Andrew E Clark
email: andrew.clark@ens.fr

Conchita D'

Ambrosio Anthony Lepinteur

Conchita D'ambrosio
email: conchita.dambrosio@uni.lu

Anthony Lepinteur
email: anthony.lepinteur@uni.lu

Marriage as Insurance: Job Protection and Job Insecurity in France

Keywords: Marriage, Insurance, Employment Protection, Perceived Job Marriage, Insurance, Employment Protection, Perceived Job Security, Differencein-Differences. JEL Classification Codes: I38, J13, J18

Job insecurity is one type of risk that workers face on the labour market. As with any risk, individuals can choose to insure against it. We consider marriage as potential insurance against labour-market risk. The 1999 rise in the French Delalande layoff tax for older workers produced an exogenous rise in job insecurity for younger workers. A difference-in-differences estimation in panel data reveals that this greater job insecurity for the under-50s led to a significant rise in their probability of marriage, and especially with partners who had greater job security, consistent with marriage providing insurance on the labour market.

Introduction

Why do people get married? [START_REF] Weiss | The formation and dissolution of families. Why marry? Who marries whom? And what happens upon divorce[END_REF] suggests that marriage is associated with a number of benefits. The first reflects the benefits of specialisation between spouses [START_REF] Becker | A theory of marriage: Part I[END_REF][START_REF] Becker | Altruism in the family and selfishness in the market place[END_REF]. Second, in a context of imperfect credit markets, marriage may also relax credit constraints via implicit credit arrangements within households [START_REF] Borenstein | How to carve a medical degree: human capital assets in divorce settlements[END_REF] and enhance investment (for example, one partner may work while the other is in education investing in their human capital). Collective and non-rival goods are also jointly produced and consumed within partnerships, with common examples being children or housework [START_REF] Chiappori | Collective labor supply and welfare[END_REF][START_REF] Van Klaveren | A public good version of the collective household model: An empirical approach with an application to British household data[END_REF]. [START_REF] Stevenson | Marriage and divorce: Changes and their driving forces[END_REF], in their empirical review of changing trends in marriage and divorce in the US, highlight the roles of pre-marital cohabitation (which has risen), specialisation in marriage (now argued to be less important), the tax implications of partnership, birth control, changes in relative wages, Divorce Laws, and the marriage "matching function" (via education, the workplace and the internet).

The benefit from marriage that we will address here, which appears in both [START_REF] Weiss | The formation and dissolution of families. Why marry? Who marries whom? And what happens upon divorce[END_REF] and [START_REF] Stevenson | Marriage and divorce: Changes and their driving forces[END_REF], is that of risk-sharing. As noted by [START_REF] Hess | Marriage and consumption insurance: What's love got to do with it?[END_REF] and [START_REF] Shore | For better, for worse: Intrahousehold risk-sharing over the business cycle[END_REF], partnerships provide insurance by allowing couples to diversify risk, if the exogenous income shocks that the two partners receive are not perfectly (positively) correlated. Couples can in addition adjust their relative labour supply to reduce the impact of shocks.

A number of contributions have provided indirect evidence consistent with marriage providing insurance. In [START_REF] Rosenzweig | Consumption smoothing, migration, and marriage: Evidence from rural India[END_REF], arranged marriages between families from different villages in South India significantly reduce the variability in food consumption.

Farm households with greater income risks are more likely to engage in arranged marriages at longer distances. In US data, Halla and Scharler (2011) find that the influence of idiosyncratic output-growth shocks on consumption is smaller in States where the percentage of married is higher. [START_REF] Bertocchi | Marriage and other risky assets: A portfolio approach[END_REF] consider household investment decisions, and conclude from their analysis of 14 years of Italian SHIW data that the married invest more in risky assets (as marriage is considered to be a safe asset). [START_REF] Anderson | Missing unmarried women[END_REF] show that marriage protects against the risk of death, especially for women.

With respect to the labour market, there is a considerable literature on marriage and the business cycle. [START_REF] Schaller | For richer, if not for poorer? Marriage and divorce over the business cycle[END_REF] analyses 32 years of US State-level panel data: marriage is shown to be pro-cyclical, with unemployment being associated with less marriage. Lichter et al. (2006) appeal to individual-level NLSY-79 data, and conclude that the probability of transition from cohabitation to marriage rises with partner's education and the partner working; it is lower for the unemployed. Early labour-market experiences also seem to matter. Ekert-Jaffé and[START_REF] Ekert-Jaffé | Unemployment, marriage, and cohabitation in France[END_REF]2002) and [START_REF] Landaud | From employment to engagement? Stable jobs, temporary jobs, and cohabiting relationships[END_REF] analyse different French datasets to show that early-career unemployment and temporary jobs reduce the probability of forming a couple; De La [START_REF] De La Rica | Career planning in Spain: Do fixed-term contracts delay marriage and parenthood?[END_REF] come to similar conclusions using Spanish data. One interpretation is that unemployment provides a negative signal about the potential partner's unobserved characteristics.

Some work has explicitly looked not at events that have already taken place, but rather future risk on the labour market. Schneider et al. (2018) discuss the role of economic resources in marriage, which they extend to include wealth and expected future earnings. [START_REF] Schneider | Marrying ain't hard when you got a union card? Labor union membership and first marriage[END_REF] continue in the same line, and find that union membership (as an indicator of economic security) is a predictor of marriage in NLSY-79 data. [START_REF] Xie | Economic potential and entry into marriage and cohabitation[END_REF] are also individual-level and forward-looking, and calculate five different measures of current and future "earnings potential": they show that all five are positively correlated with the transition from cohabitation to marriage using US Census and cohort data.

We here also consider labour-market risk, but here with respect to job loss. The role of forward-looking job insecurity in partnership has already been mentioned: Schneider et al. (2018) explicitly cite job security as a component of future earnings, but note that it is difficult to pin down exogenous changes in resources, and in particular that job security is not observed in their PSID data. However, we are not aware of any work that has been able to appeal to exogenous variation in job insecurity at the individual level in this context. We here propose a difference-in-differences analysis from a quasi-natural experiment to establish a causal effect of individual job insecurity on the probability of marriage. As opposed to past individual unemployment or current macroeconomic shocks, we are able to identify a plausible exogenous change in job insecurity: our analysis sample consists of workers, some of whom became more at risk than others of future job loss, following a French labour-market reform.

As in [START_REF] Clark | A natural experiment on job insecurity and fertility in France[END_REF]), we use 1994[START_REF] Clark | What really matters in a job? Hedonic measurement using quit data[END_REF] French data from the European Household Community Panel (ECHP) to show that the 1999 rise in the French Delalande tax on layoffs of those aged 50+ increased job insecurity for the under-50s in large firms (as compared to the under-50s in small firms, where the Delalande tax did not change in 1999).

We are interested in how individuals react to this exogenous greater risk. [START_REF] Clark | A natural experiment on job insecurity and fertility in France[END_REF] suggest that one reaction is to reduce risk exposure, via lower fertility; we instead here ask whether individuals will take out more insurance against risk, via their marital status. 1We conclude that greater job insecurity amongst French workers increased women's probability of marriage by four percentage points; there is no effect for men. This is consistent with evidence on gender differences in preferences [START_REF] Croson | Gender differences in preferences[END_REF]: women are generally less willing to take risks in the context of lotteries [START_REF] Hartog | Linking measured risk aversion to individual characteristics[END_REF][START_REF] Holt | Risk aversion and incentive effects[END_REF][START_REF] Fehr-Duda | Gender, financial risk, and probability weights[END_REF] and portfolio selection [START_REF] Sunden | Gender differences in the allocation of assets in retirement savings plans[END_REF][START_REF] Finucane | The affect heuristic in judgments of risks and benefits[END_REF][START_REF] Charness | Strong evidence for gender differences in risk taking[END_REF] and as such may react more to the threat of future job loss than do men.

We check that our estimates are robust to a number of potential confounding factors, such as European macroeconomic trends and the French 35-hour workweek that was announced in 1998 and introduced in 2000; they are also qualitatively similar using a number of different estimation methods. While we do identify a reform effect on marriage, there is no change in the probability of entering a partnership in general, or indeed of leaving one: the greater probability of marriage for women then mostly reflects a shift into marriage from pre-reform cohabitation. The effect of job insecurity on women's marriage probability is the same by age, education and wage, but larger for women who were already mothers before the reform. Last, as predicted by risk-sharing, the probability of marriage only rises when the partner is employed and did not experience greater job insecurity due to the layoff-tax rise.

The remainder of the paper is organised as follows. Section 2 describes the institutional background and the identification strategy for our analysis of individual-level insecurity, and Section 3 the ECHP data and the estimation sample. The main results then appear in Section 4, and the robustness checks and heterogeneity analyses in Section 5. Section 6 discusses the importance of partner characteristics in the light of risk-sharing theory. Last, Section 7 concludes.

Institutional Background and Identification

The Delalande tax was introduced into French Law in 1987 to tackle the rise in layoffs among older workers. Despite a number of changes over time, the experience-rating principle of the tax remained unchanged: firms laying off workers of over a certain age have to pay the Delalande tax to the government. This tax, which was also meant to help balance the unemployment-insurance system, is proportional to the laid-off worker's gross wage and is applied to private-sector workers with permanent contracts. From its introduction in 1987 up to 1992, this tax was three months of gross wages for all workers aged 55 and over who were laid off. Major changes to this tax were then introduced in July 1992, January 1993 and January 1999; in particular, starting in 1992 the layoff tax applied to all workers aged 50 or above. The Delalande tax was finally abolished in 2008.

Table 1 shows how the Delalande tax changed over time as a function of the age of the laid-off worker and firm size. From 1993 to December 1998, the tax was a function of worker age only, and independent of firm size. The tax then rose in January 1999, but only for firms with 50 or more employees.

As predicted by the theoretical model in [START_REF] Behaghel | La protection de l'emploi des travailleurs âgés en France : une évaluation ex ante de la contribution Delalande[END_REF], a higher Delalande tax reduces the separation rate of those workers covered by the reform (those aged 50 or more) but increases the separation rate of the younger workers (aged under 50) in the same firms. Using the same ECHP data as we do here, [START_REF] Georgieff | Partial employment protection and perceived job security: evidence from France[END_REF] empirically confirm this prediction: the higher Delalande tax had perverse effects on younger workers in larger French firms by increasing both their perceived job insecurity and their actual risk of layoff.

We here wish to assess the causal effect of this exogenous change in job security from the tax reform on the probability of marriage of younger workers. We do so by exploiting the firmsize discontinuity and the resulting rise in job insecurity for younger workers in larger firms.

The reform then provides a natural quasi-experimental design for a difference-in-differences (D-i-D) estimation, in which younger workers in large private firms are the treatment group and younger workers in smaller private firms the control group.

The 1999 reform to the Delalande tax was announced by the French government one year beforehand (in early 1998), and the reintroduction of the firm-size discontinuity was also public knowledge by the end of 1998 (the ECHP interviews took place in November and December of each year). As such, employers may have been able to strategically adjust their labour demand before the change in the Law. [START_REF] Georgieff | Partial employment protection and perceived job security: evidence from France[END_REF] find evidence of such anticipation effects, as employers in (to-be) treated firms laid off relatively more workers just after the announcement of the reform but prior to its implementation. Higher layoffs are found for both those aged over 50 and younger workers, so that the tax rise brought about some restructuring in larger firms. Given this anticipation, job insecurity for the under-50s in large firms may well have started to rise before the reform's official implementation. We take this possibility into account by estimating the following D-i-D equation, including both a post-1999 treatment effect and a 1998 announcement effect of the reform:

𝑌 𝑖𝑡 = 𝛼 1 𝑇𝑟𝑒𝑎𝑡 𝑖𝑡 + 𝛼 2 𝑇𝑟𝑒𝑎𝑡 𝑖𝑡 * 𝜆 1998 + 𝛼 3 𝑇𝑟𝑒𝑎𝑡 𝑖𝑡 * 𝑃𝑜𝑠𝑡1998 𝑡 + 𝛼 4 𝑋 𝑖𝑡 + 𝜇 𝑖 + 𝜆 𝑡 + ε 𝑖𝑡 . (1)
This equation is estimated only for workers under the age of 50. Here 𝑌 𝑖𝑡 first represents the perceived job security of worker i in year t and then a dummy for worker i being married in year t. 2 The variable Treatit is the treatment dummy, and is one for younger workers in large private firms (50+ employees) and zero for younger workers in smaller private firms. The variable 𝑃𝑜𝑠𝑡1998 𝑡 is a dummy for observations after January 1999 (the implementation date of the higher Delalande tax), λt are year fixed effects (so that λ1998 refers to the policyannouncement year of 1998) and Xit is a vector of standard individual socio-demographic controls. This includes age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. This equation also controls for individual fixed effects µi. The year dummies in equation (1) entirely subsume the main effects of λ1998 and 𝑃𝑜𝑠𝑡1998 𝑡 . The coefficients of interest in the above equation are α2 and α3, which respectively capture the effects of the reform's announcement in 1998 and its implementation starting in 1999 on first job security and then marital status.

The risk-sharing hypothesis predicts positive and significant α2 and α3 coefficients for workers in the marriage-probability regression, reflecting their rise in risk from job insecurity and the subsequent greater demand for insurance. However, it is also possible that the treatment reduce the probability of marriage, as workers who have become more at risk of layoff are now seen to be "riskier" partners.

We expect the effect of the reform's announcement and implementation to be of the same sign, so that we can also estimate the following D-i-D regression:

𝑌 𝑖𝑡 = 𝛽 1 𝑇𝑟𝑒𝑎𝑡 𝑖𝑡 + 𝛽 2 𝑇𝑟𝑒𝑎𝑡 𝑖𝑡 * 𝑃𝑜𝑠𝑡1997 𝑡 + 𝛽 3 𝑋 𝑖𝑡 + 𝜇 𝑖 + 𝜆 𝑡 + ε 𝑖𝑡 , (2)
where 𝑃𝑜𝑠𝑡1997 𝑡 is a dummy for observations after 1998 (the announcement year of the higher Delalande tax). The coefficient β2 in equation ( 2) now captures what we call the total effect of the reform, starting from its announcement (β2 thus corresponds to equation (1) when α2 = α3). Both Equations ( 1) and (2) will be estimated using linear techniques (although we will also estimate non-linear regressions in the robustness checks).

Data and Estimation Sample

The data we use here come from the European Community Household Panel (ECHP), a nationally-representative longitudinal survey of households that covered 15 European countries (including France) between 1994 and 2001. The sample size in France was on average 12,000 adults per wave. The interviews mainly took place between November and December of each year. The ECHP contains detailed information on respondents' socio-economic characteristics, income, employment conditions, social relations and so on. 3 Respondents report their marital status at each ECHP wave.

The 1999 rise in the Delalande tax only applied to firms with 50 or more employees. The ECHP records the number of employees in the firm in which the respondent works using the following categories: "None", "1 to 4", "5 to 19", "20 to 49", "50 to 99", "100 to 499" and "500 or more". This is the variable that we will use to assign younger workers to the treatment or control group.

In the first part of our analysis, we show that the higher layoff tax for those aged 50 or over in larger firms increased job insecurity for younger (aged under 50) workers in these same firms; the main analysis will address the question of whether this same tax rise affected marriage.

Regarding job insecurity, we consider the following ECHP question on perceived job security:

"How satisfied are you with your present job in terms of job security?"

The answers to this satisfaction question were given on a 6-point scale, with 1 referring to "Not Satisfied" and 6 "Fully Satisfied". 4 This measure of perceived job security is a strong predictor of individual choices such as future job quits [START_REF] Clark | What really matters in a job? Hedonic measurement using quit data[END_REF], and reflects objective changes in layoff and hiring rates [START_REF] Böckerman | Job security and employee wellbeing: Evidence from matched survey and register data[END_REF]. It has also been shown to be related to permanent contracts, unemployment-insurance benefits and employment protection legislation [START_REF] Clark | Job security and job protection[END_REF].

We consider respondents between the ages of 20 and 49 working in the private sector with permanent contracts, and with valid information on the sociodemographic variables, job characteristics and perceived job security. As the reform was announced many months before its implementation, we last may suspect that firms strategically adjusted their workforce. To rule out concerns regarding self-selection into the treatment, we will analyse only workers who reported no change in their firm's size from 1997 onwards. This ends up dropping only around six per cent of the baseline sample (the resulting estimated coefficients for the effect of job insecurity on the probability of being married are actually not materially affected by this restriction). Note that we do not consider here the workers who were protected by the reform, i.e. workers aged 50+. Almost 80% of respondents in this group were already married, and there was little subsequent movement out of marriage (97.5% of those aged 50+ reported the same marital status before and after the reform). This limited within-variation considerably attenuates the statistical power for this older group.

Our analysis sample consists of 10,371 observations on 2,797 different individuals from 1995 to 2001 (we cannot use the first 1994 wave of ECHP here, as the information on whether the firm is public or private is missing) between the ages 20 and 49. Figure A1 in the Appendix shows the number of observations at each stage of our sample selection. 5 The descriptive statistics for this analysis sample appear in Table 2; 47% of the sample are in the treated group.

With respect to our two dependent variables, 57% of our observations come from individuals who report being married, and average job security on the one-to-six scale is a little over four.

Although we here focus on a specific part of the French population, i.e. young privatesector workers with a permanent contract, the share of married workers in our estimation sample is similar to the national value (see Figure 1). The share of unmarried partnered workers in our sample is slightly higher than the national figure, but this is very likely because we exclude individuals above age 49. The marriage share in the French adult population has steadily decreased from 1990 to 2009 in Figure 1, falling from 56% to 52%. Over the same period, the share of unmarried partnered individuals rose markedly by 9.5 percentage points (from 6.7% to 16.2%).

Main Results

Table 3 first shows how reported job security for younger workers changes with the employment protection of older workers in the French sample of ECHP panel data. We here use the analysis sample described in Table 2. Columns (1), ( 3) and ( 5) of Table 3 refer to the D-i-D estimates of Equation ( 1), where we allow for a post-1999 treatment effect as well as an announcement effect of the reform in 1998; the results in columns ( 2), ( 4) and ( 6) come from the estimation of Equation ( 2), where the announcement and implementation dummies are combined into one "total" effect. Columns ( 1) and ( 2) of Table 3 show the results for the whole sample, while columns (3) -( 4) and ( 5) -( 6) respectively refer to those for women and men.

As can be seen in column (1), the 1999 rise in the layoff tax for older workers in larger firms significantly reduced the perceived job security of younger workers in these larger firms (as compared to younger workers in smaller firms, where there was no change in the layoff tax). Job security fell significantly after both the announcement and the implementation of the rise in the Delalande tax. The magnitude of the estimates is in line with the findings in Georgieff and [START_REF] Georgieff | Partial employment protection and perceived job security: evidence from France[END_REF] and [START_REF] Clark | A natural experiment on job insecurity and fertility in France[END_REF]. 6 Pairwise Wald-tests confirm that the estimated announcement and implementation effects of the reform in rows 1 and 2 are not statistically different from each other. Column (2) then combines these into the total effect of the reform, which is naturally negative and significant and of a similar size to the figures in column (1). We estimate that the higher Delalande tax reduced the perceived job security of younger workers in treated firms by 0.2 points, which from Table 2 is around one-sixth of a standard deviation. We find similar estimates for women and men in the remaining columns of Panel A. Although the reform effects look larger for men, given the associated standard errors these gender differences are not significant. 7 We can replicate these results using a simple binary variable for job security (comparing values 1-4 against 5-6): all of the treatment estimates continue to be significant, with an effect that is larger, but not significantly so, for men.

Panel B of Table 3 then estimates the relationship between job insecurity and the probability of being married in the same analysis sample. 8 The estimated coefficients for the whole sample in columns ( 1) and ( 2) are positive but not significant at conventional levels. As it has been suggested that women are on average more risk averse than men [START_REF] Sunden | Gender differences in the allocation of assets in retirement savings plans[END_REF][START_REF] Finucane | The affect heuristic in judgments of risks and benefits[END_REF][START_REF] Hartog | Linking measured risk aversion to individual characteristics[END_REF][START_REF] Holt | Risk aversion and incentive effects[END_REF][START_REF] Fehr-Duda | Gender, financial risk, and probability weights[END_REF][START_REF] Croson | Gender differences in preferences[END_REF][START_REF] Charness | Strong evidence for gender differences in risk taking[END_REF], we might expect these estimates to differ by gender. The results in columns (3) and ( 4) show that women are significantly more likely to be married following the implementation of the reform. The pairwise Wald-tests again reveal that the anticipation and implementation effects of the reform are statistically identical. The results combining these two effects in column (4) reveal that the higher Delalande tax increased the probability of being married for women by just over four percentage points. 9 This corresponds to 7.5% of the pre-reform share of married women in the treated group (57%). It is half of the observed difference in female marriage rates between the early and late 20's (see Table A1).

There is no significant marriage effect for the corresponding sample of men in columns ( 5) and ( 6). A first possibility is that prime-age women who worked in permanent privatesector jobs in the 1990s in France were more selected than their male counterparts. The comparison of the pre-reform characteristics of men and women who do and do not appear in our estimation sample actually reveals only small differences: there is more positive selection of women into the estimation sample by education than there is for men, and less selection by hours of work. However, we control for both of these variables in our estimations (and will, in addition, show below that there is no differential effect of the reform treatment on marriage by either education or hours of work).

Second, this may reflect that men are on average less risk-averse: the rise in job insecurity from the 1999 rise in the Delalande tax may not have had much effect on their demand for insurance. Last, men who looked for insurance through marriage may not have been able to find it: their greater job insecurity may make them less attractive. This is consistent with Ekert-Jaffé and Solaz (2001 and 2002) and [START_REF] Landaud | From employment to engagement? Stable jobs, temporary jobs, and cohabiting relationships[END_REF], where men without a job or in temporary employment were less likely to be partnered.

One of the requirements for D-i-D estimation to produce causal effects is that there would have been a common trend in the dependent variable (here perceived job security and the probability of being married) in the control and treatment groups in the absence of the policy reform. We also need to make sure our reform effect is not influenced by changes in other individual characteristics. We do not find significant changes between the treatment groups before and after the reform's announcement for most of the observable characteristics, as

shown in Tables A2 andA3. However, we do see that the working time of the treated groups dropped significantly more (in the whole and female sample only). This is not surprising: in 2000, the standard weekly hours in France dropped from 39 to 35 for workers in firms with 20 employees and more. While we do not worry about the whole sample (because we do not find a significant effect of the 1999 rise of the Delalande tax on the probability to be married for the whole sample), our treatment estimates for the sample of women might capture the influence of the mandatory 2000 working-time reduction. We will rule out this possibility in our robustness section by excluding workers from companies with fewer than 20 employees from our estimation sample.

Last, we ask in Table A4 whether the total effect of the rise in the Delalande Tax led to other changes in terms of marital status and couple formation. The first column of this table reproduces the estimated marriage coefficients from columns (4) and ( 6) of Table 3 for comparison purposes. We then look in column (2) at the probability of being in a partnership, irrespective of legal marital status: the estimates show that the greater job insecurity from the reform had no effect on being in a couple in general. Combined with the results for marriage, we thus expect (for women) a negative reform effect on cohabitation. This is indeed what we find in column (3) of Panel B: women whose job insecurity rose following the change in the Delalande tax are less likely to be in a non-married relationship. As the ECHP is a household panel, where all adults are interviewed, and as we here focus on the transition from cohabitation to marriage, we might expect the estimation results here for men and women to be identical (as we are looking at either side of a couple). This turns out not to be the case in Table A4. The explanation is that the men and women in this table do not come from the same sample of cohabitees: fully one half of treated women who we observe to switch from cohabitation to marriage marry men who are not in the sample in Panel C (as their jobs are temporary or in the public sector, they are not active in the labour force, or are aged 50 or over).

Last, Columns (4) and ( 5) of Table A4 look in turn at being divorced/separated or never having been in a relationship, finding no significant effect for men or women, or for the whole sample.12

Robustness Checks and Heterogeneity

The results in Table 3 refer to the effect of the reform on first job security and then marital status for the whole analysis sample. We now turn to a number of robustness tests, and then ask whether the effects of job insecurity on the probability of being married are larger for certain types of workers. The analyses that we will carry out here refer to the total effect of the reform, as in Equation (2). 13 We have also estimated the analogous effect of all of our robustness and heterogeneity tests for the estimated effect of the reform on perceived job security; these results appear in Appendix Table A5 2), ( 4) and ( 6) of Panel B in Table 3). Note that when we exclude workers in firms with under 20 employees from our estimation sample, the differences in working time observed in Tables A2 andA3 are no longer statistically different from zero.

As part of our identification relies on changes over time, we would like to be sure that these changes reflect the evolution in the French layoff tax, rather than some broader macroeconomic developments. One way of testing for the latter is to re-estimate our baseline regressions on similar samples of workers in arguably similar countries (where of course the French layoff tax did not apply), as the ECHP is harmonised across European countries. Data limitations restrict this comparison to Spain, Italy and Denmark. 14 We present the resulting Di-D estimates for these three countries in columns (2), ( 3) and (4) of Table 4, none of which is significantly different from zero. Macroeconomic trends do not then seem to lie behind our main result of greater job insecurity increasing the share of married women.

ii.

The estimation method

Our main results above come from fixed-effect analyses, comparing the same individual before and after the labour-market reform. We expect fixed-effects and OLS analyses to produce different estimates as the former introduce attenuation bias when there is measurement error (with the resulting OLS estimates being larger than their FE counterparts in absolute terms) and for omitted-variable reasons, where the OLS estimates will be biased if the treatment is correlated with unobserved individual time-invariant characteristics. The baseline results without fixed effects in column (5) of Table 4 are slightly larger than the baseline fixed-effect estimates, but not significantly so.

We also ask whether these results are affected by the way in which we define the dependent variable. Our baseline regressions treat the probability of being married as a cardinal variable (and are thus fixed-effect linear-probability models). However, it can be argued that non-linear estimation is more suitable for this dummy dependent variable. Column (6) of Table 4 thus reestimates our main regression using a conditional fixed-effect logit model; the results here continue to produce a positive significant estimated coefficient for women, with job insecurity increased the probability of being married.

iii. Sample composition

Firm size is reported by the respondent and may not be accurate. In this case, individuals can be mis-allocated to firm-size groups, and hence to the control or treatment groups. This mis-reporting may be random, in which case we estimate a lower bound of the treatment (as some of the control group are treated, and some of the treated group are not). A potentially more serious problem arises if the mis-allocation is not random, conditional on the control variables in our regressions. We address mis-reporting using a test inspired by the donut regression-discontinuity design, and drop workers who are close to the firm-size treatment threshold of 50 employees. From the firm-size categories listed in Section 3, this implies reestimating the treatment without respondents who say they work in firms with "20 to 49

employees" or "50 to 99 employees". Intuitively, mis-judgement may cause workers to erroneously report a firm-size category above or below the correct value, but not to jump three categories (so that they report a firm size of under 20 employees when the real value is over 100 employees, for example).

The estimated treatment coefficients from the baseline analysis (in panel B of Table 3) and these "donut" regressions (in the last column of Table 4) are of the same size, although the estimate of the latter for women is no longer significant (due to the smaller sample size when we drop two firm-size categories, producing larger standard errors). That the estimated coefficient does not change between the two specifications helps to dispel any worries about systematic mis-reporting of firm size. 15 We last consider attrition. From the announcement of the reform onwards, 16% of our treatment group left the estimation sample before the last wave (this figure is the same in the control group, with no noticeable differences between men and women). We may worry that attrition is not independent of the reform's implementation so that our estimates are biased, especially if the marriage probability of leavers decreases after they leave the sample. A first point is that the ECHP does supply two weights, both of which are called attrition weights (our main regression results do not use weights). Applying these attrition weights does not change the nature of our results. 15 As in [START_REF] Clark | A natural experiment on job insecurity and fertility in France[END_REF], we can consider public-sector workers as an alternative control group but none of our treatment estimates was significantly different from zero at conventional levels. Note however that the marriage probability pre-trends differ significantly between the treatment group and public-sector workers, which cast doubts about the validity of the estimation strategy in this particular sample. All of these results are available upon request.

We can also calibrate the "unobserved" difference-in-differences in the attrition group that would be required produce a main estimate of zero: this is 0.21 (= 0.04*84%/16%). Our main result is that the difference in the probability of being married between women in large and small firms rose by 4 percentage points post-reform. To cancel this figure out, we would require the analogous difference in the 16% of women in the attrition group to be 21 percentage points lower after the reform. This figure is more than double the largest age effect on marriage in column (4) of Table A1, and does not seem plausible.

b. Heterogeneity

The D-i-D estimates in Panel B of Table 3 show the average treatment effect for workers in large firms. In Table 5 we consider whether these effects might differ across groups. We first consider age, and interact the total effect of the reform with a dummy for being born in 1963 or before. The resulting estimates appear in columns ( 1) and ( 6) of Table 5 respectively for women and men: neither interaction term here is significant. 16 We second know that the relationship between fertility decisions and job insecurity likely depends on education and earnings [START_REF] Chevalier | Economic uncertainty, parental selection, and children's educational outcomes[END_REF][START_REF] Clark | A natural experiment on job insecurity and fertility in France[END_REF].

We here ask whether an analogous relationship is found for marriage. We thus interact the reform with "High-education" and "High-wage" dummies, corresponding respectively to workers with post-secondary education and those with above-median wage: both of these interaction variables are measured in the pre-reform years only. 17 The resulting estimates on these interactions in columns (2), ( 3), ( 7) and (8) of Table 5 indicate no significant difference in the effect of job insecurity on marriage by education or wages. 18

16 1963 is the median birth year in our estimation sample. The interaction terms from different birth-year thresholds continue to be insignificant. 17 We also considered an interaction between the treatment and a continuous measure of monthly wages (in logs), which produces similar results. Using household income rather than the monthly wage makes also no difference here.

18 With respect to hours of work, interactions with pre-reform hours either as a continuous variable or as a dummy for part-time work (between 1 and 29 hours per week) yielded no significant estimates.

Our last interactions concern pre-reform family characteristics. Columns (4) and ( 9) shows the estimated coefficient on the interaction with a dummy for the treated workers having children before the higher Delalande tax: this is positive and significant only for women. One natural interpretation is that women with children are exposed to greater risk than men with children, as in France the former ended up with sole custody of the children in 80% of separations in the early 2000s. 19 The figures in columns ( 5) and ( 10) refer to the interactions with the number of children the respondent had at the time of the reform. The resulting estimated coefficients are positive and significant (and of the same size) only for women with one or two children (although that for women with three or more children is not statistically different from that for mothers with one or two children).

Why does the effect of job insecurity differ across some groups of workers? One possibility is that the relationship between the layoff tax and job insecurity may be more pronounced for some workers, and especially those who already had children. We look for evidence of this in Appendix Table A6, where the dependent variable is now perceived job security. None of the interaction terms in this table is significantly different from zero: as such, all of the different groups of employees in this table react similarly to the reform in terms of their perceived job security.

A second possibility is that the link between perceived job security and marital status may differ across groups, for reasons of risk-aversion. In [START_REF] Görlitz | Parenthood and risk preferences[END_REF], the higher riskaversion due to parenthood is larger for women. As such, mothers arguably constitute the most risk-averse group of workers in our estimation sample, which might explain why they are the most likely to get married after a rise in their job insecurity.

Risk-Sharing Theory

Our results above are in line with risk sharing theory, as the rise in marriage after the 1999 rise in the Delalande tax appears only for the arguably most risk-averse workers (i.e. women with children), although we have not yet provided any explicit test of this theory. In [START_REF] Hess | Marriage and consumption insurance: What's love got to do with it?[END_REF] and [START_REF] Shore | For better, for worse: Intrahousehold risk-sharing over the business cycle[END_REF], couples manage income risk by trying to ensure that the two partners' exogenous income shocks are not positively perfectly correlated. In the context of the reform we analyse here, we expect a stronger treatment effect for women whose partner has a stable job.

This is what we test in Table 6, where we interact the reform effect with dummy variables for different types of partners. Columns ( 1) and ( 4) show the average effect of the reform for women and men, as in Panel B of Table 3, while columns (2) and ( 5) show the estimated coefficients of the interaction of the reform with a dummy for "Employed Partner". As risksharing theory would predict, the shift from cohabitation to marriage (following the results in Table A4) is only higher for women whose partners are currently working. 20 We find no significant results for any of the groups of men.

Last, we take the treatment status of the partner into account. Under risk-sharing, household members try to avoid correlated risks. The marriage incentives from job insecurity should then be weaker for women whose partner is also affected by the reform. The estimates in column

(3) are in line with this prediction: marriage only rises significantly for women whose partner does not currently suffer from exogenously-higher job insecurity. We found no significant differences in this respect for the partner working in the public vs. private sector or having a permanent vs. temporary contract (although this latter might reflect a lack of statistical power, 20 The interactions in Table 6 refer to the partner's current labour-market position. As such, the employed in row 2 may have started work after their partner was treated. Equally, in rows 3 and 4, partner treatment may have caused individuals to switch into more secure jobs (i.e. those that are not affected by the higher Delalande tax). If we only consider the partner's pre-reform employment status, we do not allow for these behavioural reactions (if we do so we actually find similar estimates, although the coefficients are less precisely-estimated).

as only around 3% of partners in our estimation sample had a temporary contract). We continue to find no significant marriage results for any of the groups of men (in the last column of Table 6).

The results in Table 6 are in line with the idea that the security of the partner's job acts as insurance for women. We provide additional evidence in Table A7, where we re-estimate the effect of the 1999 rise of the Delalande tax on perceived job security by partner's employment status. Column (1) reproduces the analysis in Panel A of Table 3: women's job security fell after the reform. However, this fall was not uniform. In column (3), consistent with the results in Table 6, there was no fall in job security for women whose partner was unaffected by the reform. This again suggests that the partner's labour-market position can provide insurance against risk. 21

Conclusion

Job insecurity the probability of marriage for women. The 1999 layoff-tax reform in the French labour market protected older workers, but to the detriment of younger workers.

As this reform was applied only in larger firms, we can carry out a difference-in-differences analysis. The exogenous change in the future probability of job loss affected perceived job security; it also produced a robust significant rise in the probability of being married for women. Our identification strategy here evaluates the effect of job insecurity on the probability of being married for workers who were employed both before and after the reform (and not those who changed their labour-force status): this is probably what most people will understand by job insecurity, in the sense that insecurity is forward-looking. 21 The estimates in the last column of Table A7 provide some evidence that men's lower perceived job security following the reform is entirely compensated by their partner also being exposed (although the coefficient on the latter is not particularly accurate). While this is not consistent with the risk-sharing theory, it is in line with social comparisons: unemployed or overemployed men report higher levels of well-being and health when their partner has similar experiences on the labour market [START_REF] Clark | Unemployment as a social norm: Psychological evidence from panel data[END_REF][START_REF] Lepinteur | Working time mismatches and self-assessed health of married couples: Evidence from Germany[END_REF].

Our results are novel as they are, to the best of our knowledge, the first that appeal to a natural labour-market experiment to show that risk-sharing is one of the causes of marriage.

Job insecurity increased the probability of marriage for women, and more so for those who are probably more risk-averse (mothers). In line with risk-sharing theory, we show that this marriage effect was not found for couples in which the layoff risk for both partners rose after the 1999 tax rise (i.e. couples where both members worked in treated firms). The lack of any effect for men may reveal their lower risk-aversion with respect to job insecurity, or the greater difficulty that insecure men face on the marriage market.

Part of the attraction of marriage then seems to be the risk-sharing it provides. Why then don't all couples get married? There are a wide variety of factors at play here, including cultural norms. Some of these can be argued to be economic. In the same way that employment protection legislation might discourage hiring due to the costs of firing, more rigid or expensive divorce procedures may discourage some couples from marrying. In this case, more flexible divorce procedures may lead to more people getting married, as would a more advantageous tax treatment of the married relative to the cohabiting. The flexibility of marriage and the labour market can thus be considered as intertwined.

Figures and Tables

Figure Each dot shows the effect of being in the treatment group (i.e. being a younger worker in a firm with 50 or more employees) in that year on the outcome in question compared to the control group (being a younger worker in a firm with fewer than 50 employees). These numbers come from regression analyses that include individual and year fixed-effects, as well as age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. The error bars represent the 90% confidence intervals. Note: These numbers refer to permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. Notes: These are linear regressions. The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. There are 10371 observations in the whole sample (2797 individuals), 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). The announcement effect of the reform refers to the treatment from the beginning of 1998, when the reform to the Delalande tax was announced, up to its implementation on January 1 st 1999; the reform-implementation effect considers the implementation treatment starting on January 1 st 1999. These two effects correspond to α2 and α3 in Equation (1). The total effect of the reform corresponds to β2 in Equation (2). Standard errors in parentheses are clustered at the individual level. All of the regressions include individual and year fixed-effects, as well as age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively. Notes: These are linear regressions, except in column (6). The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49 (except in columns (2), ( 3) and ( 4), where it is their Spanish, Italian and Danish counterparts). The total effect of the reform corresponds to β2 in Equation ( 2). Standard errors in parentheses are clustered at the individual level, except in columns (6). The conditional FE logit coefficients in column (6) refer to the log of the odds ratio. All of the regressions include year fixed effects, age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. Notes: These are linear regressions, except in column (6). The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49 (except in columns (2), ( 3) and ( 4), where it is their Spanish, Italian and Danish counterparts). The total effect of the reform corresponds to β2 in Equation (2). Standard errors in parentheses are clustered at the individual level. The BUC ordered logit coefficients in column (6) refer to the log of the odds ratio and the number of observations is artificially higher due to the estimation method. All of the regressions include year fixed effects, age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. Notes: These are linear regressions. The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. There are 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). The total effect of the reform corresponds to β2 in Equation (2). The standard errors in parentheses are clustered at the individual level. All of the regressions include individual and year fixedeffects, as well as age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

Online Appendix

  Figure 2 thus plots the estimated yearly effects of being in the treatment (as opposed to the control) group on perceived job security (in Panel A) and the probability of being married (Panel B). The left-hand side shows the results for the whole sample and the right-hand figure those for men and women separately. 10 None of the pre-reform announcement estimates (that can be considered as placebos) in Figure 2 are significantly different from zero, providing evidence in favour of the common-trend assumption. 11

  Figure 1: Marriage and Cohabitation Rates in France from 1990 to 2009

Figure 2 :

 2 Figure 2: Parallel-Trend Assumption -Panel Results Panel A: Perceived Job Security

Figure

  Figure A1: Sample Selection

Figure A2 :

 A2 Figure A2: The Distribution of Perceived Job Security in the ECHP

Figure A3 :

 A3 Figure A3: Average Perceived Job Security and the Probability of being Married by Treatment Group Panel A: Perceived Job Security

  The individual time-invariant controls are gender and education dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

  .As mentioned earlier, the 2000 working-time reduction was another notable labour-market reform around the time of the change in the Delalande tax. In 1998, the French Ministry of Labour announced a reduction in the standard workweek from 39 to 35 hours in companies with more than 20 employees. This could potentially have affected the perceived job security of workers in those firms, and hence our estimated coefficients. We check that our main estimates do not pick up the effect of the 35-hour week by re-running our baseline regression

	a. Robustness Checks
	i.	Ruling out confounding shocks

excluding workers in firms with under 20 employees (which ensures that all of the individuals in our estimation sample are equally-affected by the 35-hour week): this drops around 15% of the initial estimation sample. The estimated reform coefficients in column (1) of Table

4

are similar to those in the baseline (in columns (

Table 1 :

 1 The Evolution of the Delalande Layoff Tax over Time

			Worker's age
	50	51	52 53 54	55	56-57 58 59

Source: Legislative texts. Note: For each age group, the table shows the tax to be paid by the firm to the unemployment-insurance system if it lays off a worker of that age. The tax is a function of the worker's wages, and is stated in months of gross wage. This tax applies to private-sector workers with permanent contracts only.

Table 2 :

 2 Descriptive Statistics of the ECHP Analysis Sample

	Mean	SD	Min	Max

Table 3 :

 3 The Delalande Tax, Job Security and the Probability of Being Married -Panel Results

	Panel A: Job Security	Whole Sample	Women		Men
		(1)	(2)	(3)	(4)	(5)	(6)
	Reform Announcement	-0.188 ***		-0.150 *		-0.224 ***
		(0.057)		(0.090)		(0.074)
	Reform Implementation	-0.202 ***		-0.160 *		-0.241 ***
		(0.053)		(0.086)		(0.067)
	Total Effect of the Reform		-0.198 ***	-0.157 **	-0.236 ***
			(0.048)	(0.077)	(0.062)
	Panel B: Married (Dummy)	Whole Sample	Women		Men
		(1)	(2)	(3)	(4)	(5)	(6)
	Reform Announcement	0.016		0.032		0.006
		(0.012)		(0.020)		(0.016)
	Reform Implementation	0.015		0.047 *		-0.007
		(0.015)		(0.025)		(0.019)
	Total Effect of the Reform		0.015	0.042 **		-0.003
			(0.013)	(0.021)	(0.017)

Table 4 :

 4 The Rise in the Delalande Tax and the Probability of being Married -Robustness Checks 20+ employees

		Spanish sample	Italian sample	Denmark sample	OLS	Conditional FE Logit	Donut DiD
	(1)	(2)	(3)	(4)	(5)	(6)	(7)

  The individual time-invariant controls are gender and education dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

Table 5 :

 5 The Rise in the Delalande Tax and the Probability of being Married -Heterogeneity Analysis These are linear regressions. The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. There are 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). The total effect of the reform corresponds to β2 in Equation (2). Standard errors in parentheses are clustered at the individual level. All of the regressions include individual and year fixed-effects, as well as age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

	Women

Notes:

Table 6 :

 6 The Rise in the Delalande Tax and the Probability of being Married by Partner's Employment Status -Panel Results These are linear regressions. The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. There are 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). The total effect of the reform corresponds to β2 in Equation (2). The standard errors in parentheses are clustered at the individual level. All of the regressions include individual and year fixed-effects, as well as age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

		Women			Men
	(1)	(2)	(3)	(4)	(5)	(6)

Notes:

Table A1 :

 A1 The Delalande Tax and Marriage -Panel results with the full set of controls These are linear regressions. The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. There are 10371 observations in the whole sample (2797 individuals), 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). The announcement effect of the reform refers to the treatment from the beginning of 1998, when the reform to the Delalande tax was announced, up to its implementation on January 1 st 1999; the reformimplementation effect considers the implementation treatment starting on January 1 st 1999. These two effects correspond to α2 and α3 in Equation (1). The total effect of the reform corresponds to β2 in Equation (2). Standard errors in parentheses are clustered at the individual level. All of the regressions include individual fixed-effects, as well as wave, occupation and region dummies.

		Whole Sample	Women	Men
		(1)	(2)	(3)	(4)	(5)	(6)
	Reform Announcement	0.016		0.032		0.006
		(0.012)		(0.020)		(0.016)
	Reform Implementation	0.015		0.047 *		-0.007
		(0.015)		(0.024)		(0.019)
	Total Effect of the reform		0.015		0.042 **		-0.003
			(0.013)		(0.021)		(0.017)
	Age: 26-30	0.102 *** 0.102 ***	0.085 *** 0.085 ***	0.118 *** 0.117 ***
		(0.021)	(0.021)	(0.030)	(0.030)	(0.028)	(0.028)
	Age: 31-35	0.096 *** 0.096 ***	0.075 **	0.074 **	0.116 *** 0.115 ***
		(0.024)	(0.024)	(0.033)	(0.033)	(0.033)	(0.033)
	Age: 36-40	0.073 *** 0.073 ***	0.043	0.042	0.097 *** 0.096 ***
		(0.026)	(0.026)	(0.035)	(0.035)	(0.036)	(0.036)
	Age: 41-45	0.050 *	0.050 *	-0.006	-0.006	0.090 **	0.090 **
		(0.028)	(0.028)	(0.041)	(0.041)	(0.038)	(0.038)
	Age: 46-49	0.010	0.010	-0.075	-0.077	0.069 *	0.068
		(0.032)	(0.032)	(0.050)	(0.050)	(0.042)	(0.042)
	Monthly Wage (in log)	0.020	0.020	-0.005	-0.006	0.047 **	0.048 **
		(0.016)	(0.016)	(0.023)	(0.023)	(0.021)	(0.021)
	Weekly Working Hours	-0.001 *	-0.001 *	-0.000	-0.000	-0.001 ** -0.001 **
		(0.000)	(0.000)	(0.001)	(0.001)	(0.001)	(0.001)
	Self-Assessed Health [1-5]	-0.001	-0.001	-0.006	-0.006	0.003	0.003
		(0.004)	(0.004)	(0.007)	(0.007)	(0.005)	(0.005)
	Number of Children in the Household	0.062 *** 0.062 ***	0.057 *** 0.057 ***	0.064 *** 0.064 ***
		(0.008)	(0.008)	(0.012)	(0.012)	(0.011)	(0.011)

Notes: *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

Table A2 :

 A2 Differences in observable characteristics between the treatment and control group before and after the reform's announcement Before the announcement of the 1999 rise in the Delalande tax

		Treatment Control Difference	After the announcement of the 1999 rise in the Delalande tax Treatment Control Difference	Difference-in-Differences
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Age	34.128	33.092	1.036 ***	36.140	35.143	0.997 **	-0.040
		[6.082]	[6.517]	(0.175)	[7.024]	[7.302]	(0.199)	(0.266)
	Female	0.386	0.441	-0.056 ***	0.380	0.425	-0.045 ***	0.011
		[0.487]	[0.497]	(0.014)	[0.486]	[0.494]	(0.014)	(0.019)
	High Education	0.266	0.187	0.079 ***	0.298	0.217	0.081 ***	0.002
		[0.442]	[0.390]	(0.012)	[0.458]	[0.412]	(0.012)	(0.017)
	No. Children in Household`	0.918	0.921	-0.003	0.872	0.870	0.002	0.005
		[0.988]	[1.020]	(0.028)	[0.951]	[0.940]	(0.026)	(0.038)
	Health Status	3.901	3.916	-0.015	3.839	3.851	-0.013	0.002
		[0.740]	[0.752]	(0.021)	[0.706]	[0.673]	(0.019)	(0.028)
	Weekly Working Hours	40.108	39.516	0.592 ***	38.851	39.097	-0.246	-0.838 ***
		[6.898]	[9.151]	(0.218)	[6.557]	[8.285]	(0.218)	(0.309)
	Monthly Wage (log)	9.004	8.818	0.227 ***	9.143	8.930	0.214 ***	-0.013
		[0.440]	[0.471]	(0.013)	[0.472]	[0.482]	(0.013)	(0.018)

Notes: There are 10371 observations in the whole sample (2797 individuals). Standard errors are in parentheses and standard deviations are in square brackets. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

Table A3 :

 A3 Differences in characteristics between the treatment and control group before and after the reform's announcement by gender Before the announcement of the 1999 rise in the Delalande tax There are 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). Standard errors are in parentheses and standard deviations are in square brackets. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

		Treatment Control Difference	After the announcement of the 1999 rise in the Delalande tax Treatment Control Difference	Difference-in-Differences
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Panel A: Women
	Age	33.925	32.902	1.024 ***	35.712	35.117	0.595 *	-0.428
		[6.117]	[6.617]	(0.278)	[7.105]	[7.327]	(0.318)	(0.422)
	High Education	0.312	0.219	0.093 ***	0.338	0.255	0.082 ***	-0.011
		[0.464]	[0.414]	(0.019)	[0.473]	[0.436]	(0.020)	(0.027)
	No. Children in Household	0.494	0.546	-0.052 **	0.477	0.557	-0.081 ***	-0.028
		[0.500]	[0.498]	(0.022)	[0.500]	[0.497]	(0.022)	(0.031)
	Health Status	3.888	3.876	0.012	3.801	3.835	-0.034	0.045
		[0.718]	[0.754]	(0.032)	[0.710]	[0.678]	(0.030)	(0.044)
	Weekly Working Hours	37.701	35.646	2.054 ***	36.755	35.635	1.119 ***	-0.935 *
		[6.725]	[9.122]	(0.355)	[6.220]	[8.023]	(0.319)	(0.478)
	Monthly Wage (log)	8.901	8.625	0.277 ***	8.993	8.759	0.235 ***	-0.042
		[0.447]	[0.468]	(0.020)	[0.472]	[0.493]	(0.021)	(0.029)
	Panel B: Men
	Age	34.257	33.243	1.014	36.402	35.162	1.240	0.226
		[6.058]	[6.434]	(0.227)	[6.963]	[7.286]	(0.256)	(0.343)
	High Education	0.236	0.161	0.075	0.274	0.189	0.085	0.010
		[0.425]	[0.368]	(0.014)	[0.446]	[0.392]	(0.015)	(0.021)
	No. Children in Household	0.540	0.516	0.024	0.552	0.523	0.029	0.005
		[0.499]	[0.500]	(0.018)	[0.497]	[0.500]	(0.018)	(0.026)
	Health Status	3.910	3.948	-0.038	3.862	3.864	-0.002	0.036
		[0.753]	[0.748]	(0.027)	[0.703]	[0.669]	(0.025)	(0.037)
	Weekly Working Hours	41.619	42.573	-0.954	40.538	41.661	-1.123	-0.169
		[6.571]	[7.940]	(0.265)	[6.428]	[7.508]	(0.252)	(0.365)
	Monthly Wage (log)	9.134	8.970	0.164	9.235	9.056	0.179	0.015
		[0.411]	[0.414]	(0.015)	[0.448]	[0.434]	(0.016)	(0.022)

Notes:

Table A4 :

 A4 The Delalande Tax and Other Types of Partnerships -Panel Results These are linear regressions. The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. There are 10371 observations in the whole sample (2797 individuals), 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). The total effect of the reform corresponds to β2 in Equation (2). Standard errors in parentheses are clustered at the individual level. All of the regressions include individual and year fixed-effects, as well as age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

	Panel A: Whole Sample	Married Partnered	Partnered but not married	Divorced or Separated	Never in a relationship
		(1)	(2)	(3)	(4)	(5)
	Total Effect of the Reform	0.015	-0.010	-0.023	-0.004	0.013
		(0.013)	(0.013)	(0.015)	(0.007)	(0.011)
	Panel B: Women	Married Partnered	Partnered but not married	Divorced or Separated	Never in a relationship
		(1)	(2)	(3)	(4)	(5)
	Total Effect of the Reform	0.042 **	-0.013	-0.052 **	0.006	0.010
		(0.021)	(0.023)	(0.025)	(0.013)	(0.020)
	Panel C: Men	Married Partnered	Partnered but not married	Divorced or Separated	Never in a relationship
		(1)	(2)	(3)	(4)	(5)
	Total Effect of the Reform	-0.003	-0.008	-0.002	-0.008	0.014
		(0.017)	(0.014)	(0.018)	(0.009)	(0.012)

Notes:

40

Table A5 :

 A5 The Rise in the Delalande Tax and Perceived Job Security -Robustness Checks

		20+ employees	Spanish sample	Italian sample	Denmark sample	OLS	BUC Logit Ordered	Donut DiD
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Panel A: Whole Sample
	Total Effect of the reform	-0.168 **	-0.018	-0.049	0.032	-0.111 ***	-0.475 ***	-0.142 ***
		(0.069)	(0.064)	(0.058)	(0.077)	(0.042)	(0.114)	(0.055)
	Individual Time-Invariant Controls	.	.	.	.	Yes	.	.
	Individual Fixed Effects	Yes	Yes	Yes	Yes	.	Yes	Yes
	Observations	6657	8938	11373	4682	10371	16479	7523
	Individuals	1740	3127	3411	1432	2797	2797	2067
	Panel B: Women
	Total Effect of the reform	-0.201 *	0.143	-0.065	0.167	-0.131 *	-0.381 **	-0.097
		(0.109)	(0.103)	(0.105)	(0.145)	(0.070)	(0.187)	(0.087)
	Individual Time-Invariant Controls	.	.	.	.	Yes	.	.
	Individual Fixed Effects	Yes	Yes	Yes	Yes	.	Yes	Yes
	Observations	2599	3084	4265	1739	4248	6546	3018
	Individuals	691	1134	1340	572	1175	1175	860
	Panel C: Men
	Total Effect of the reform	-0.151 *	-0.092	-0.037	-0.019	-0.103 **	-0.547 ***	-0.192 ***
		(0.090)	(0.081)	(0.069)	(0.092)	(0.052)	(0.144)	(0.073)
	Individual Time-Invariant Controls	.	.	.	.	Yes	.	.
	Individual Fixed Effects	Yes	Yes	Yes	Yes	.	Yes	Yes
	Observations	4058	5854	7108	2934	6123	9933	4505
	Individuals	1049	1993	2071	860	1622	1622	1207

Table A6 :

 A6 The Rise in the Delalande Tax and Perceived Job Security -Heterogeneity Analysis These are linear regressions. The sample here is permanent-contract private-sector workers in the French ECHP between the ages of 20 and 49. There are 10371 observations in the whole sample (2797 individuals), 4248 observations in the sample of women (1175 individuals) and 6123 observations in the sample of men (1622 individuals). The total effect of the reform corresponds to β2 in Equation (2). Standard errors in parentheses are clustered at the individual level. All of the regressions include individual and year fixed-effects, as well as age dummies (in five-year bands), the number of children in the household, health status, weekly working hours, the log of the monthly wage, and occupation and region dummies. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively.

				Women					Men
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	Total Effect of the Reform -0.148 -0.181 ** -0.205	-0.035	-0.034	-0.245 *** -0.220 *** -0.300 *** -0.136	-0.136
		(0.117) (0.090) (0.135) (0.138) (0.138)	(0.091)	(0.071)	(0.089)	(0.106)	(0.106)
	Interacted with:
	Born after 1963	-0.022					0.010
		(0.154)					(0.123)
	High Education		0.112					-0.059
			(0.170)					(0.139)
	High Monthly Wage			0.072					0.190
				(0.167)					(0.125)
	Parent beforehand				-0.164					-0.138
					(0.165)					(0.129)
	1 child beforehand					-0.191					-0.151
						(0.193)					(0.156)
	2 children beforehand					-0.038					-0.109
						(0.184)					(0.156)
	3+ children beforehand					-0.690					-0.172
						(0.436)					(0.201)

Notes:

Table A7 :

 A7 The Rise in the Delalande Tax and Perceived Job Security by Partner's Employment Status -Panel Results

			Women			Men
		(1)	(2)	(3)	(4)	(5)	(6)
	Total Effect of the Reform	-0.157 ** -0.279 ** -0.271 ***	-0.236 *** -0.243 *** -0.247 ***
		(0.077)	(0.120)	(0.120)	(0.062)	(0.079)	(0.079)
	Interacted with:
	Employed Partner		0.193			0.003
			(0.135)			(0.102)
	Employed Partner Not Affected by the Higher Delalande Tax			0.285 **			-0.073
				(0.145)			(0.109)
	Employed Partner Affected by the Higher Delalande Tax			-0.268			0.320 *
				(0.169)			(0.172)

The analysis in[START_REF] Clark | A natural experiment on job insecurity and fertility in France[END_REF] does not use the same sample as we do here. Their fertility analysis is carried out on the sample of workers who were already married before the reform and continued to be married after it. On the contrary, we explicitly model the move into marriage.

We also consider in Appendix TableA2the following types of marital outcomes: partnered, partnered but not married, divorced or separated, and never in a relationship.

More details are available at http://ec.europa.eu/eurostat/web/microdata/european-community-household-panel.

FigureA2in the Online Appendix shows the distribution of self-reported job security. It can be seen that 70% of responses on the 1-6 scale were 4 or

This negative skewness is commonly found for subjective measures.

The fall in the number of observations due to missing values (from 13,966 to 10,936 observations) is mostly due to missing firm size. As firm size is essential in defining treatment status, we do not impute missing values here. Balance tests confirm that the observable characteristics of the observations dropped due to missing firm size are not significantly different from those with valid information. Around 1,000 observations are also lost because of missing values for working time. Again, these dropped observations have characteristics similar to those in the estimation sample.

The figures are not exactly the same as the analysis samples differ across the papers. In[START_REF] Georgieff | Partial employment protection and perceived job security: evidence from France[END_REF], the ECHP analysis sample pools together workers above and below age 50, and the authors estimate a triple difference-in-differences to separately identify the effect of the reform on workers below and above age 50.[START_REF] Clark | A natural experiment on job insecurity and fertility in France[END_REF] analyse the same age group as we do here, namely the under-50's, but focus on the fertility behaviour of those who were already married before the reform and continued to be so afterwards.

Using an estimation sample with the same characteristics as in this paper and the French Labour Force Survey,[START_REF] Georgieff | Partial employment protection and perceived job security: evidence from France[END_REF] show that the actual layoff probability of the treated workers below age 50 significantly increased after the announcement of the reform. We have replicated their analysis separately for men and women and find no significant gender differences. These results are available upon request.

The full set of marriage results, including the estimated coefficients on all of the control variables, appears in Appendix TableA1.

These regressions include a number of sociodemographic controls, as noted at the foot of the table. The inclusion of these controls has no effect on our treatment effects. This is to be expected: if the assignment to the treatment is random, the inclusion of additional controls will not affect the coefficients but should increase the precision of the estimates. The results without these control variables are available upon request.

In these latter figures we have slightly horizontally-shifted the curves for men and women so that the confidence intervals around the estimates can be seen clearly.

FigureA3in the Online Appendix plots the time profile of average perceived job security and the probability of being married in the treatment and control groups, providing additional supporting evidence for the paralleltrend assumption.

The marital-status categories in TableA4are not mutually-exclusive: an individual can be both divorced and in a new relationship. We find similar results to those in TableA4when we estimate a multinomial-logit model on the following mutually-exclusive categories: "Married in a partnership", "Non-married in a partnership", "Divorced or separated with no partner" and "Never in a relationship" (we exclude widows here, as there are too few observations). These results are available upon request.

The results of the robustness and heterogeneity analyses when we split the reform up into announcement and implementation effects are very similar.

The information in the final waves of the ECHP in Belgium and Germany does not allow us to accurately distinguish the public from the private sector, or to measure perceived job security.

See Table 2 in http://www.justice.gouv.fr/art_pix/stat_Infostat%20132%20def.pdf.

Marion Leturcq, Giorgia Menta and Anne Solaz for their help and feedback. We gratefully acknowledge financial support from CEPREMAP, EUR grant ANR-17-EURE-0001 and the Fonds National de la Recherche Luxembourg (Grant C18/SC/12677653).


Éric Le Bourg
email: eric.le-bourg@univ-tlse3.fr

E Le Bourg

Characterisation of the positive effects of mild stress on ageing and resistance to stress

Keywords:

The positive effects of mild stress on ageing, lifespan and resistance to stress have been studied mainly in Drosophila melanogaster flies and in the nematode Caenorhabditis elegans.

These studies now allow to know the effects of the strength of the mild stress and of the number of exposures, the duration of the positive effects, if mild stress is effective when applied at any age, and whether combining two or three mild stresses is more efficient than a single one. This article summarises these results.

Introduction

In 1977, the gerontologist George Sacher wrote in a review article dealing partly with hormesis, i.e. the positive effects of mild stress, that "hormetic effects are unlikely to occur in the healthy active individual, and are more likely to be significant in the ill or depressed animal". He concluded that "hormesis is in one sense an obstacle in the path of gerobiological research, and efforts to understand and annul it would be well justified", which could be done by developing "living environments that are optimal for… behavioral, physiological, and immunological health" of animal models. Clearly speaking, this article could not encourage other scientists to publish results showing hormetic effects and one can bet that such results have been kept in the bottom drawer of the desk. At the same time, Vladimir Frolkis (1982, p.9), in the Soviet Institute of Gerontology in Kiev, Ukraine, reported that 100-day-old rats subjected to "repeated brief stress" had longer mean (+19%) and maximal (+12%) lifespans. Later on, he indicated that "cold, sound, electrical stimulation, physical load, and a temporary restriction of motor activity" increased mean (+18%) and maximal lifespans (+11%), while the "rough stress" decreased lifespan [START_REF] Frolkis | Stress-age syndrome[END_REF].

Unfortunately, this author was stingy with details and these results were simply ignored by other scientists. Thus, on the one hand, a US author denigrated hormesis, while, on the other hand, a Soviet author did not publish in international journals his results showing such effects. In such conditions, there was only a little chance to deepen the knowledge on hormesis.

Times have changed, and numerous results have now been published by various teams in international journals, showing clearly that hormetic effects do exist and that we should wonder whether and how they can be used in therapy (Rattan and Kyriazis 2019). Since the review article of [START_REF] Neafsey | Longevity hormesis. A review[END_REF], mainly dealing with changes of mortality rates because of hormesis, and the review on hormesis and ageing by [START_REF] Minois | Longevity and aging: beneficial effects of exposure to mild stress[END_REF], many new results have been published and hormesis has been discussed in books (Le Bourg and Rattan 2008;Mattson and Calabrese 2010, Rattan and Le Bourg 2014, Rattan and Kyriazis 2019) or in special issues of Ageing Research Reviews (see e.g. [START_REF] Mattson | Hormesis defined[END_REF] or Dose-Response (see Le [START_REF] Bourg | Is hormesis applicable as a pro-healthy aging intervention in mammals and human beings, and how?" Introduction to a special issue of Dose-Response[END_REF].

One could suppose that observing hormetic effects could depend on various experimental conditions, such as the duration and/or strength of the mild stress, the observed phenotype (e.g. lifespan or resistance to a severe stress), the age of application of the mild stress, and so on. Thanks to many studies performed since the turn of the century, it is now possible to characterise the hormetic effects by relying on numerous experimental results, and not only on theoretical thinking.

Therefore, this article does not describe hormetic effects in various species but focuses on their features, which have been widely studied in the fly Drosophila melanogaster, but not only.

Strength of the mild stress and number of exposures to it

The definition of hormesis is "a dose-response phenomenon which is characterized with a low dose stimulation and a high dose inhibition" [START_REF] Calabrese | ) Mild stress and healthy aging[END_REF]. Thus, a first problem is to determine the range of the low doses inducing a hormetic effect, before the no observed adverse effect level is reached (Fig. 1A). A simple procedure is to vary the duration of exposure to a mild stress.

A clear example of a perfect hormetic curve is that of [START_REF] Cypser | Multiple stressors in Caenorhabditis elegans induce stress hormesis and extended longevity[END_REF] showing that Caenorhabditis elegans nematodes live longer if exposed for a short time to a mild heat stress (35 °C), this mild stress also increasing the survival time at 35 °C. However, deleterious effects are observed when the time at 35 °C increases (Fig. 2, see also [START_REF] Wu | The U-shaped response of initial mortality in Caenorhabditis elegans to mild heat shock: does it explain recent trends in human mortality?[END_REF][START_REF] Pickering | Oxidative stress adaptation with acute, chronic, and repeated stress[END_REF]. Similar results are observed for D. melanogaster male flies kept in hypergravity (HG) for various durations, i.e. at gravity levels higher than that of the Earth (1-5 g, Fig. 3). HG increased lifespan if lasting for less than ca 30 days (Le [START_REF] Bourg | A mild stress due to hypergravity exposure at young age increases longevity in Drosophila melanogaster males[END_REF], in accordance with previous experiments showing that keeping flies in HG for life decreased lifespan (Le Bourg andLints 1989, Lints et al. 1993). However, in most of experiments, HG had no positive effect on lifespan of females (Le [START_REF] Bourg | Increased longevity and resistance to heat shock in Drosophila melanogaster flies exposed to hypergravity[END_REF] or slightly decreased it (Le [START_REF] Bourg | A mild stress due to hypergravity exposure at young age increases longevity in Drosophila melanogaster males[END_REF]. This last study also showed that 14, 19 or 24 days in HG (1-7.38 g) had a similar positive effect in males and that the HG level was of a minor importance. Therefore, these experiments in flies and nematodes show that a mild stress may have positive effects if not lasting for a too long time but also that, once a positive effect is observed, the level of the mild stress (strength or duration) may be of a minor importance.

Similarly, even if repeating a mild stress up to five times (35 °C at 1, 4, 7, 10, and 13 days of age for respectively 60, 55, 50, 40 and 30 min) increases lifespan in C. elegans, the size of the positive effect decreases with the number of repeats [START_REF] Wu | Multiple mild heat-shocks decrease the Gompertz component of mortality in Caenorhabditis elegans[END_REF].

By contrast, if the duration of the mild stress is too short, it can have no effect even if it occurs several times. Figure 3 shows that fractionating 12 days of HG in 3 periods of 4 days separated by 3 days at 1 g did not increase lifespan of males, probably because a 4 days exposure is a too mild stress. Similarly, female flies live longer than control ones only if they are subjected to 4 successive heat shocks (1 hour at 36 °C) and kept in groups of 10 females with 3 males, but 1, 2, or 3 heat shocks have no effect (Hercus et al. 2003, Fig. 4A). However, it has also been observed that a too mild dose can nevertheless have a positive effect if it is repeated. In C. elegans, 4 hours at 30 or 33 °C do not increase lifespan (Olsen et al., 2006, Fig. 4B, compare with 2 hours at 35 °C in Fig. 2) but repeating this 4 hours exposure at successive ages increased it, this result being observed in a wild-type line (N2) and in the mutant TJ1060. Similarly, subjecting male flies to daily one-hour exposures at 0 °C had no effect on lifespan if done for 5 days from the age of 5 days or that of 12 days, but increased it in flies exposed from 5 days of age during two periods of 5 days separated by 2 days (Le [START_REF] Bourg | Hormetic effects of repeated exposures to cold at young age on longevity, aging and resistance to heat or cold shocks in Drosophila melanogaster[END_REF].

All these results modify the shape of the theoretical hormetic curve because it may happen that very low doses have no effect and that, once a dose has a positive effect, a plateau is observed (Fig. 1B). This proposal does not substitute to the usual hormetic curve but is a possible refinement of it.

Is mild stress effective when applied at any age?

It has been reported in C. elegans, either that a single heat shock had no positive effect on lifespan at 4, 8, 12, or 16 days of age (mutant TJ1060), or that a positive effect was observed at 8 and 12 days of age only in the N2 wild-type line (Olsen et al. 2006, Fig. 5A). In flies, applying a mild cold stress at increasing ages during two weeks (weeks 1 and 2, weeks 2 and 3, weeks 3 and 4, or weeks 4 and 5) increased survival time at 37 °C at 6 weeks of age of both sexes (Le Bourg 2011, Fig. 5B). This mild cold stress also increased lifespan of males and their lifespan after infection with a fungus at 6 weeks of age (Fig. 5B), except if it was applied at the oldest ages (weeks 4 and 5).

Therefore, a mild stress applied at various ages can have hormetic effects at old age, but these effects can be less observed when the mild stress is applied at very old ages (weeks 4 and 5).

Is mild stress effective for life?

The previous results (Fig. 5B) indicate that a mild cold stress applied during the first two weeks of age can increase resistance to heat at 6 weeks of age in these flies living at 25 °C, which have a mean lifespan of ca 7-8 weeks. One can thus wonder whether the mild stress has positive effects for a duration of 4 weeks or rather for life, whatever its length can be. Because decreasing the temperature increases lifespan, this hypothesis was tested by transferring flies, after the last cold pretreatment at 2 weeks of age, at 19 or 22 °C, a last group of flies being kept at 25 °C. Survival time at 37 °C was observed at 6 or 8 weeks of age in flies kept at 25 °C, at 6 or 10 weeks of age in flies kept at 22 °C, and at 7 or 10 weeks of age in flies kept at 19 °C. In males, the cold pretreatment increased survival time at 37 °C at any age and in any temperature group, no clear effect being observed in females. Therefore, the mild cold stress applied at young age was efficient not only for 4 weeks but for life whatever its length could be, and at least for 8 weeks after the last cold pretreatment (Le Bourg 2016).

The effects of combining a mild stress and other stresses

Combining a mild stress with a factor having positive, neutral, or negative effects

In real life, various events happen at the same time and one could wonder what would happen when a mild stress co-occurs with a stimulus having deleterious, neutral or positive effects on the trait under study, particularly because [START_REF] Sacher | Life table modification and life prolongation[END_REF] wrote that "hormetic effects are unlikely to occur in the healthy active individual, and are more likely to be significant in the ill or depressed animal". This has been studied by combining in the same flies a mild cold stress with hormetic effects and the removal of live yeast from the feeding medium, which has positive, neutral or negative effects, depending on the studied trait. When this removal had no effect, as on survival time at 37 °C, the positive effect of the mild cold stress was still observed. When removal had a slight deleterious effect, as on lifespan after infection with a fungus, the positive effect of the mild stress was still observed but to a lesser extent. Finally, when removal was very deleterious, as on survival after a severe cold stress, the mild cold stress was unable to mitigate this effect (Fig. 6). By contrast, when removal of live yeast had positive effects, as on the ability to climb on a vertical surface, these effects were additive with the positive effects of the mild cold stress (Le Bourg 2010).

Similarly, the positive effect of HG on lifespan of virgin males is abolished in mated flies which live less than virgin ones, and the same result is observed if virgin males live at 30 °C rather than at 25 °C (Le [START_REF] Bourg | Male Drosophila melanogaster flies exposed to hypergravity at young age are protected against a non-lethal heat shock at middle age but not against behavioral impairments due to this shock[END_REF]. By contrast, when virgin flies live in individual vials, which increases lifespan, the positive effect of HG on lifespan is more important (Le [START_REF] Bourg | A mild stress due to hypergravity exposure at young age increases longevity in Drosophila melanogaster males[END_REF].

These results showing that hormetic effects can also be observed in longevous flies, and not in short-lived ones, are in accordance with those of [START_REF] Sarup | Life extension and the position of the hormetic zone depends on sex and genetic background in Drosophila melanogaster[END_REF] reporting hormetic effects in long-lived strains of flies.

These results indicate, in sharp contrast with [START_REF] Sacher | Life table modification and life prolongation[END_REF], that hormetic effects are more prone to be observed in flies in "living environments that are optimal for… behavioral, physiological, and immunological health" than in those decreasing lifespan, such as mating and high temperature.

One could summarise all these results by saying that when a factor has a positive effect this effect adds to the positive effect of the mild stress and that, when a factor has increasing negative effects, the positive effect of the mild stress is erased up to be nullified.

Combining mild stresses

Previous studies have shown that mild cold stress (e.g. [START_REF] Bourg | Hormetic effects of repeated exposures to cold at young age on longevity, aging and resistance to heat or cold shocks in Drosophila melanogaster[END_REF], HG (e.g. Le [START_REF] Bourg | A mild stress due to hypergravity exposure at young age increases longevity in Drosophila melanogaster males[END_REF], and short heat shocks (e.g. Le Bourg et al. 2001[START_REF] Hercus | Lifespan extension of Drosophila melanogaster through hormesis by repeated mild heat stress[END_REF] may have positive effects in flies, even if the effects of short heat shocks are often modest in various invertebrate species [START_REF] Lagisz | Life extension after heat shock exposure: assessing meta-analytic evidence for hormesis[END_REF]. Combining HG and mild cold stress had additive effects on survival at 37 °C or on male lifespan (Le Bourg 2012). Similarly, combining heat shock (31 or 35 °C) and desiccation (0 % relative humidity) mild stresses in Drosophila simulans female flies can increase survival time at 38 °C and/or to desiccation more than each mild stress alone, but with a slight cost on lifespan that was similar when only one mild stress or their combination are used [START_REF] Bubliy | Stress-induced plastic responses in Drosophila simulans following exposure to combinations of temperature and humidity levels[END_REF].

When a mild stress has positive effects in one sex and negative ones in the other one, its combination with another mild stress with the same effects is thus expected to induce more positive effects in the former sex and more negative ones in the second sex. This can be observed in flies subjected to a mild cold stress and HG, which each can decrease female lifespan and increase that of males: while males show additive positive effects of the two mild stresses, females display additive negative effects (Le Bourg 2012, Fig. 7).

The survival of flies to a severe cold stress can be increased by a mild cold stress, HG or fasting. However, while combining two stresses among these three ones was more efficient than a single stress, combining the three stresses was not more or even less efficient than combining only two stresses (Le Bourg 2017).

Conclusions

On the one hand, it can be concluded that combining two mild stresses with positive effects can be more efficient than using a single mild stress. However, combining three mild stresses is not more efficient than combining two ones. Similar results can be observed in humans: combining physical exercise and thermal therapy (6 hours at 40 °C daily on the painful knee) has additive positive effects on knee pain in elderly women [START_REF] Kim | Effectiveness of exercise with or without thermal therapy for community-dwelling elderly Japanese women with non-specific knee pain: a randomized controlled trial[END_REF].

On the other hand, combining a mild stress with positive effects with another one with negative effects can decrease the positive effects of the former mild stress.

Conclusions

These studies have allowed to better characterise the hormetic effects, mainly in flies but also in nematodes. It is unfortunate that studies on vertebrates are scarce, particularly because the hormetic effects could be used in therapy. For instance, carbon monoxide could be used in cardiology, as studies on pigs have shown that it can minimise the consequences of ischemiareperfusion (e.g. [START_REF] Lavitrano | Carbon monoxide improves cardiac energetics and safeguards the heart during reperfusion after cardiopulmonary bypass in pigs[END_REF][START_REF] Goebel | Protective effects of inhaled carbon monoxide in pig lungs during cardiopulmonary bypass are mediated via an induction of the heat shock response[END_REF], and clinical studies have used remote ischemic conditioning in humans, but with not still significant effects [START_REF] Hausenloy | Remote ischemic preconditioning and outcomes of cardiac surgery[END_REF][START_REF] Vanezis | The broken promise of remote ischaemic conditioning[END_REF], Meybohm et al. 2015, see Garratt et al. 2016[START_REF] Vanezis | The broken promise of remote ischaemic conditioning[END_REF] for a discussion of these results).

Similarly, local heat has been used to decrease inflammation of knees (e.g. [START_REF] Forestier | Spa therapy in the treatment of knee osteoarthritis: a large randomised multicentre trial[END_REF], and sauna seems to decrease cardio-vascular and all-cause mortality and protect from stroke [START_REF] Laukkanen | Association between sauna bathing and fatal cardiovascular and all-cause mortality events[END_REF], Kunutsor et al. 2018, review in Laukkanen et al. 2018). At variance with the Sacher's opinion (1977) that "hormetic effects are unlikely to occur in the healthy active individual", it seems that mild stress can be either used by healthy people, for relaxation and pleasure purposes (sauna), and by unhealthy ones for therapy purposes (e.g. [START_REF] Forestier | Spa therapy in the treatment of knee osteoarthritis: a large randomised multicentre trial[END_REF][START_REF] Kim | Effectiveness of exercise with or without thermal therapy for community-dwelling elderly Japanese women with non-specific knee pain: a randomized controlled trial[END_REF][START_REF] Scapagnini | Thermal hydrotherapy as adaptive stress response. Hormetic significance, mechanisms, and therapeutic implications[END_REF]).

The previous studies, mainly performed in nematodes and flies, can allow to conclude: 1: Mild stresses can have hormetic effects if their strength/duration is not too low/short and not too strong/long. In such conditions, the hormetic curve can be different from the traditional one (Fig. 1A) and is rather a succession of two plateaus, before deleterious effects linked to a too strong stress are observed (Fig. 1B).

2: Mild stresses can have hormetic effects not only at young age, but also at older ages.

However, this could depend on the trait under study as applying the mild stress at old age can also have no effect. It could be that in some cases a mild stress at a young age is becoming a stronger stress at old age.

3: A mild stress applied at young age can have long-lasting effects (like a vaccine, in a way). This is obviously shown as an increased lifespan, but not only, as survival to a severe stress can be increased at old age. In addition, the positive effects can be observed for life, whatever its length could be, and not only for a fixed duration. This could be of a particular importance for human therapy issues if this would also be observed in clinical studies.

4:

The positive effects of two different mild stresses can be additive, which means that the addition of two mild stresses is not inducing a strong stress with deleterious effects, provided these two mild stresses have positive effects. By contrast, if one of these mild stresses has negative effects on a given trait, the positive effects of the other stress can be minimised and even nullified. Turning to therapy issues, it would mean that a risk-benefit assessment is needed if combining two mild stresses (e.g. sauna and physical activity) to be sure that their effects are additive in all cases. To consider a fictitious example, if sauna and physical activity could add their positive effects on cardio-vascular mortality but increase the risk for stroke, while each mild stress has a positive effect on the occurrence of stroke, combining the two mild stresses would be an issue despite the positive effects on cardio-vascular mortality. Finally, it seems that combining three mild stresses does not give better positive effects than combining two ones, maybe because their combination brings the strength of the combined stresses near the end of the hormetic zone (Fig. 1B).

All these studies point in the same direction: studying the effects of mild stress is useful and better knowing their features could pave the way for new tools in therapy and prevention of agerelated issues. However, translating the results of experimental studies in clinics is always a challenge and one cannot conclude that the results observed in animal models will be observed, mutatis mutandis, in human beings. -15 -Figure 3. Relative lifespan of D. melanogaster males flies subjected to hypergravity (HG: 3 or 5 g, 3 or 5 times the Earth's gravity level) for various durations (3 to 46 days). A positive effect of HG was never observed in females. Flies were either kept in vials of 15 virgin males ("group") or in individual vials ("individual"). In the experiments with a continuous line and in the "fractionated" groups, lifespan was observed daily from emergence. In the other experiments, lifespan was observed from the day of transfer to 1 g (only some flies died except if transfer from HG to 1 g occurred after the age of 46 days). Each point is the mean of ca 60 flies (redrawn from Table 1 in Le [START_REF] Bourg | A mild stress due to hypergravity exposure at young age increases longevity in Drosophila melanogaster males[END_REF], except in the fractionated experiment for which it is 75. In this last experiment, flies were kept for 12 days in HG in 3 periods of 4 days separated by 3 days at 1 g.

Figures

Figure 1 .

 1 Figure 1. A. Theoretical hormetic curve showing, as the dose is increasing (abscissae), the

  Figure 1. A. Theoretical hormetic curve showing, as the dose is increasing (abscissae), the point of maximal hormetic effect and the no observed adverse effect level. The plus sign, on the ordinates, indicates a positive effect (e.g. a longer lifespan) and the minus one a deleterious effect. B. Proposal for a new theoretical hormetic curve, taking into account experimental results, the maximal hormetic effect point being replaced with a maximal hormetic zone.

Figure 2 .

 2 Figure 2. Relative thermotolerance and lifespan of C. elegans nematodes subjected to a pretreatment at 35 °C. Thermotolerance is the survival time at 35 °C (hours) and lifespan is observed at 20 °C (days). Each point is the mean of 33-55 worms for thermotolerance and of 283-584 ones for lifespan (redrawn from Cypser and Johnson 2002).

Figure 4 .

 4 Figure 4. A. Mean lifespan ± SEM of D. melanogaster female flies subjected to one or up to 4 heat shocks at 36 °C at successive ages (3, 6, 9, 12 days of age, total n is ca 400, redrawn from table 1 in Hercus et al. 2003). B. Mean lifespan ± SEM of C. elegans nematodes subjected to one or up to 4 heat shocks at 30 °C (TJ1060) or 33 °C (N2) at successive ages (4, 8, 12, 16 days of age, for each point n = 76-137, redrawn from table 1 in Olsen et al. 2006).

Figure 5 .

 5 Figure 5. A. Mean lifespan ± SEM of C. elegans nematodes subjected to one heat shock at 30 °C (TJ1060) or 33 °C (N2) at various ages (n = 41-137, redrawn from table 1 in Olsen et al. 2006). The two left points are the same as the two left points in Fig. 4B. B. Mean lifespan or survival time at 37 °C ± SEM or D. melanogaster flies. Flies were cold-pretreated daily (0 °C for 60 min) or not during two periods of 5 days separated by 2 days, starting at 5, 12, 19, or 26 days of age (weeks 1-2, weeks 2-3, weeks 3-4, and weeks 4-5). Their lifespan from emergence (days, n is ca 100 for each bar), survival time at 37 °C observed at 6 weeks of age (minutes, n = 33-35), and lifespan after infection at 41 days of age with the fungus Beauveria bassiana (days, n = 25-37) were observed. Non-significant results in females are not shown (redrawn from Le Bourg 2011).

Figure 7 .

 7 Figure 7. Combination of two mild stresses, HG and mild cold stress, with opposite effects on mean lifespan ± SEM of males and females. Flies were cold-pretreated daily (0 °C for 60 min) or not during two periods of 5 days separated by 2 days, starting at 5 days of age, and lived either at 1 g or 5 g. Each bar is the mean of 86-101 flies (redrawn from Le Bourg 2012).