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Extracted abstract

Amidst young adults' increasing labour market insecurity and rates of parental co-residence, this article examines how unemployment and underexplored forms of non-standard employment (NSE)-underemployment and temporary and agency work (TAW)-are associated with inter-generational co-residence in the United Kingdom. Refining the feathered nest/gilded cage hypothesis to incorporate forms of non-NSE, we analyse how parental social class moderates this relationship across the transition to adulthood phase, driven by both protective and propellant motives. We estimate logistic regression models using the 2021-2024 waves of the UK Labour Force Survey, which allow for a precise identification of time-related underemployment and agency working. Results suggest that states of labour underutilization (underemployment) and impermanence (TAW) as well as unemployment are all associated with higher probabilities of parental co-residence relative to standard employment. This relationship is in part mediated by earnings disparities. Further, socio-economic background matters-the positive insecurity co-residence association is most pronounced amongst young adults from service-class backgrounds. This is consistent with a refined feathered nest/gilded cage hypothesis whereby higher parental resources facilitate co-residence at earlier phases of adulthood transitions, especially for young adults facing labour market insecurities, but this slightly tapers off with age.

Introduction

Attaining residential independence remains an expected part of a 'successful' transition to adulthood in many societies (Billari et al., 2021) . However, labour market insecurities and high housing costs make residential independence increasingly difficult to attain (Warner and Sharp, 2024) . In countries where welfare and income support policies for young adults have become more restricted, economic dependency of young adults on parents is prolonged, with families becoming increasingly important for adulthood transitions (Furlong and Cartmel, 2006; Arundel and Lennartz, 2017) . Moreover, the inter-generational bond between adult children and their parents has become more salient (Fingerman, Huo and Birditt, 2020) with growing expectations for parents to stay actively engaged in the lives of their children even after they have left the parental home (Gillespie, 2020; Sørensen and Nielsen, 2021) .

This 'active engagement' can come in the form of parental co-residence, which is driven by both parental resources and individual circumstances that change over the life course (Meggiolaro and Ongaro, 2024) . Although the parental home can be a comfort-zone and a preferred option for young adults (Schoon, 2020) , it is often a coping mechanism for economic insecurity (Roberts et al., 2016) . Amongst those who experience labour market insecurities such as being unemployed or in non-standard employment (NSE), parental co-residence may serve as a protective 'buffer' or a propellant 'launching pad'. The centrality of parental resources in moderating the relationship between insecurity and co-residence, and how this differs across the young adulthood phase, thus warrant closer inspection.

The UK context

inter-generational co-residence has been increasing in recent decades (Stone, Berrington and Falkingham, 2011; Esteve and Reher, 2021) because of delays in initial departure and increased returns (Stone, Berrington and Falkingham, 2014) . Economic insecurity, especially amongst those with lower education, has increased (Bell and Blanchflower, 2013; Palumbo et al., 2023) as a consequence of the collapse of the youth labour market during the late 1970s and 1980s (Schoon, 2020) , job flexibilization associated with globalization (Francesconi and Golsch, 2006; Maguire, 2020) , and restrictions in access to welfare and housing support since the 1980s (Furlong and Cartmel, 2006; Berrington and Stone, 2014) . This 'precarization' accelerated after the 2008-2009 global financial crisis, which disproportionately affected youth unemployment and wage levels (Sironi, 2018) and reduced access to credit (e.g., for mortgage loans) (Lennartz, Arundel and Ronald, 2016) . Most recently, young people's transitions to economic independence have been stalled by the economic impact of the COVID-19 pandemic (Crossley et al., 2023) and the subsequent cost-of-living crisis. Rapid inflation of basic goods disproportionately affected those on low incomes with young adults particularly affected by increases in the cost of private rented accommodation (Clegg and Corlett, 2024) .

Given these structural constraints, young adults need further support in achieving residential independence. Repeated welfare cuts, including reductions in availability of state-subsidized housing (Berrington and Stone, 2014) , mean that this support is less likely to be state-provided, with financial risks becoming more individualized and parental resources increasingly important (Arundel and Lennartz, 2017; Gilligan, Karraker and Jasper, 2018) .

Research questions and contributions

These developments make the United Kingdom a relevant context to appraise the relationship between labour market insecurity and parental co-residence, and the moderating role of parental background, across the adulthood transition phase. We conceptualize 'labour market insecurity' to encompass two understudied forms of NSE-underemployment and TAW, as well as unemployment. We ask: (i) what is the association between insecurity and parental co-residence amongst economically active young adults? (ii) Is this relationship mediated by earnings? (iii) How does this relationship vary by parental social class? and (iv) Do these interrelationships between insecurity, class, and co-residence vary across the transition to adulthood phase?

We contribute to the literature in three ways. First, recognizing that there are other insecure yet understudied labour market positions in life course research, we distinguish between two forms of NSE-a state of underutilization (e.g., time-related underemployment) and a state of impermanence (TAW). Whereas, prior studies on the relationship between labour market insecurity and parental co-residence use fixed-term contracts and part-time work as conventional operationalizations of NSE (Stone, Berrington and Falkingham, 2011; Baranowska-Rataj et al., 2015; Gousia et al., 2021) , we contend that underemployment and agency work are relevant yet often overlooked forms of NSE. Second, we analyse the moderating role of parental social class in this relationship, recognizing that parents from different socio-economic backgrounds have different material and non-material resources that can serve as protective 'buffers' and propellant 'launching pads'. Finally, we refine the seminal feathered nest/gilded cage hypothesis (Avery, Goldscheider and Speare, 1992) by integrating employment conditions. Empirically testing this expanded hypothesis, we identify whether and how parental co-residence differs throughout the (extended) period of post-education young adulthood (aged 18-34).

Hypotheses

Young adults' labour market insecurity

Labour market insecurities are typically conceptualized and operationalized using positional markers. Recognizing that certain types of employment may be more insecure than others, prior studies demonstrate that objective indicators, such as being in a fixed-term contract or a casual/seasonal worker, have consequences on economic outcomes, well-being, and family formation (Kalleberg, 2000; Unt et al., 2021) . Some articles distinguish between 'standard' and 'nonstandard' employment (NSE), with the latter encompassing the less common positions. Moving beyond objective markers, some studies also use the level of job worries or financial worries to capture 'economic uncertainty' (Kreyenfeld, 2010; Palumbo et al., 2023) , recognizing that workers who prefer their current employment arrangements are not inherently at a disadvantage.

This article recognizes that certain forms of NSE remain understudied. Building on existing literature on insecure employment (Baranowska-Rataj et al., 2015; O'Reilley et al., 2017; Unt et al., 2021) , this article focuses on economically active young adults and identifies three states of interest: (i) being unemployed; (ii) having underutilized labour (underemployment); and (iii) lacking job permanence and autonomy (TAW). First, relative to (any) employment, unemployment is arguably the most insecure labour market position that can yield persistent effects (i.e., 'scarring') on laterlife economic outcomes (Gousia et al., 2021) . The succeeding paragraphs conceptualize the latter two distinct states.

First schema: underemployment

Amongst working young adults, underemployment is best understood as a state of labour underutilization (Greenwood, 1999) . Depending on its operationalization, it is underutilized in the sense that there exists an 'imperfect' match between either workers' preferences (subjective underemployment) or qualifications (objective underemployment) with their current occupation. Fauser and Mooi-Reci (2023) estimate that a fifth of 25-34 year-olds in Australia are underemployed and this share is higher amongst women. In the United Kingdom, underemployment is most pronounced for those aged 18-24, followed by those aged 25-34 (Bell and Blanchflower, 2013; Torres et al., 2023) . Underemployment is detected through 'revealed preference' and therefore also partly reflects individual's subjective views about their job. A worker on a part-time contract might well be satisfied with their arrangement and income but if 'part-time workers' are automatically considered to be insecure, then that worker will be classified as such, regardless of whether their lived experience is otherwise.

Underemployment partly addresses this because it captures only those who want to work more for any reason. While there are different types of underemployment (i.e., skills-related and pay-related), this article focuses on time-related underemployment-capturing the extent to which workers perceive they are underutilizing the amount of labour that they are capable of and, consequently, underpaid (Torres et al., 2023) . Figure 1 shows our underemployment schema with three types of workers in: involuntary part-time employment; employed but want to work more hours at the current rate; and looking for a new job specifically because want to work more hours. Time-related underemployment is likely to be associated with living arrangements if young adults consider full labour utilization as an economic prerequisite to residential independence.

Second schema: TAW

Our second schema captures workers with experience of job impermanence. In the United Kingdom, fixedterm contracts are less prevalent than they are in other European countries, accounting for 5 per cent of overall employment as of 2023. 1 To capture more workers in similar states of impermanence, we additionally consider agency workers within the same TAW group, regardless of whether they hold a permanent or fixed-term contract. This extends prior work that identifies agency workers with term-limited contracts as a subset of temporary workers, leaving permanent agency workers (PAW) undistinguished from permanent direct hires (Judge and Tomlinson, 2016; Fauser and Scheuring, 2022) . Agency employment is widely considered an insecure working condition where the individual is employed by a third-party agency, which then supplies these workers to firms ('principals'). Agency workers can either be temporarily or permanently employed, with the latter being assigned to different principals over time characterized by impermanence in roles and task assignments (Smith and Zheng, 2022) . There are around 440,000 in the United Kingdom (Judge and Tomlinson, 2016) . Figure 2 shows that in addition to the common composition of temporary employment (fixed-term, seasonal/casual, and temporary agency workers), we include PAWs in the overarching category of TAW.

The income penalties experienced by TAWs plausibly hinder their objective and subjective readiness for residential independence. Rouvroye et al. (2024) demonstrate that Dutch young adults, especially those living independently of their parent(s), prefer not to undertake and are less likely to apply for agency work, although their preferences are not always met. LABOUR MARKET INSECURITY AND PARENTAL CO-RESIDENCE IN THE UK

This highlights that young adults put a premium on having both a stable contract and being a direct hire, thus necessitating a closer look at temporary workers in addition to PAWs in one broad category.

Labour market insecurity and parental co-residence

The implications of both unemployment and NSE ultimately depend on what support others, most often parents or partners, can provide. 'Support' can be material such as financial help or in-kind (e.g., lending a car or using parental assets as collateral) (West et al., 2017) . Emotional support and the 'comfort of the home' are likewise valuable in coping with 'turning points' in young adulthood (van Stee, 2023) . Parental co-residence is a form of parental support which fulfils two non-mutually exclusive motives: a protective 'safety net' and a propellant 'launching pad' for young adults (Roberts et al., 2016) . We expect all forms of labour market insecurity to be related to increased inter-generational co-residence, with those being unemployed being the most likely to be living with parents, followed by both the underemployed and TAWs, respectively.

Protective 'safety net' motive

The parental 'safety net' hypothesis suggests that when adult children face financial constraints, parents offer extended material assistance that effectively serves as 'buffers' to protect economic well-being (Aquilino, 1990; Swartz et al., 2011; Van Stee, 2023) . Parental co-residence lowers or eliminates housing and other subsistence costs and thus provides shelter for those without employment, or those whose insecure employment mean that they do not have the financial stability to live independently. The 'boomerang' literature has identified relationships between labour market transitions (typically from employment to unemployment) and parental co-residence (Stone, Berrington and Falkingham, 2014; South and Lei, 2015; Arundel and Lennartz, 2017) . Under the safety net hypothesis, parental co-residence has protective economic underpinnings-young adults live with their parents primarily due to financial constraints (Swartz et al., 2011; Christopoulou and Pantalidou, 2022) .

Propellant 'launching pad' motive

On the other hand, inter-generational support can be driven by propellant motives whereby material and non-material resources are used to subsidise and 'propel' economic and residential independence. Parental co-residence, as a form of this support, increases the likelihood of future successful transitions to adulthood, though this may involve a delay in the timing of these transitions (Wellsch, Gelech and Mazurik, 2024) . The launch pad hypothesis suggests that parental co-residence, and the lack of responsibility for running a household, allows young adults to concentrate on completing education or training and on gaining a 'good' job (Roberts et al., 2016) .

Living in the parental home gives young people time to establish their careers while taking insecure jobs in the meantime (Burgess and Muir, 2020; Schoon, 2020) . The launch pad hypothesis also captures how parental co-residence gives access to more 'hands-on' support and access to cultural and social capital (Toft and Friedman, 2021) which can be important for subsequent occupational mobility (Sage, Evandrou and Falkingham, 2013; Andersson, 2021) . These propellant motives are also captured by the savings bank hypothesis as young adults to save up money to fund a future departure while accessing the capital and networks of their parents (Friedman and Laurison, 2023) .

One can also consider that young adult preferences and expectations. In the context of NSE, young adults may choose to take these jobs while searching for a desirable career job since they can still stay at the parental home. Prior qualitative evidence also points to young adults valuing the comfort and privacy they have in the parental home, where they perceive their day-to-day lives as easier and safer (Smits, van Gaalen and Mulder, 2010; Roberts et al., 2016) . Consistent with the 'privileged dependence' hypothesis (van Stee, 2023), these preferences are also arguably heterogeneous by class, with upper and middle class young adults being more likely to have homeowner parents with larger living spaces than those from disadvantaged backgrounds . This young adult preference may align with the parents' perspective, since many parents in the United Kingdom expect their adult children to return after education and consider supporting them as part of their obligations (West et al., 2017) .

If one were to consider only these 'propellant' motives, the relationship between labour market insecurity and co-residence is theoretically ambiguous. Propellant motives can facilitate co-residence as young adults who want to take their time finding a 'good job' can stay at the parental home. On the other hand, propellant motives can likewise dissuade co-residence if parents subsidize residential independence through financial transfers. The observed association between labour market insecurity and parental co-residence will be the net of these competing expectations. Most studies find a positive insecurity co-residence association in the United States (Lei and Mai, 2024) , United Kingdom (Stone, Berrington and Falkingham, 2011) , Italy (Bertolini and Goglio, 2019) , Canada (Tomaszczyk and Worth, 2020) , and Greece (Christopoulou and Pantalidou, 2022) . However, Gousia et al. (2021) find that compared to those in permanent full-time employment, young adults in parttime work have a lower likelihood of achieving housing autonomy in the United Kingdom, but this was not found for temporary workers (full-or part-time). These findings lend support to the idea that insecure employment may not necessarily 'entrap' young adults. Taking both strands of motives along with the existing empirical evidence, we test whether:

H1a (labour market insecurity): Both forms of NSE (underemployment and TAW) and unemployment are associated with a higher probability of parental coresidence relative to standard employment.

Next, we determine whether the relationship between NSE and co-residence is mediated by earnings. In recent literature, examining the consequences of NSE on a variety of life course outcomes including family formation (Van Wijk, De Valk and Liefbroer, 2021) , property ownership (Fauser and Scheuring, 2022) , and parental co-residence (Lei and Mai, 2024) is significantly mediated by earnings differentials. In other words, the relatively lower earnings experienced by those non-standard employed explains part of the inequalities in these outcomes. For the two forms of NSE, we are interested in, there is ample evidence suggesting that, underemployed (Bell and Blanchflower, 2013) , workers in temporary (or fixed-term) contracts (Gebel, 2009) , and agency workers (Judge and Tomlinson, 2016) generally experience earnings penalties relative to those in standard employment. Thus, we hypothesize that:

H1b (earnings): Among employed young adults, the association between labour market insecurity and parental coresidence is mediated by earnings.

Differences by age

In western countries, young adults are expected to have left the parental home by their late 20s/early 30s (Billari et al., 2021) and this is confirmed in the age patterns of co-residence (Berrington and Murphy, 1994; Esteve and Reher, 2021) . When faced with insecurity, those in the early phases of transitioning to adulthood may need greater support. Berrington, Tammes and Roberts (2014) show that for under-25s in the United Kingdom, unemployed and precariously employed young adults have a higher likelihood of co-residence than their stably employed counterparts but for over-25s, only unemployed and some types of precariously employed men (low income and routine occupations) have a significantly higher likelihood of co-residence. At older ages other factors, such as presence of a partner, likely determine whether an economically insecure young adult remains living with a parent. We expect therefore that insecurity will be less relevant as age increases:

H2 (age): The (positive) association between insecurity and parental coresidence is more pronounced at younger ages.

Labour market insecurity and parental co-residence: the moderating role of parental class

The linked-lives aspect of life course theory emphasizes interrelationships between the economic positions of members within the same family (Aquilino, 1990; Gilligan, Karraker and Jasper, 2018) and the increasing role of parental resources in facilitating transitions to adulthood (Fingerman et al., 2015; Fingerman, Huo and Birditt, 2020) . The moderating role of parental resources in the insecurity co-residence nexus operates through counteracting mechanisms. On the one hand, young adults in insecure positions are less likely to be financially supported if their parents also face financial uncertainty (Maroto, 2017) , which may facilitate intergenerational co-residence for resource pooling motives. On the other hand, we might expect co-residence to be more common amongst economically insecure young adults from wealthier backgrounds for multiple reasons. First, a higher proportion of young adults from wealthier backgrounds move out of the parental home at around age 18 to study at university and many return home upon completion (Champion, Green and Kollydas, 2024) . Hence, at the earlier phases of the transitions to adulthood (early mid 20s), we might expect a higher proportion of this group to be co-resident.

Second, prior research has highlighted lack of privacy as a key concern of young adults inter-generationally co-resident (Smits, van Gaalen and Mulder, 2010 ) and hence we might expect economically insecure young adults from richer backgrounds to be more likely to remain co-resident as they are likely to come from more spacious homes. Finally, in the United Kingdom coming from a wealthier parental background is associated with a greater likelihood of being raised by two parents in a 'stable' family structure (Panico et al., 2010) . Family complexity, where young adults may have to negotiate new relationships with step-parents and step/ half-siblings is generally associated with an earlier departure from the parental home (Panico et al., 2010; Fomby and Bosick, 2013) and weaker norms towards adult child-to-parent support (Van Houdt, Kalmijn and Ivanova, 2018) .

Empirical evidence is mixed. Some studies find that (higher) parental economic resources are significant predictors of parent-adult child co-residence (Maroto, 2017; Wang and Squires, 2024) . Qualitative research in England found that wealthier parents are 'better placed to offer support' and partly explains why some highly educated young adult children decide to move back to the parental home after completing university (Roberts, et al., 2016; West, et al., 2017) . Other studies show that wealthier and more highly educated parents are more likely to provide financial and practical support to children living away from home, especially those without work or with low income (Steele et al., 2024) . This parental resource gradient has also been observed in the United States, whereby (higher) parental education transmits both economic and noneconomic (e.g., information and 'access' to support) resources to children, facilitating home-leaving for economic independence rather than non-economic (e.g., partnership) reasons (Goldscheider, Hofferth and Curtin, 2014) .

Taking these literatures together, we argue that service-class parents are better positioned to provide co-residential support than those in lower class positions (Arundel and Lennartz, 2017; van Stee, 2023) . Beyond this resource advantage, parents from upper socio-economic backgrounds possess cultural capital (e.g., values, attitudes, and preferences) and social support that can further support their adult children while co-residing (Toft and Friedman, 2021; Friedman and Laurison, 2023) . We test whether:

H3 (class): The (positive) association between insecurity and parental coresidence is more pronounced for young adults from service-class parents.

The moderating role of parental class across the adulthood transition phase

The preceding hypothesis masks the potential contradiction between the 'protective' and 'propellant' motives. Assuming sufficient resources, parents can support their children by letting them stay at the parental home to save on housing costs or to support them financially and subsidize independent living. The feathered nest/gilded cage hypothesis (Avery, Goldscheider and Speare, 1992) suggests that the association between parental resources and co-residence attenuates with age -at earlier ages, young adults are more reluctant to leave their (more comfortable) parental home. Whereas at older ages, adult children benefit from financial support from their parents to achieve independence. The changes with age in the moderating effect of parental class is presented schematically in Figure 3 . As earlier established in hypothesis 2, co-residence decreases throughout the transition to adulthood phase, steeply so throughout the mid-20 s as young adults enter the labour market causing an inverse-S shape. However, we hypothesize, in line with the feathered nest hypothesis, that this inverse-S curve is steeper for service-class parents or those in managerial and professional occupations, implying that at younger ages, higher rates of co-residence capture the material advantage of parental financial stability in supporting their children-in-need, while for older ages, lower rates of co-residence capture the financial support that parents can provide for their children to meet their own residential preferences. Some evidence lends support to this age gradient. Avery, Goldscheider and Speare (1992, p. 384) find that in the US context, parental income decreases residential independence (or nest-leaving) earlier but increases it in later ages. The same age gradient is observed in Europe in the late 1990s where well-off parents tend to keep their adult children close to home at younger ages and support their independence as they get older (Iacovou, 2010) . More recent analysis confirms that co-residence indeed declines with age and that highly educated parents tend to have lower co-residence rates (rightward part of Figure 3 ) at older ages (Swartz et al., 2011) . While these studies do not make a distinction between the level of insecurity of young adults, we can infer that our hypothesized elevated co-residence probabilities amongst service-class households is most pronounced at younger ages than at older ages. This captures what van Stee (2023) describes as 'privileged dependence'-the ability of young adults from more privileged backgrounds to delay economic independence. Focusing primarily on unemployed and NSE, we hypothesize a tapering off effect such that:

H4 (class and age): The moderating role of parental class is heterogenous by age. The association between insecurity and coresidence among service class parents is more pronounced at younger ages and tapers off at older ages.

Data and methods

Sample

We use the third quarter (July-September) 2021-2024 waves of the UK Labour Force Survey (LFS) that contain information about the respondent's parental social class. This period follows the lifting of most COVID-19 mobility restrictions. Empirical work on parental co-residence often uses longitudinal data, including the US NLSY97 (Lei and Mai, 2024) , Understanding Society in the United Kingdom (Bayrakdar and Coulter, 2018; Gousia et al., 2021) , and the German SOEP (Bayrakdar et al., 2019) . However, our research aims, particularly the precise definition of underemployment and TAW and the moderation analyses by narrow age bands, necessitate the use of a dataset with sufficiently detailed employment information and high case numbers. Our analytical sample consists of 20,144 economically active young adults aged 18-34. Given that it is compulsory in the United Kingdom to remain in education and training until age 18, 2 we start our analysis at this age. 34 is generally used as an upper age limit in life course research of youth transitions and is above the average age suggested by survey respondents as the upper limit for inter-generational co-residence in the United Kingdom (Billari et al., 2021) . While many economically inactive individuals will experience economic insecurity, heterogeneity within this group (which includes students, family carers and the long-term sick) warrants a separate analysis outside the scope of this paper. A closer look at the active population, which is our focus, allows for meaningful comparisons between stably employed, non-standard employed, and unemployed young adults.

Key variables Outcome variable

We identify respondents according to whether they are living with at least one biological, step or adoptive parent. Young adults living in a hall of residence and those living with a grandparent without their own parent are not classified in this category. In our analytical sample, 32.5 per cent live with their parents, but this share varies considerably across demographic groups.

Labour market insecurity

We compare those in standard employment, the unemployed and those who experience our two forms of NSE, running the analyses separately for each. First, we identify those who are in time-related underemployment. Following Torres and colleagues (2023) , this definition covers workers: (i) in involuntary part-time employment-part-time workers who say they are working part-time because they cannot find a full-time opportunity; (ii) who want to work longer hours at their current rate-workers, either part-time or fulltime, who prefer and are open to working longer hours than they currently have; and (iii) looking for a replacement job and more hours: workers who are looking for a different job than what they have right now due to wanting to work more hours. The second approach identifies NSE in terms of both the duration of employment contract and the nature of employer. Temporary and agency workers include those in casual, seasonal, and fixed-term contracts or arrangements as well as agency workers who may either be in permanent or

LABOUR MARKET INSECURITY AND PARENTAL CO-RESIDENCE IN THE UK temporary contracts. Table 1 shows the tabulation of parental coresidence by these measures of NSE. There is also notably little overlap between the two schemas of NSE such that a majority of temporary and agency workers are not underemployed and vice versa: only 1.4 per cent are underemployed temporary and agency workers (Supplementary Table A1 for the full tabulation).

Age

Our key demographic variable of interest is age, operationalized as a categorical (18-22, 23-26, 27-30, and 31-34) ; 18-22 is 5-year age band given that a substantial share (around 40 per cent) of this group is still in education of training. Starting the second age group at 23 is ideal since, in the United Kingdom, the majority young adults would have left higher education by this age and in 2021-2024, 23 was the qualification age for the UK Government's adult minimum wage (Francis-Devine, 2024) .

Parental class

Respondent's reports of the occupation of the main earner parent when they were 14 years old are grouped using the three-level Erikson-Goldthorpe-Portocarero (EGP) schema (Erikson, Goldthorpe and Portocarero, 1979) , distinguishing between service, intermediate, and lower/routine/working classes. The service class refers to managerial, professional, and technical occupations. The intermediate class includes small employers, own-account workers, and other intermediate occupations, while the routine class includes those in lower, semi-routine, and routine occupations. In analyses available on request, we show that the expansion of the EGP schema from three to six categories does not change the substantive interpretation of our analysis. The 'class advantage' is strongest for the three highest social classes consistent with the substantive interpretation of the 3-category version.

Analytical strategy

We estimate logistic regression models of the association between insecurity and co-residence net of the confounding associations of class, age, and other controls.

P(PC

= 1) = α + βI i + δPSC i + γDC i + θST i + ϵ i , (1)

where I is a vector of insecurity (NSE-underemployment and TAW-and unemployment) and PSC is a vector of parental social class categories.

Control variables

As suggested by Kohler, Class and Sawert (2024) , the selection of control variables is critical in model specification and should ideally emanate from a well-reasoned graphical causal model (see Supplementary Figure A1 ). In our baseline model, DC is a vector of controls including sex (male-female), ethnicity (grouped into four major categories), migration background (binary indicator for those born outside the United Kingdom and arrived after age 15), qualification, age group, parenthood, and health status (a binary indicator for those who indicated a health problem). Parenthood status is also included since the eligibility to receive welfare support through parenthood may likewise confound the relationship between insecurity and co-residence. Finally, we control for region and year of interview dummies (ST).

Mediating role of earnings

To examine the mediating role of earnings in the insecurity co-residence nexus, we use the KHB method (Kohler, Karlson and Holm, 2011) , which residualizes the hypothesized mediator to account for rescaling and allows us to compare our parameter of interest between the reduced and full model (Van Wijk, De Valk and Liefbroer, 2021; Fauser and Scheuring, 2022; Lei and Mai, 2024) . We use gross (pre-tax) earnings in the main job split into quintiles for ease of interpretation. As the earnings question in the UK LFS is only asked to employees, there is plausibly non-random selection into the earnings analysis. To address this, we use inverse probability weighting techniques which first estimates the probability of being employed (vs. unemployed) as a function of the same set of variables in the co-residence model. We then multiply the inverse of the probabilities with the cross-sectional income weights in the UK LFS to account for the fact that the earnings question is asked only in 40 per cent of the respondents each survey and that this question has higher non-response rates. This gives us the full surveyweighted inverse probability weights (Ridgeway et al., 2015) which we use in the KHB analysis.

Interaction models for age and class

To test hypotheses 2 and 3, we treat age and parental class as moderators and employ two-way interaction models of insecurity with each of these variables. Hypothesis 4 on the moderating role of parental class across age groups is tested using a three-way interaction model. In all these separate specifications, we present average marginal effects for the NSE and unemployment category relative to standard employment while controlling for the same set of variables. The main text shows the AME plots, while full model results are in the Online Appendix. Table 2 shows the univariate weighted proportions and standard errors of parental co-residence and the unweighted counts and weighted frequencies in the analytical sample. Around 31 per cent stably employed young adults aged 18-34 live with their parents whereas 43 per cent of the underemployed, 46 per cent of temporary and agency workers and 64 per cent of the unemployed do so. These descriptive figures preliminarily confirm a NSE gradient in our outcome variable.

Results

Labour market insecurity and parental co-residence

Relative to stable employment, underemployment and TAW are associated with higher probabilities of parental co-residence (by 5.4 percentage points (pp) and 5.1 pp respectively), net of observed confounders (Figure 4 ). Meanwhile, unemployed young adults have a 12.6 pp have a higher probability of co-residence compared to the stably employed. These results, taken together, lend support to our first hypothesis that NSE and unemployment are all positively associated with co-residence.

Table 3 shows that gross earnings quintile plays a strong mediating role in the insecurity co-residence nexus. In both underemployment and TAW specifications, the association with parental co-residence is largely explained away when these earnings are controlled, lending support to a material and income-related explanation-young adults in underemployment and TAW might be residing with parents due to earnings-related constraints. The significant 'income effect' of NSE on co-residence echoes earlier findings by Van Wijk, De Valk and Liefbroer (2021) that the negative association between temporary employment and family formation is largely driven by income. We show in Supplementary Figure A3 that this strong earnings gradient is explained by the disproportionate share of NSE in lower earnings quintiles. These results are substantively robust when using a continuous measure of earnings instead of quintile categories (Supplementary Table A4 ).

Age differences in the insecurity-parental co-residence nexus

Figure 5 shows the AMEs for unemployment and NSE by age group. Compared to standard employment, underemployment, TAW, and unemployment are all associated with significantly higher probabilities of parental co-residence at older ages (underemployment: P < 0.001; TAW: P < 0.001). While we find support for age differences (H2), results show that at the youngest age group when parental co-residence is near-universal, there are no differences across employment states. Unemployment and TAW are positively associated with parental co-residence in the three older age groups, while underemployment is significant for the two older groups. While earlier findings focused on the fact that parental co-residence is most pronounced at younger ages (Berrington and Murphy, 1994; Stone, Berrington and Falkingham, 2011) , we go further in demonstrating that the potential 'buffering' role of parental co-residence for those experiencing labour market insecurity is more prominent at older ages. The full results from this and all subsequent interaction models are shown in Supplementary Tables A5 to A7 .

Insecurity and co-residence: the moderating role of parental class

Descriptively, the rates of co-residence across different parental classes shown in Table 2 do not seem to differ greatly. However, the association between insecurity and co-residence is moderated by parental social class, as shown in Figure 6 . While underemployment is significantly associated with higher probabilities of unemployment, are more strongly associated with parental co-residence amongst young adults from more advantaged parental backgrounds, lending support to H3. This substantive interpretation of a 'class advantage' is robust to an alternative and a more disaggregated grouping of class using the collapsed six categoryversions, as shown in Supplementary Figure A5 .

Age differences in the moderating effect of parental class

In unadjusted analyses (Supplementary Figure A6 ), we find some support for the feathered nest/gilded cage hypothesis; co-residence is slightly higher for service-class than routine-class parents at the youngest age group but tapers off and reverses at older ages. As a formal test of whether the moderating effect of parental class changes significantly across ages, controlling for other covariates in equation 1, we present AMEs from threeway interaction models in Figure 7 . While the joint three-way interactions between employment status, parental class, and age group were not statistically significant in global tests (underemployment: P = 0.461; TAW: P= 0.344), cell-level contrasts suggest that the magnitude of the insecurity co-residence association varies across specific combinations of class and age. For example, significant effects were observed amongst underemployed individuals aged 27-30 and 31-34 from service-class backgrounds but not at younger ages. Meanwhile, amongst respondents from routine-class families, the association between NSE and co-residence is largely nonsignificant across age groups, suggesting the limited ability of routine-class parents to 'buffer' economically insecure situations through co-residence. Taken together, these results suggest heterogeneities in the moderating role of parental class across age groups. Partially supporting the feathered nest hypothesis, adult children of service-class parents-

Discussion and conclusion

Motivated by the steady increase in inter-generational co-residence in the context of increased economic uncertainty, this paper examines the interrelationships between labour market insecurity, parental social class, and parental co-residence amongst young adults in the United Kingdom. We contribute new insights by extending the operationalization of labour market insecurity to a state of labour underutilization (time-related underemployment) and a state of impermanence (TAW), recognizing the inherent subjective and objective uncertainties that these workers face compared to those in standard employment (Maroukis and Carmel, 2015; Shanks, 2023; Torres et al., 2023) . Further, we put forward arguments and test hypotheses that the association between insecurity and parental co-residence is heterogeneous across age and parental class. We find that labour market insecurity is positively associated with parental co-residence. Underemployed, TAW, and unemployed young adults all have significantly higher probabilities of co-residence compared to those stably employment. This baseline finding is consistent with prior work showing how insecurity is generally associated with parental co-residence, either through delaying the age at leaving home or increasing the probability of returning (Stone, Berrington and Falkingham, 2014; Gousia et al., 2021; Lei and Mai, 2024) . Second, this relationship is moderated by agethe association between insecurity and co-residence is more prominent amongst the oldest age bands (27-30 and 31-34) .

We find that the positive insecurity co-residence gradient is only present amongst those with service-class parents, and for the unemployed group, follows a hump shape that tapers off with age. Simply put, when adult children are in insecure labour market positions a 'class advantage' exists in terms of parental co-residence. This might be driven by multiple nonmutually exclusive reasons including (i) the 'resource channel' whereby parents from richer backgrounds are more likely to be homeowners (Bayrakdar and Coulter, 2018) and have the physical space to respect privacy and boundaries (Smits, van Gaalen and Mulder, 2010) , making the parental home a feasible residential option; (ii) intangible emotional support from parents as young adults transition into the labour market; and (iii) being an exercise of individual agency whereby young adults willingly take temporary insecure jobs close to home as they look for and establish their long-term careers; amongst others. Further work examining co-residence across the life course would ideally incorporate more closely the reasons for co-residence and disentangling the never-leavers from the returnees, where data exist.

Recognizing how some demographic groups are simply less likely to live at the parental home (e.g., those with children or those with a migration background whose parents are likely to live outside the United Kingdom), we conduct sensitivity analyses using alternative model specifications and sample restrictions (natives, non-partnered, childless, etc.) presented in Supplementary Tables A2 and A3 , showing that results substantively hold. In addition, we also tested for whether having a partner attenuates the insecurity co-residence relationship and our exploratory estimates in Supplementary Figure A4 lend support to this. While unpartnered underemployed young adults are more likely to co-reside with parents, partnered underemployed young adults are not. Given that parental resources seem to matter for co-residence, future studies could examine 'stock' measures such as homeownership (Steele et al., 2024) , the size and quality of parental home (Burgess and Muir, 2020) , and savings (Maroto, 2017) and 'flow' measures including income (Olofsson et al., 2020) . Further, resources have also been contextually inferred from parents' educational attainment (Schwanitz et al., 2017) and employment status (Goldscheider, Hofferth and Curtin, 2014; Christopoulou and Pantalidou, 2022) . Most of these papers point to how more and better parental resources serve as 'stronger' buffers for adult children in need. Using the LFS data, however, presented a unique advantage of capturing the main earner's occupation when the respondent was aged 14. Thus, while our measure captures parental class position when respondents were at their formative adolescence stages, further work could explore alternative measures of parental resources and disentangle whether this moderating role is due to material or cultural explanations, or both.

We are cognizant that the labour market insecurity co-residence nexus can likewise be moderated by the inter-section of demographic and socio-economic identities, including ethnicity (Morris, 2023) . Unfortunately, even with its considerable sample size, the UK LFS does not permit analyses by individual ethnic groups due to small cell counts in some ethnic groups. Finally, future research could incorporate, if data were available, the reasons for co-residence, the role of young adults' preferences, and norms surrounding familial support across ethnic groups.

Our results show that while any form of employment appears to lower the probability of parental co-residence relative to unemployment, young adults in non-standard work-both underemployment and TAW-still face significant disadvantages, such as having lower earnings., Young adults in insecure labour market positions have heterogeneous probabilities to co-reside with parents depending on their socioeconomic background. This 'class advantage' in co-residential arrangements warrants our closer attention to the broader question of how class-based differences in inter-generational exchange exacerbate within-cohort inequalities.

Notes 1. See the latest and most updated figures from ONS (2023). https://www.ethnicity-facts-figures.service.gov.uk/work- pay-and-benefits/employment/permanent-and-temporary- employment/latest/ . 2. See latest guidance from Department of Education. https:// educationhub.blog.gov.uk/tag/minimum-school-leaving- age-uk/.

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78. at the University of Southampton working on inter-generational co-residence and labour market inequalities. Concurrently, he is Principal Investigator of projects on concentration, representation, and bargaining in Philippine labour markets and the life course consequences of restrictive covenants in employment contracts. His work has been published in Work, Employment and Society, Population Research and Policy Review, and the European Journal of Population, amongst others. He obtained his PhD from the Hertie School Berlin (summa cum laude) and his current research interests are in social and economic demography and labour market institutions. Ann Berrington is Professor of Demography and Social Statistics, and leads the Fertility and Family strand of the Centre for Population Change University of Southampton Vincent Ramos is a postdoctoral researcher at the ESRC Centre for Population Change Her research interests concern transitions to adulthood