possible that social support alone is not effective in protecting the health of children, who are probably more involved in caregiving than other non-coresiding caregivers.

**Table of contents :**

**GENERAL INTRODUCTION **

1. Demographic and epidemiological issues

1.1. Population aging

1.2. Old-age dependency is hard to define

1.3. …and hard to predict

2. The support for dependent elderly people in Europe

3. Research questions

4. Research outline / summary

**CHAPTER 1 – DOES HOME CARE FOR DEPENDENT ELDERLY PEOPLE IMPROVE THEIR MENTAL HEALTH? **

1. Introduction

2. Background

3. Method

3.1. Data

3.2. Variables of interest

3.3. Econometric model

3.4. Instruments

4. Results

4.1. Descriptive statistics

4.2. Estimation results

4.3. Additional tests

5. Discussion

Appendix A. Additional information on IV and OLS models.

Appendix B. Simultaneous equations models.

ERRATUM to Chapter 1. Clustering at the departmental level.

**CHAPTER 2 – FORMAL HOME CARE, INFORMAL SUPPORT AND CAREGIVER HEALTH: SHOULD OTHER PEOPLE CARE? **

1. Introduction

2. Background

3. Method

3.1. Data

3.2. Variables of interest

3.3. Econometric model

3.4. Instruments

4. Results

4.1. Descriptive statistics

4.2. Estimation results

4.3. Additional tests

5. Discussion

Appendix C. Description of the sample selection.

Appendix D. Effect of formal support on caregivers’ health.

Appendix E. Effects of control variables.

**CHAPTER 3 – FINANCING LONG-TERM CARE THROUGH HOUSING IN EUROPE **

1. Introduction

2. Aging and housing

2.1. Downsizing

2.2. Home reversions

2.3. Reverse mortgages

2.4. Housing and LTC financing

3. Data

3.1. Disability status

3.2. Income and assets

4. Methodology

4.1. Transition model

4.2. Microsimulation

4.3. LTC cost

4.4. Simulation of reverse mortgages

4.5. Ability to pay for LTC needs

5. Results

5.1. Long-term care risk

5.2. Ability to pay for LTC

5.3. Sensitivity tests

5.4. Reverse mortgage on a fraction of the home

5.5. The role of informal care and public LTC coverage

6. Discussion

6.1. Summary of the results

6.3. Limitations of this study

Appendix F. Additional details on the methodology.

Appendix G. LTC risk and duration in the literature.

Appendix H. Characteristics of dependent individuals who have no partner.

Appendix I. LTC duration that dependent individuals are able to finance at the country level.

Appendix J. Ability to pay for long-term care needs by income quintile.

Appendix K. The role of public LTC coverage

GENERAL CONCLUSION

**REFERENCES**