1 Introduction

Over the last several years, a substantial body of research has attempted to identify some of the potential determinants that may induce youths to continue living with their parents. Economists have primarily focused on parental economic resources (Edmonds et al. 2005; Manacorda and Moretti 2006; Battistin et al. 2009), labor market conditions for youth (Card and Lemieux 2000; Becker et al. 2010), prevailing characteristics in housing markets (Börsch-Supan 1986; Ermisch 1999; Alessie et al. 2004) and cultural factors (Giuliano 2007; Alesina and Giuliano 2011). While this investigation is particularly relevant for Italy and other Southern European countries, such as Spain and Greece, where young people tend to remain with their parents until their late 20s and early 30s, leaving home only when they get married, the ways in which children respond to these factors have attracted increasing attention in the public policy debate in most European countries. For example, policymakers may be interested in reducing the adverse impact of delayed cohabitation on an array of children’s outcomes, including individual motivations and ambitions, reservation wages, labor market entry and geographical mobility (Billari and Tabellini 2010). A further cause of concern involves the phenomenon of falling fertility rates associated with prolonged co-residence (Giuliano 2007). Combined with the effects of population aging, this phenomenon raises the elderly dependency ratio, thereby contributing to placing extra pressure on the long-term financial sustainability of pension systems.

In the literature to date, many studies have shown that parental retirement significantly affects children’s living arrangements decisions, thus suggesting that household composition responds to changes in household income. For example, Edmonds et al. (2005), exploiting a special feature of the South African pension system as a source of exogenous variation in household income, show that in African households, when a woman becomes pension eligible, there is a rise in the numbers of young women of childbearing age and children younger than five but a fall in the number of prime working-age women, who leave the parental home in search of work. Using a similar identification strategy from the exogenous variability in the Italian pension reforms during the 1990s, Manacorda and Moretti (2006) and Battistin et al. (2009) also show that there are sizeable changes in household composition when a parent becomes pension eligible. However, while both studies find that parental retirement in Italy induces a significant decline in the number of adult children living with their parents, they offer two competing explanations for this pattern. On the one hand, Manacorda and Moretti (2006) argue that once parents retire, they are no longer able to make a financial transfer to their children and thus are unable to bribe them to stay at home because of the drop in their post-retirement income. On the other hand, Battistin et al. (2009) emphasize that liquidity considerations are unlikely to play a role because Italy is one of the few European countries where most Italian employees receive a generous lump-sum payment upon retirement. Therefore, they suggest that parents may use part of their severance payment to buy a house for their sons and daughters, who can then leave the parental home. Nonetheless, not only changes in family income but also social factors may alter children’s decisions to leave the parental home. For example, Angelini and Laferrère (2013) find that the nest-leaving age is influenced not only by the parental income but also by the housing quality. The authors point out that the housing quality effects are indeed important: children’s nest-leaving is delayed with a more comfortable, less crowded home or which offers more privacy.

Overall, the lack of a cross-country analysis severely limits the ability to clarify whether the housing emancipation of young adults upon parents’ retirement can be attributed to cash problems faced by parents, as suggested by Manacorda and Moretti (2006), to the receipt of a sizeable retirement allowance, as noted by Battistin et al. (2009), or to social factors, including, for instance, housing characteristics at the time of children’s nest-leaving. Thus, there is a need for empirical work to test which of the channels dominates in practice.

This paper contributes to the extant literature by using a European dataset to investigate whether and to what extent paternal retirement affects children’s nest-leaving, and then to test the relative weight of these alternative hypotheses and shed some light on the mechanism. To address problems of reverse causation and endogeneity of paternal retirement, I estimate a bivariate discrete-time hazard model with shared frailty (Abbring and Van den Berg 2003) for the impact of paternal retirement on the timing of children’s nest-leaving. Furthermore, to provide random variation in the timing of paternal retirement, I strengthen my identification strategy by employing changes in eligibility rules for early retirement benefits that were implemented across European countries during the period 1961–2007 as an exclusion restriction. To the best of my knowledge, this is the first paper that makes use of this exogenous source of variation to children’s living arrangements to assess whether and to what extent paternal retirement caused their children to leave the nest. Compared to the linear IV strategy, the hazard specification provides a more appropriate statistical framework for modeling time-to-event/survival outcomes and accounting for right-censoring, thereby allowing me to overcome certain limitations faced by previous IV studies. Finally, the bivariate hazard model offers greater flexibility in handling nonlinear baseline hazards and nonlinear effects of covariates and provides a novel approach to identifying treatment effects by modeling unobserved heterogeneity explicitly through bivariate specification.

To conduct this analysis, I use data from the second wave (2006) of the Survey of Health, Ageing and Retirement in Europe (SHARE). This European dataset has three important features. First, it collects data on the current economic, health and family conditions of over 30,000 individuals aged fifty and above in several European countries. Second, it provides retrospective information on the retirement age of the respondents and the nest-leaving ages of their children. This information is exploited to construct duration variables that indicate the time elapsed before each event occurs. Lastly, because it is designed to be cross-nationally comparable, this dataset enables me to properly conduct a multi-country analysis. Furthermore, I employ data regarding European early retirement legislation by relying on Angelini et al. (2009), Mazzonna and Peracchi (2012) and the country-specific studies discussed in Gruber and Wise (2004). It should be noted, however, that across the countries considered in the present investigation there are very different cultural histories, labor market institutions and social characteristics. Such differences may play a lasting role in explaining the substantial heterogeneity in the ages of children when they leave home across Europe (Aassve et al. 2002; Billari et al. 2001) and may not be entirely captured by including country fixed effects in the model estimated using the pooled sample from multiple countries. To mitigate this concern, I conduct the main analysis by European region. These regions correspond to the geographical aggregation into Northern European countries (Sweden, Denmark and the Netherlands), Central European countries (Austria, Germany, Switzerland, France and Belgium) and Southern European countries (Italy, Spain and Greece). According to the previous literature (see, for example, Albertini et al. 2007; Albertini and Kohli 2013), this aggregation is particularly relevant because it reflects profound differences in welfare states and family regimes across the above-mentioned country groups. One implication of this division is that the conditional impact of early retirement eligibility rules on paternal retirement and children’s nest-leaving outcomes is allowed to vary between Northern, Central and Southern European countries.

Overall, my results demonstrate that paternal retirement has a positive and significant effect on the timing of children’s nest-leaving only in Southern European countries. In this European region, the magnitude of the effect varies between 1.2 and 5 %, and there are no significant differences between sons and daughters. Focusing on Southern Europe, I find that the mechanism through which this pattern may occur remains an open issue because it cannot be attributed to families’ liquidity problems or a severance payment at the time of paternal retirement. One must probably focus on channels involving the provision of informal child care provided by grandparents or the home quality at the time of children’s nest-leaving. These findings are robust to a number of specification checks. On the policy side, the results of this paper suggest that in Southern Europe there are potentially unintended and undesirable consequences of pension reforms that raise the retirement age on decisions by young people to move out of their parents’ homes. Therefore, it is important that such pension reforms are accompanied by policy programs (e.g., interventions in the housing market) that encourage home-leaving of young adults.

The remainder of this paper is organized as follows. The next section presents a description of the data and provides background information on the eligibility ages for retirement in Europe. Section 3 describes the empirical specification and identification strategy. The main results of the paper are presented in Sects. 4, and 5 illustrates the robustness checks. I discuss the results in Sect. 6, and concluding remarks are provided in Sect. 7.

2 Data and institutional context

In my empirical analysis, I draw data from the Survey of Health, Ageing and Retirement in Europe (SHARE). This survey collects key information on demographics, current socio-economic status, health, expectations and social and family networks for nationally representative samples of European individuals aged fifty and above who speak the official language of their respective countries and who do not live abroad or in an institution, plus their spouses or partners irrespective of age. In this paper, I use data from the second wave collected in 2006/2007. The main advantage of this data source lies in the representativeness of the sample of elderly individuals in Europe because this survey is constructed to ensure the comparability of the analysis across the different countries. In this study, I present evidence from eleven countries for which I was able to collect information on the legislated early and normal ages at which individuals become eligible for a public old-age pension. These countries cover the various regions of continental Europe, ranging from Scandinavia (Sweden and Denmark), through Central Europe (Austria, Belgium, France, Germany, Switzerland and the Netherlands) and the Mediterranean countries (Italy, Spain and Greece).

In my sample selection, I constrain the sample of parents to fathers because of the problems associated with labor market interruptions that typically characterize the careers of women of childbearing age. Manacorda and Moretti (2006) and Battistin et al. (2009) also focus on fathers. Moreover, I restrict my attention to fathers who were either working or retired at the time of the survey, who have at least one biological child, and who were born between 1920 and 1957. Overall, these cohorts of fathers were affected by changes in the eligibility for old-age and early retirement benefits resulting from reforms that gradually came into effect across Europe over the period from 1961 to 2007 to respond to the demographic transition. To construct the sample of children, I include all children, both first-born and later-born children, and the cohorts of interest were born between 1940 and 1988. The choice of this interval allows me to consider virtually all the cohorts of children who were at least 18 at the time of the interview. I then link the socio-demographic characteristics of each child to the data of the corresponding father to create an intergenerational dataset. After these restrictions, I obtain a working sample of parents that contains 4935 fathers and a sample that consists of 10,720 children (5525 sons and 5195 daughters).Footnote 1 The distribution of the sample of fathers as well as the sample of children across the countries is presented in Table 1.

Table 1 Sample of fathers and children, by country
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Descriptive statistics on the primary variables of interest are reported in Table 2. As expected, the vast majority of the fathers (72 %) are retired in the interview year of wave 2. The individuals in my sample of children’s generation are, on average, 38 years old, 52 % are men and they have much better educational outcomes than their fathers (approximately 40 % of adult children have completed their undergraduate or graduate studies versus 23 % of the first generation).

Table 2 Summary statistics, sample of fathers and children
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To determine the retirement age of the fathers and age at which children leave the nest, I exploit recall information from the following two questions in the questionnaire asked to the parents: “In what year did you retire?” and “In what year did the child move from the parental household?”. The availability of such information relating events that occurred at some point in time before the year of the survey is essential because it allows for the creation of a retrospective panel dataset. For this reason, to conduct the analysis, I assume that individuals can locate past events along the time-line with adequate precision. While these retrospective data are self-reported and may be susceptible to recall error that may bias coefficient estimates, it is reassuring that Korbmacher (2014) finds that overall, the majority of respondents report their retirement year correctly. Some limitations of my data are worth mentioning. First, with the exception of the year of nest-leaving, I lack any source of time-varying information on children, such as the year of marriage, the year young people left education or their employment history. Second, I lack information regarding the reason for children’s nest-leaving, and there is no information on the characteristics of the house at the time of children’s moving-out.

As discussed in the introduction, I conduct the main analysis by grouping countries into Southern (Italy, Spain and Greece), Northern (Sweden, Denmark and the Netherlands) and Central (Austria, Germany, Switzerland, France and Belgium) Europe. Figure 1 illustrates the mean age at which children leave the nest by gender and country group. As expected, young adults living in Southern Europe moved out much later than their counterparts in the other regions. To be more specific, compared to youths in Northern European countries, Italians, Spanish and Greek children left approximately 5 years later (26.9 years in Southern Europe vs 22.1 years in Northern Europe). Young people in the Central European countries fall somewhere between these extremes. The figure also shows the presence of a gender gap in nest-leaving age: daughters leave the parental home earlier than sons, ranging from approximately 1 year in Northern and Central Europe to approximately 2 years in Southern Europe. This gap can partly be explained by the fact that age at marriage, which is positively correlated with the postponement of home-leaving, is lower for women.Footnote 2

Fig. 1
figure 1

Children’s nest-leaving mean age, by European region

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With regard to the institutional context, I use data on early eligibility ages across the above-mentioned European countries, building on the work by Angelini et al. (2009), Mazzonna and Peracchi (2012) and Gruber and Wise (2004).Footnote 3 Figure 2 shows the distribution of the actual paternal retirement age for each country. The vertical red and blue lines denote, respectively, the eligibility ages for old-age and early retirement benefits, whereas the red and blue areas indicate changes in eligibility ages for the cohorts in my sample. As expected, there are sizeable jumps in retirement rates that occur at early and standard retirement ages. The overall picture reveals that across eleven countries with very different social security systems and labor market institutions, there are noticeable differences in many respects. For example, the normal age of eligibility for pension benefits is currently set at 65 in almost all countries, but ranges from a low of 60 in a couple of countries (Italy and France) to a high of 67 in some Nordic countries (Denmark and Sweden). A further feature worth emphasizing is that there is even larger multi-country variability in early eligibility ages. Especially striking is that the early retirement age ranges from 52 in Italy before 1998 to 61 in Sweden after 1997.

Fig. 2
figure 2

Histogram of father’s retirement age, by country. Notes: Source: Angelini et al. (2009), Mazzonna and Peracchi (2012), Gruber and Wise (2004) and Duval (2003). The vertical blue and red lines, respectively, mark the eligibility ages for early and normal retirement age, whereas the blue and red areas represent changes in the eligibility ages for the cohorts in my sample (Color figure online)

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3 Empirical specification

3.1 Bivariate discrete-time hazard model with shared frailty

In this section, I describe my approach to investigating the extent to which paternal retirement affects the probability of the first nest-leaving of children. To do this, I use a bivariate discrete-time hazard model with shared frailty. This novel strategy for identifying treatment effects in the presence of an endogenous treatment when both the treatment and outcome are survival variables of a duration process was pioneered by Abbring and Van den Berg (2003). This class of models is specified in terms of the hazard, defined as the conditional probability of an event occurring at a point in time provided that it has not already occurred. In this study, I am interested in jointly estimating a bivariate hazard model for the first episode of a child leaving the nest (first equation) and the first time that the father retires (second equation), allowing for correlations between the unobserved heterogeneity terms that affect these two transitions (shared frailty).Footnote 4 Formally, the model can be written in the following manner:

$$\begin{aligned} {\left\{\begin{array}{ll} h_{1,it} =\lambda _{1}\left( t\right) \phi _{1}\left( X_{it}\beta _{1}+\delta Retired_{it}+u_{1,i}\right) \\ h_{2,it} =\lambda _{2}\left( t\right) \phi _{2}\left( X_{it}\beta _{2}+\gamma Eligible_{it}+u_{2,i}\right) \end{array}\right. } \end{aligned}$$
(1)

where the unit of observation i represents the child–father pair residing in a given country, the outcome \(h_{1,it}\) is the hazard that child i leaves the parental home at age t, \(h_{2,it}\) refers to the hazard that father i retires at age t, and u reflects the individual-level, time-invariant, unobserved heterogeneity. The terms \(\lambda _{1}(t)\) and \(\lambda _{2}(t)\) represent the baseline hazard functions for the first and second equations, respectively. These functions capture the time dependence of the transitions into the two states, and they are modeled using a flexible piecewise constant function.Footnote 5 Formally, the baseline hazard can be written as follows:

$$\begin{aligned} \lambda _{j}(t)=\sum _{s}^{20}\lambda _{js}I_{s}(t) \end{aligned}$$
(2)

where j \((j=1,2)\) refers to the equation, s indexes the 1-year intervals and \(I_{s}(t)\) are dummy variables that take value 1 if the recorded duration is in the s interval. I use an open interval from \(s=19\) onwards because after 19 years the survival and censoring times occur with insufficient frequency to use finer intervals. Because I include a constant in the model, \(\lambda _{11}\) and \(\lambda _{21}\) are normalized to 0.

As for the hazard functions \(\phi _{1}\) and \(\phi _{2}\), my preferred specification uses a logistic regression. The variable \(X_{it}\) is a matrix of individual controls that may affect the hazard. Specifically, I include child’s age and age squared, child’s gender, a dummy that takes value 1 if the child is married at the time of the interview, household size, and an indicator for the father having a college-level education or above (\(\hbox {ISCED}\ge 5\), tertiary education) or a high school education (ISCED = 3 or 4, secondary and post-secondary education). I do not include paternal occupation because of the large fraction of missing observations (approximately 30 % of the cross-sectional sample); however, education is strongly correlated with occupation. Both equations also entail a full set of country dummies that capture country-level, time-invariant confounding factors affecting co-residence and paternal retirement. Such factors might include, for example, cross-national differences in preferences and attitudes regarding co-residence and retirement due to discrepancies in cultural and institutional backgrounds. In the variable \(X_{it}\), I then add birth cohort fixed effects for fathers (in 1-year intervals) to control for possible cohort trends in retirement, i.e., younger cohorts of fathers are likely to retire later, and include controls for the birth order of the child. \(Retired_{it}\) is my variable of interest and is equal to 1 if father i is retired at time t. Thus, the treatment effect \(\delta\) indicates whether the child becomes more likely to leave the nest upon the father’s retirement.

With regard to the unobserved heterogeneity terms \(u_{1,i}\) and \(u_{2,i}\), I follow the latent class approach adopted by Melberg et al. (2010), who estimate a bivariate hazard model for the impact of cannabis on the risk of consuming hard drugs using a finite mixture framework.Footnote 6 Therefore, unobserved heterogeneity is assumed to divide the sample into two latent classes.Footnote 7 The intuitive explanation for the presence of these two classes is that individuals are clustered into two sub-groups that differ in terms of their unobservable propensity for nest-leaving and retirement. For instance, as I demonstrate in Sect. 5, one group is composed of young people who appear more likely to leave the nest later, whereas the other is more prone to leave the parental home earlier. Consistent with Melberg et al. (2010), I then allow all the coefficients to differ across the two latent groups; other studies (see, for instance, Pudney 2003; van Ours 2003), in which the unobserved heterogeneity is assumed to affect only the constant term, limit this flexibility.

Allowing for correlated unobserved heterogeneity is crucial to the identification of the treatment effect \(\delta\), because there may be a potential problem of reverse causality or because there may be individual-level, unobservable factors, such as paternal ability, that determine both paternal retirement and children’s decisions to leave home. In particular, if unobservable heterogeneity exists and is ignored, the estimated coefficient may be vulnerable to omitted variable bias. Abbring and Van den Berg (2003) show that an appealing feature of the shared frailty model is that it is identified without the need for any exclusion restrictions or assumptions about the functional form of either the baseline hazard or the joint distribution of the unobserved heterogeneity, as long as the actual timing of the treatment (paternal retirement) is random and is unaffected by the anticipation of the subsequent outcome (children’s nest-leaving). However, there may still exist concerns that these two latter conditions are not entirely satisfied in model (1). The main threat to identification is that, even after correlation between frailty terms has been corrected for, the precise timing of the treatment may not occur randomly at year t, i.e., the “no anticipation” assumption is unlikely to hold. As is well known, retirement is a life event that affects various decisions of the family, including consumption, saving, fertility and labor supply. For this reason, children may be able to predict when their fathers will retire, and in response to this expected event, they may modify their lifestyle behaviors and their propensity to become independent. Hence, the anticipation of paternal retirement by adult children would violate one of the key identification assumptions described above, thereby producing biased estimates. To circumvent this problem, I strengthen the identification by providing an exclusion restriction for paternal retirement. The exclusion restriction that I use is based on cross-country early retirement rules and is measured by the indicator \(Eligible_{it}\), which equals 1 if father i residing in a given country was eligible for early retirement benefits at age t. These early retirement rules are not only correlated with retirement decisions (Gruber and Wise 2004), but they also provide a potentially valid instrument. Manacorda and Moretti (2006) and Battistin et al. (2009), using an instrumental variable (IV) strategy, recognize this instrument as valid because pension reforms produce variation in paternal retirement that is credibly exogenous and unlikely to be related to unobservable characteristics of the fathers that might explain the different nest-leaving outcomes of their offspring.Footnote 8 As a result, once the correlation between unobserved factors across both equations and the non-randomness of the timing of the treatment have been corrected for, the remaining difference between the probability of nest-leaving before and after paternal retirement can be interpreted as a causal effect of paternal retirement. To account for within-family correlation, all standard errors are clustered at the household level.Footnote 9

To estimate model (1) using maximum likelihood, I expand the data from a cross-section to a panel dataset by exploiting the retrospective information on the year in which the father retired and his child left home. Thus, each individual i \(\left( i=1,\ldots ,n\right)\) is associated with multiple time periods \(t_{i}\) \(\left( t_{i}=1,\ldots ,T_{is}\right)\), where \(T_{is}\) is the total number of years subject i was at risk for the event.Footnote 10 For simplicity of exposition, it is useful to distinguish between the two equations \((j=1,2)\) because they refer to two different outcomes. For the first equation, age 18 is assumed to be the initial period in which the exposure to the risk of nest-leaving begins,Footnote 11 such that \(t_{i}\) goes until the age at which the first event is observed (the child’s departure from the parental home). If this event does not occur by the end of the survey, then the child is a right-censored observation and \(t_{i}\) lasts until her age at the time of the interview. A similar reasoning applies to the second equation, where I now define the father’s age when his child is 18 as the onset of risk,Footnote 12 thereby allowing \(t_{i}\) to go until either the father’s age at which the second event occurs (his retirement) or the father’s age at the time of the survey if the father is employed at the end of the observation period (right-censored case). As a result of this reorganization of the data, I obtain an unbalanced panel, as each individual in the two equations is associated with a different number of time units. Furthermore, a new binary dependent variable \(y_{it}\) must be created. If individual i is right-censored, then \(y_{it}\) is always equal to zero. If individual i is not censored, \(y_{it}\) takes a value of zero for all but the last of i’s periods (i.e., year \(1,\ldots , T_{is}-1\)) and takes a value of one in the last period (i.e., year \(T_{is}\)). After having experienced the event, the subject no longer contributes to the risk set and is dropped from the sample (right-truncated cases). It is worth noting that one of the main advantages of the duration analysis over the linear IV setting adopted by previous studies is the allowance for censoring, which leads to the elimination of any constraints on the age at which children left their parents’ home. For example, Manacorda and Moretti (2006) focus only on youths aged 18–30, whereas Billari and Tabellini (2010) and Becker et al. (2010) limit their analysis to adult children aged up to 35 years old.

Consistent with Melberg et al. (2010), the overall log-likelihood function for the bivariate model (1) depends on both the hazard function and the survival function and is given by:

$$\begin{aligned} logL=\sum _{i=1}^{n}\left\{ \sum _{k=1}^{2}\pi _{k}\left\{ \sum _{j=1}^{2}\left\{ \sum _{t=1}^{T_{i,j}-d_{i,j}}log\left[ 1-h(\theta _{k})_{kj,it}\right] +d_{i,j}log\left[ h(\theta _{k})_{kj,it}\right] \right\} \right\} \right\} \end{aligned}$$
(3)

where the prior probabilities \(\pi _{k}\) (each \(\pi _{k}\ge 0 \text{ and }\sum _{k=1}^{2}\pi _{k}=1\)) represent the proportion of the sample composing each latent class k. The variable \(d_{i,j}\) is a dummy with a value of 1 if individuals are non-censored and a value of 0 if observations are right-censored, and \(\theta _{k}\) is a vector of parameters that includes \(\beta _{1}\), \(\delta\), \(\beta _{2}\) and \(\gamma\) and that varies also at the latent class level. It is worth noting that the likelihood of the non-censored individuals differs from that of the censored ones. For the former group, the likelihood is composed of two elements: the survival function from \(t=1\) to \(t=T-1\) and the hazard function in the last period \(t=T\) the subject was exposed to the risk. For the latter group, because the censored individuals are never exposed to the event, the likelihood is given solely by the survival function from \(t=1\) to \(t=T\).

To maximize (3) under the presence of unobserved heterogeneity, I follow Melberg et al. (2010) and employ the expectation-maximization (EM) algorithm.Footnote 13

4 Main results

Before presenting the results, I provide a visual analysis of the evolution of the estimated hazard function for nest-leaving. In particular, Fig. 3 illustrates the pattern of nest-leaving for each European region, with the variable time measured in terms of the number of years since the child turned 18. Overall, this figure shows a number of cross-region differences. These differences include the following: (a) in the beginning, in Northern Europe, the hazard of nest-leaving for sons and daughters is considerably higher compared to that in the other country regions; (b) in all country groups, daughters initially have significantly higher rates of nest-leaving compared to those of sons; (c) in Southern Europe, there is a proportion of adult children who are at high risk of leaving home even when they are in their 40s, thereby providing further evidence of the prolonged cohabitation of Mediterranean youths in their parents’ homes.Footnote 14

Fig. 3
figure 3

Empirical hazard rate of children’s nest-leaving, by European region. Notes This figure plots the estimated hazard function of nest-leaving of children by European region. This hazard function is estimated using a nonparametric kernel-smoothing methodology (STS package in STATA). Recall that children who were <18 (i.e., \(t<0\) ) are left-truncated. Notice that the reason why the smoothed hazard estimate is not depicted for \(t<5\) is associated with the choice of the bandwidth

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4.1 Instrumental variable analysis

Although the bivariate hazard model described in Sect. 3 provides the most appropriate description of the relationship between paternal retirement and the timing of children’s nest-leaving, there may still be concerns regarding the sensitivity of my results to their stability or to the parametric assumptions made in the estimation. To address these concerns, I begin my analysis with the following linear version of model (1) estimated using two stage least squares (2SLS):

$$\begin{aligned} Pr(H_{it}=1)=\alpha +\beta Retired_{it}+\gamma X_{it}+\epsilon _{it} \end{aligned}$$
(4)

where the outcome variable \(H_{it}\) is a dummy taking the value 1 if a child i residing in a given country left the parental home at age t. The treatment dummy \(Retired_{it}\) and the variable \(X_{it}\) are defined in the same way as in Sect. 3. Therefore, \(X_{it}\) contains child’s age and age squared, child’s gender, a dummy that takes value 1 if the child is married at the time of the interview, household size, paternal education, country fixed effects, cohort fixed effects for fathers, and controls for the birth order of the child. Following Manacorda and Moretti (2006), I focus on youth aged 18–30 years. Finally, \(\epsilon _{it}\) represents an idiosyncratic error term, which is presumably correlated with the outcome variable because it embodies unobserved factors of fathers, including ability, which might affect children’s home-leaving decisions.

I identify the causal effect of paternal retirement on children’s nest-leaving using cross-country changes in eligibility rules for early retirement benefits for the period 1961–2007 as an instrument for paternal retirement. As discussed in Sect. 3, this instrument is recognized to be relevant and arguably exogenous to children’s living arrangements. In this setup, the first stage regression is given by:

$$\begin{aligned} Retired_{it}=\delta _{0}+\delta _{1}Eligibility_{it}+\pi X_{it}+\nu _{it} \end{aligned}$$
(5)

where the dummy \(Eligibility_{it}\) represents the instrument introduced in Sect. 3. It is important to acknowledge that this instrumental variable strategy is relevant only for the subset of compliers, i.e., fathers who retire as a consequence of early retirement schemes.

Panel A of Table 3 reports the 2SLS results. The treatment dummy on paternal retirement is positive and significant at the 1 % level only for Southern Europe (see column 1). This dummy variable, however, becomes negative and non-significant for Northern Europe (see column 2), and negative and significant only at the 10 % level for Central European countries (see column 3). In the pooled sample the dummy variable becomes positive although not significant (see column 4). Panel B contains the first stage results. As expected, these estimates indicate that eligibility for early retirement benefits is an important determinant for paternal retirement. Altogether, the IV analysis provides evidence that only for Southern Europe there is a positive causal relation between paternal retirement and children’s nest-leaving, a finding that calls for further analysis and explanation.

Table 3 Effects of paternal retirement on children’s nest-leaving, IV analysis
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4.2 Model without shared frailty

I begin by estimating a discrete-time duration model for the hazards of children leaving the nest and paternal retirement without correcting for correlated unobserved heterogeneity. Thus, each equation in model (1) is estimated using a separate logistic hazard equation. Table 4 contains the results, with average marginal effects of covariates on the hazard associated with retirement listed next to their average marginal effects on the hazard of children’s nest-leaving. In each specification, I include child’s age and age squared, child’s gender, a dummy that takes value 1 if the child is married at the time of the interview, household size, paternal education, country fixed effects, cohort fixed effects for fathers, and include controls for the birth order of the child. Specifically, in columns 1, 3 and 5, I estimate the equation explaining the probability of leaving the nest for the first time by dividing the sample into Southern, Northern and Central European countries. When examining Southern Europe (see column 1), I find that the estimated effect of paternal retirement is positive and strongly statistically significant (at the 1 % level). Paternal retirement implies an increase in the probability of children’s nest-leaving of 2 %. However, when focusing on the Northern and Central European countries (see columns 3 and 5), the coefficient on paternal retirement becomes insignificant, and the magnitude becomes 0.036 and 0.007, respectively. Overall, the non-significant effects obtained for Northern and Central Europe are presumably because most youths have already left their parental homes at the time of their fathers’ retirement.Footnote 15 Moreover, I find that coefficients on household size are negatively correlated with the probability of children’s nest-leaving, and that the probability to leave the parental home is larger for married or female adult children.Footnote 16 As expected, in each macro-region, the eligibility status for early retirement benefits matters for the hazard of paternal retirement (see columns 2, 4 and 6). While eligible fathers are more likely to retire, the differences in the magnitude of the coefficient on paternal eligibility are remarkable, ranging from 2.7 % in Northern Europe to 8.2 % in Southern Europe. In columns 7 and 8, I separately estimate the two equations in model (1) using the pooled sample. Interestingly, the point estimate of the coefficient of interest remains positive and significant, with a magnitude of 0.022. It seems clear that this significant impact on the full sample is driven by the highly significant effects of paternal retirement obtained from the regression on the sample of Southern European countries (see column 1).

In sum, although these correlations may suffer from problems of confounding, they provide a first indication that paternal retirement is significantly associated with a higher probability of first nest-leaving by children (first equation) only in the Mediterranean countries, and that early retirement rules strongly predict the hazard of paternal retirement (second equation). In the next subsection, I attempt to establish whether this positive and significant correlation obtained from the regression on the sample of Southern European countries has a causal interpretation.

4.3 Model with shared frailty

The primary concern regarding the point estimates presented in Table 4 is that they may not adequately account for the correlation between unobserved characteristics that affect children’s nest-leaving and unobserved factors that determine paternal retirement, thereby generating omitted variable bias.

Table 4 Model for the hazard of children’s nest-leaving and paternal retirement—without shared frailty
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To address this concern, I allow for the possibility of correlated unobserved heterogeneity terms across both equations by using the latent class approach suggested by Melberg et al. (2010) in which individuals are divided into two sub-groups of the population. Table 5 presents the estimation results of logistic regressions on the hazard of children’s nest-leaving for Italy, Greece and Spain, countries for which I found a positive and significant association between paternal retirement and the probability of first nest-leaving.

Table 5 Model for the hazard of children’s nest-leaving in Southern Europe—with shared frailty
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To facilitate comparisons, in column 1, I report the average marginal effects corresponding to the model in which unobserved heterogeneity is ignored (see, also, column 1 of Table 4). In columns 2 and 3, I present the same predicted effects when unobserved heterogeneity is allowed for by using the individual probabilities of belonging to Group 1 and Group 2 as weights, respectively. Thus, a different logistic hazard regression is estimated for each of the two groups. The results suggest that paternal retirement is a statistically significant predictor of children’s nest-leaving. For those belonging to Group 1, the treatment effect of paternal retirement is positive and strongly statistically significant (at the 1 % level). With respect to the magnitude, paternal retirement increases the probability of children’s first nest-leaving by 4.9 %. The treatment effect remains significant, albeit quantitatively less important (1.2 %), for those who belong to Group 2.Footnote 17

To learn more about the characteristics of the two groups, Table 6 displays summary statistics on selected covariates for Southern Europe. Specifically, individuals in the sample with a posterior probability of falling into Group 1 below the median are assigned to that group, whereas the remaining individuals are placed in Group 2. As evidenced in Table 6, these two groups differ substantially with respect to the proportion of retired fathers. For Group 1, this proportion is approximately 27 % greater than the mean of Group 2 (25 vs 19 %). Such large differences in the fraction of retired fathers can contribute to explaining why young people in Group 1 (labeled “low-propensity” nest-leaving types or “late” nest-leavers) are much more affected by paternal retirement than their counterparts in Group 2 (labeled “high-propensity” nest-leaving types or “early” nest-leavers). Interestingly, these two groups also differ in a number of other observable characteristics, such as educational outcomes and children’s age at time of leaving home. For instance, adult children in Group 1 are more likely to leave the parental home later and have better outcomes in terms of their own and their fathers’ education.

Table 6 Differences between unobserved groups in Southern Europe
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It is worth noting that when restricting the analysis to Northern Europe and Central Europe, I find that as expected, the dummy variable for paternal retirement is generally no longer statistically significant; therefore, for brevity, I do not report results from these regressions (the results are available from the author upon request).Footnote 18 Overall, the evidence presented above suggests that, although quantitatively small, there are positive causal effects of paternal retirement on the timing of first nest-leaving of children living in Southern European countries.

Finally, in an attempt to disentangle the treatment effects of paternal retirement on sons from the effects on daughters in Southern Europe, I consider the samples of male and female children separately. The results for sons and daughters are presented in columns 4–9 of Table 5. When restricting the analysis to sons (see columns 4–6), the coefficient on paternal retirement is 2.3 % in the model in which unobserved heterogeneity is ignored (see column 4), and varies between 5.2 % for individuals in Group 1 (see column 5) and 1.1 % for those belonging to Group 2 (see column 6). A similar pattern is observed in the regressions for daughters (see columns 7–9), with the difference being that the treatment effect for daughters in Group 2 is no longer significant, which may be partly due to the smaller sample size. However, these differences between sons and daughters are not significantly different from zero.

5 Sensitivity analysis

Before proceeding to discuss and test empirically the potential mechanisms, I perform a robustness analysis for Southern Europe to determine if the results change when I use a different specification of the model.

I begin by investigating the robustness of my estimates to the use of an alternative definition of the treatment dummy for paternal retirement. A common concern is that as children age, they are more likely to leave the parental home regardless of their fathers’ retirement status. To allow for this possibility, I define a time frame of 3 years and construct a binary variable that is set to 1 if the father retired prior to the child’s first move-out within the time frame and 0 otherwise. This approach is similar in spirit to that of van Ours (2003), who refers to this time frame as the “incubation period” to identify a gateway effect of cannabis on cocaine. The results are presented in Panel A of Table 7. Reassuringly, these parameter estimates resemble those obtained in the benchmark specification (see columns 1–3 of Table 5), with the only difference being that the magnitude of the estimated effects of paternal retirement becomes slightly smaller.

I then address the concern that the father may start receiving pension benefits only some years after his retirement year. To check the robustness of my results, I exploit information on the year in which the father first received pension benefits.Footnote 19 Thus, I re-estimate my model using an alternative treatment indicator variable set equal to 1 if father i collects pension income at time t. As the coefficients reported in Panel B of Table 7 show, the evidence remains substantially unchanged relative to the benchmark specification.

Table 7 Robustness checks, model for the hazard of children’s nest-leaving in Southern Europe
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6 Discussion for Southern Europe

In the literature on moving-out decisions, what remains largely unexplained is the mechanism regulating the positive causal relationship between paternal retirement and children’s nest-leaving. In this section, I start to fill this gap by focusing the analysis on Italy, Greece and Spain, countries for which I found a positive causal effect of paternal retirement.Footnote 20 A unique feature of these Southern European countries is that they can be divided into two groups. One group is composed of Italy and Greece, where there is a large bonus payment at the time of retirement that amounts to approximately three times the gross annual salary. The second group includes only Spain, where such severance payment does not exist, i.e., “unaffected” by the lump-sum payment upon retirement.Footnote 21 My information on severance arrangements is drawn from Holzmann et al. (2011), from personal communications with national experts and from other country-specific sources.Footnote 22 As previously mentioned, the literature would attribute this causal relationship mainly to two competing mechanisms. To provide an empirical test for these two mechanisms, I use model (1) and analyze the differential effects of paternal retirement by separating Southern Europe across the above-mentioned two groups.

To the extent that the Manacorda and Moretti mechanism is at play, I expect paternal retirement to bribe Italian and Greek adult children to stay at home longer as a consequence of the positive shock to the family’s liquidity associated with the retirement severance payment. However, the results reported in Panel A of Table 8 (columns 1–3) are in the opposite direction. For individuals belonging to Groups 1 and 2, the dummy variable for paternal retirement remains positive and highly statistically significant, with magnitudes of 5.4 and 1.2 %, respectively. This result indicates that cash problems faced by fathers at the time of retirement do not provide an entirely satisfactory explanation. On the other hand, if retirement severance payment mattered, as emphasized by Battistin et al. (2009), I would expect to find no evidence of significant effects of paternal retirement for Spain. Nevertheless, the coefficient estimates presented in columns 4–6 of Panel A largely contradict the prediction of this second hypothesis: for individuals in Group 1, the estimated coefficient on paternal retirement retains its significance, whereas for those in Group 2, the magnitude of the coefficient of interest becomes slightly larger with respect to the estimate in column 3, although is less precisely estimated. This result is what I expected given the substantial reduction in sample size.

One may still be concerned that Spain is not a comparable group or that in Italy and Greece self-employed workers are not entitled to retirement severance payment. To address these concerns, I propose an additional test: for Italy and Greece, I use the employed as the group which is characterized by the presence of the retirement severance pay and self-employed as the group which is unaffected by the retirement severance pay.Footnote 23 The results reported in Panel B of Table 8 indicate that overall, there are positive causal effects of paternal retirement on the timing of children’s nest-leaving for both the employed (columns 1–3) and the self-employed (columns 4–6), which I interpret as corroborating evidence that the drop in paternal post-retirement income or the boost in family’s income due to retirement severance payment does not provide a satisfactory explanation for the mechanism behind the decline in children’s cohabitation at paternal retirement.

Table 8 Changes in parental income, model for the hazard of children’s nest-leaving in Southern Europe
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For this reason, in parallel to financial considerations, it seems worthy to investigate other potential channels. In their study on the intergenerational effects of Italian pension reforms on fertility, Battistin et al. (2014) argue that the rise in retirement age has reduced the amount of informal child care provided by grandparents, which in turn has determined an increase in the children’s age at first child and of home-leaving. In particular, the authors find that an additional grandparent at home increases the likelihood of children’s nest-leaving by approximately 3 %; however, the authors do not consider grandmaternal and grandpaternal effects separately. Although this scenario can be applied to other Southern European countries, including Spain and Greece,Footnote 24 there is general consensus that grandmothers are the main providers of informal child care arrangements for their grandchildren (see, for instance, Richter et al. 1994). As discussed previously in the paper, female partners are excluded from the present analysis. Nevertheless, empirical literature has increasingly provided evidence that coupled individuals tend to plan their retirement decisions jointly (see, for example, Hurd 1990; Gustman and Steinmeier 2000; Stancanelli 2012). To account for the joint retirement hypothesis, in Table 9 I show that, when focusing on fathers whose spouses have never worked, there is a positive and quantitatively similar causal effect of paternal retirement on the likelihood of children’s nest-leaving but only for “late” nest-leaving types. Therefore, this result reveals the potential effect of grandparents’ supply of informal child care alongside other unexplained factors.

Table 9 Fathers whose wives never worked, model for the hazard of children’s nest-leaving in Southern Europe
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Anecdotal evidence invites the hypothesis that there may be a number of preference-related reasons that concern the conflicting relationship between retired fathers and their offspring: children’s departures from the parental home potentially stem from conflicting relationships with their fathers, which likely result from the paternal presence in the house upon retirement. In addition, Angelini and Laferrère (2013) emphasize that not only parental income but also the quality of the house or the desire for privacy are relevant determinants of nest-leaving outcomes. Unfortunately, it is difficult to verify this hypothesis with my data because, as already mentioned, the SHARE questionnaire does not provide information regarding the reasons for children’s nest-leaving. However, to partially address this limitation in the data, I can use a measure for overcrowding at the time of children’s nest-leaving as a proxy for the housing quality. More specifically, I create an indicator variable that is equal to 1 if the number of rooms per person is below the median for the given country.Footnote 25 To allow for the presence of household overcrowding, I estimate model (1) for Southern Europe in which I include the interaction between paternal retirement and the dummy variable for overcrowding. If the coefficient on the interaction term is positive and statistically significant, then it does appear that the housing quality is likely to play a role in explaining children’s decisions to leave their parental homes. Table 10 shows the parameter estimates. Overall, I find that the coefficient on the interaction between paternal retirement and the dummy variable for overcrowding is positive and significant (at the 10 % level). This result suggests that more children leave the nest upon paternal retirement with overcrowding, which can be interpreted as a housing quality or privacy effect.

Table 10 Housing quality effects, model for the hazard of children’s nest-leaving in Southern Europe
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7 Conclusion

In this paper, I examine the relationship between paternal retirement and the timing of housing emancipation of young adults in Europe. Taking advantage of the retrospective dimension of my micro data, I specify a bivariate discrete-time hazard model with shared frailty and exploit over time and cross-country variation in early retirement legislation. Overall, my regression results suggest that there is a positive and significant influence of paternal retirement on the probability of first nest-leaving of children living in Southern European countries. However, there is no clear evidence of positive and significant effects on children residing in Northern and Central European countries. I interpret this evidence as indicating that paternal retirement is a relevant explanatory variable of co-residence decisions only in Southern Europe, once differences in institutions, culture and other unobservable factors are controlled for.

Focusing on Southern Europe, I provide an empirical test for the two main financial channels by which paternal retirement may be considered to affect children’s co-residence. Comparing my cross-country evidence with important country-specific evidence obtained for Italy from two other studies (Manacorda and Moretti 2006; Battistin et al. 2009), it seems plausible to conclude that the increase in children’s nest-leaving around paternal retirement does not appear to be driven by changes in parental economic resources. Rather, one needs to look for channels involving the supply of informal child care provided by grandparents or the home quality at the time of children’s nest-leaving.

Empirical evidence that paternal retirement can affect children’s nest-leaving has relevant policy implications. It is well-known that because the population is rapidly aging in Europe, it is becoming increasingly important to maintain the long-term financial sustainability of pension systems. To achieve this goal, in the recent past European governments have primarily adopted a number of pension reforms that have raised the retirement age. However, the results of this paper suggest that in Southern Europe policy makers should also be aware that there may potentially be unintended and undesirable consequences of pension reforms on moving-out decisions of young people. Therefore, pension reforms should be accompanied by policy programs (e.g., interventions in the housing market) that encourage moving-out of young adults.