2.1 Studies focused on the departure of children for any reason

A few studies, mainly focused on developed countries, look at how resources are reallocated in a household with a child moving out. Among these, making use of data from Italy and Germany, Rottke and Klos (Reference Rottke and Klos2016) find that overall household consumption drops after a child moves out of the household, but at the same time, adult-equivalent consumption significantly increases. In other words, after a child's departure, parents upgrade their personal lifestyle, but also save a fraction of the resources freed up by the departing child.

Focusing on the US, Coe and Webb (Reference Coe and Webb2010) find no evidence that households decrease consumption after children leave, coupled with a significant rise in consumption per capita. This suggests that the resources freed up by the departed children are entirely consumed. Dushi et al. (Reference Dushi, Munnell, Sanzenbacher, Webb and Chen2021) also focus on US data and find that households in their sample only slightly increase 401(k) contributions after children move out. They conclude, once again, that the majority of the resources freed up by the departing child are consumed. Finally, Biggs et al. (Reference Biggs, Chen and Munnell2021) document that after the departure of their offspring, US parents do not save by paying off their mortgage or other debt, do not transfer resources to their departed children, but reduce their hours worked.

2.2 Studies focused on migration

The papers discussed in the previous sub-section do not specify the reason why the children move out of their households. Children may leave for a number of reasons such as going to college, becoming financially independent, getting married and so on. Another reason for departing may be migration. A large literature has looked at the effects of migration on the labor supply, education, and health of the left-behind household members such as parents, spouses, and/or children (see Antman, Reference Antman2012, for a review of this literature). A few studies, mainly focused on developing countries, investigate how the migration of household members affects the food consumption and/or food security of left-behind families. For instance, Abebaw et al. (Reference Abebaw, Admassie, Kassa and Padoch2020) find that Ethiopian households with migrants increase the number of daily calories they consume. Nguyen and Winters (Reference Nguyen and Winters2011) reach a similar conclusion for Vietnam. These findings can be explained by the migrants' higher income, part of which is sent home in the form of remittances. Focusing on China, Liu et al. (Reference Liu, Eriksson and Yi2021) document that the migration of offspring is associated with a significant improvement of the nutritional status of their left-behind parents. By contrast, Karamba et al. (Reference Karamba, Quiñones and Winters2011) argue that households in Ghana generally do not significantly increase their food consumption when a household member migrates, as remittances to the left-behind families are not sufficient to compensate for the loss of labor.

Only a few studies investigate the impact of migration on the overall consumption of the left-behind household members. Among these Chandrasekhar et al. (Reference Chandrasekhar, Das and Sharma2015) find that households with short-term migrants show a lower consumption per capita in India. These migrants generally work in the unorganized sector without formal contracts or legislation to protect their rights. As a result, their salary is relatively low, and they are not able to transfer a significant amount of money back to their left-behind family members. Romano and Traverso (Reference Romano and Traverso2019) argue that international migration only positively affects the per capita consumption of the poorest left-behind households in Bangladesh. In the context of China, Wang et al. (Reference Wang, Liu and Yan2021) make use of the 2013 wave of the CHARLS and find that elderly households with permanent migrant children show a higher share of expenditure on agriculture, whilst households with temporary migrant children show a higher share of food consumption.Footnote ⁵ It is, however, noteworthy that these studies make use of cross-sectional data. As such, they compare the consumption patterns of households with migrants and households without. Their focus is, therefore, different from the papers surveyed in the previous sub-section which look at the effect of the actual moving out of children between one wave and the other on the consumption of left-behind household members in a panel setting.

2.3 Contribution

Our paper speaks to these two branches of literature by analyzing the effects of the departure of members of the younger generation on the consumption of the left-behind household members in China.

Specifically, our work adds to the literature surveyed in Section 2.1 in three ways. First, for the first time, we focus on the effects of the departure of members of the younger generation on consumption in the Chinese context. This is important bearing in mind that, as a result of globalization, urbanization, and the diffusion of Western values, more and more Chinese young people move out of their parents' homes (Xu et al., Reference Xu, Wang and Qi2019). Second, considering that multigenerational co-residence is traditionally highly valued in China (Guo et al., Reference Guo, Li, Yi and Zhang2018; Xu, Reference Xu2019) and that around 40% of children are taken care of by their grandparents (Deng & Tong, Reference Deng and Tong2020), we consider, for the first time, the departure of grandchildren and children-in-law, in addition to the departure of children. Third, we take into account the effects of the age of the leavers, which has been overlooked in previous literature. This is important as the resources freed up by the leavers are likely to vary depending on their age (Fernández-Villaverde & Krueger, Reference Fernández-Villaverde and Krueger2007). Moreover, people of different ages are likely to move out of their households for different reasons. This will, in turn, impact how remaining household members deal with the resources freed up by their departure.

In our setting, one of the possible reasons why children leave their household is migration. Thus, our work also relates to the small literature which has looked at the effects of migration on total household consumption by making use of a panel data setting. This enables us to look at the effects of offspring actually moving out of the household between one wave and another.

3.1 Sample construction

Our analysis is based on the 2011 and 2013 waves of the CHARLS. The survey, which is nationally representative, collects high-quality data for residents aged 45 and above and their spouses.Footnote ⁶ 10,026 households took part in the 2011 wave and 10,624 households in the 2013 wave.Footnote ⁷ Information is also provided about how many additional household members there are, their relationship to the main respondent, and their age.

In order to compare consumption changes between 2011 and 2013 in households with and without leavers, we only consider the 8,786 households who participated in both waves. As the age structure of the household members is a key factor in our analysis, we exclude 1,726 households with missing age information on some of the members. We also exclude 376 households that reported additional members in 2013.Footnote ⁸ Furthermore, as the CHARLS focuses on respondents aged 45 and above, we drop households whose main respondent and/or spouse is aged under 45. This leaves us with 6,843 households. Next, in order to deal with outliers, we set to missing the top and bottom 1% observations of total, non-durables, and non-education expenditure, household income, and household financial wealth. Finally, we exclude observations with missing values for variables included in our models. This leaves us with 11,640 observations over the two years, corresponding to 6,584 households.

3.2 Summary statistics

Our sample is composed of 6,584 households with a total of 22,567 members. Figure 1 shows that more than 51% of these household members are main respondents (29.16%) and their spouses (22.33%). Children and grandchildren account for 21.25 and 15.82% of the total household members, respectively. If we also consider children-in-law, the younger generations' members account for 45.58% of the total.

Figure 1. Household composition (percentage) in the CHARLS (2011).

Note: The data is based on our main regression sample where respondents were aged 45 and above in both waves of the survey, and households participated in both waves of the survey and provided age information for every household member.

Source: Authors' calculations based on the CHARLS.

Figure 2 shows that 4,076 out of 6,584 households (61.91%) in our dataset have members of at least two generations within the family home (i.e., parents living with children/children-in-law and/or grandchildren). There are 1,653 households (25.11%) with at least three generations residing within the family home (i.e., parents, children/children-in-law, and grandchildren), and 1,782 households (27.07%) which only consist of respondent and spouse. These statistics illustrate the diverse composition of Chinese households.

Figure 2. Number (percentage) of households by composition in the CHARLS (2011).

Note: “All Households” are the households used in our main regression models. “With only respondent” represents the households with only one member. “With only respondent and spouse” are the households composed of only the main respondent and his/her spouse. “With child” represents the households with at least one child in residence. “With grandchild” stands for the households with at least one grandchild in residence. “With child-in-law” stands for the households with at least one child-in-law in residence. “With child/grandchild/child-in-law” stands for the households with at least one member of the younger generation in residence. “With child, grandchild, and child-in-law” represents the households who have at least three generations in residence. “With other members” stands for the households with at least one other household member (different from spouse, child, grandchild, and child-in-law) in residence. There are overlaps between certain groups.

Source: Authors' calculations based on the CHARLS.

Figure 3 shows the age distribution of household members. 96.24% of main respondents and spouses are aged between 45 and 80. Among other household members, 94.74% are aged between 0 and 50, with more than 93% belonging to the younger generation (children, children-in-law, and grandchildren of main respondents). Leavers are defined as those who were family members in 2011 but not in 2013 due to moving out from the family home, death, or other reasons. In our sample, 2,799 leavers are reported from within 1,534 households. Figure 4 shows that 87.1% of these leavers belong to younger generations: they are main respondents' children (45.23%), grandchildren (25.08%) and children-in-law (16.79%).

Figure 3. Age distribution in the CHARLS (2011).

Note: The data is based on our main regression sample where respondents were aged 45 and above in both waves of the survey, and households participated in both waves of the survey and provided age information for every household member. “Other household members” represents all the household members apart from respondents and their spouses.

Source: Authors' calculations based on the CHARLS.

Figure 4. Leavers (percentage) in the CHARLS (2013).

Note: The data is based on our main regression sample where respondents were aged 45 and above in both waves of the survey, and households participated in both waves of the survey and provided age information for every household member.

Source: Authors' calculations based on the CHARLS.

Figure 5 presents the ages of leavers in different categories: The leavers' age ranges from 0 to 111.Footnote ⁹ The most common age range of child leavers is between 20 and 40, which accounts for 88.63% of the total child leavers, and the mean age of a child leaver is 28. Children typically move out of the household when they start their own family and/or become financially independent, which usually happens when they are in their late twenties. Figure 5 also shows that grandchild leavers aged between 0 and 20 count for 92.74% of the total leavers in this category, with a mean age of 10. Most younger generation's household members who move out at ages between 0 and 16 are grandchildren of main respondents. In China, it is normal for grandparents to live with and look after their grandchildren at least for some time (Deng & Tong, Reference Deng and Tong2020; He et al., Reference He, Li and Wang2018b). Finally, 96.6% of leaving children-in-law are aged between 20 and 45, and the mean age of leavers in this category is 32.

Figure 5. Age distribution of leavers in the CHARLS (2013).

Note: The data is based on our main regression sample where respondents were aged 45 and above in both waves of the survey, and households participated in both waves of the survey and provided age information for every household member.

Source: Authors' calculations based on the CHARLS.

Table 1 presents the composition of leavers across different age groups. We can see that just under 94% of leavers in the age range 0–16 are grandchildren of the respondent. This percentage drops to 18.15% in the age range 17–24, and to 2.29% in the range 25–30. The percentage of children/spouses of children leaving the household ranges from 2.67% in the range 0–16, to 79.76% in the range 17–24, and to 96.29% in the 25–30 range. In the 31+ range, only less than 1% of leavers are grandchildren, 66.28% are children/spouse of children, and the remaining leavers are other household members (e.g., mother, father, and so on).

Table 1. Leavers by age group

Note: The data is based on our main regression sample where respondents were aged 45 and above in both waves of the survey, and households participated in both waves of the survey and provided age information for every household member.

Source: Authors' calculations based on the CHARLS.

Table 2 presents details of the various consumption categories that we consider. Appendix Table A1 presents definitions of all other variables used in the paper. Appendix Tables A2, A3, and A4 respectively present descriptive statistics for different categories of consumption, consumption changes of household with leavers between 2011 and 2013, and all the variables used in our models. It is noteworthy that according to Appendix Table A3, the average age of the main respondents in our sample is 61.34. Moreover, the average household size is 3.4 and 37.47% of households are from urban areas. Finally, 89.02% of respondents own their house.

Table 2. Consumption categories

Note: All consumption categories provided by the CHARLS are listed in the table. We further categorize them following Meyer (Reference Meyer2013).

Source: 2011 and 2013 waves of the CHARLS.

4.1 Models accounting for the departure of members of the household's younger generation

We start by studying the response of total, non-durable, and non-education consumption to the departure of any member of the household's younger generation. To this end, we estimate the following equation:

(1)$$\log C_{\,j, t} = \partial + \beta YoungMove_{\,j, t} + \theta ^{\prime}Controls_{\,j, t} + u_j + u_t + ( {u_p*u_t} ) + \varepsilon _{\,jt}$$

where log C _j,t represents in turn the logarithm of the real total, non-durable, and non-education consumption for household j in year t. We estimate the models for the above-mentioned consumption aggregates in levels and per capita.Footnote ¹⁰ Following Coe and Webb (Reference Coe and Webb2010) and Rottke and Klos (Reference Rottke and Klos2016), we focus on both total and non-durable consumption because the latter is likely to be the most responsive to changes in household composition.Footnote ¹¹ We add non-education expenditure to investigate the extent to which changes in total/non-durable consumption are driven by changes in education expenditure, once a member of the household's younger generation leaves the household. YoungMove _j,t indicates the number of members of the younger generation who moved out of household j between 2011 and 2013.Footnote ^12, Footnote ¹³

Controls_j,t represents a set of control variables. Specifically, following Rottke and Klos (Reference Rottke and Klos2016), we control for the main respondent's age, marital and health status, as well as for total household financial wealth and home ownership.Footnote ¹⁴ We also include the number of non-offspring household members,Footnote ¹⁵ as well as household income, which is defined as the sum of the income of all household members. This comprises salaries, pensions, benefits, and asset revenues of all household members, as well as remittances from non-resident children and grandchildren.Footnote ¹⁶

Following Danziger et al. (Reference Danziger, Van Der Gaag, Smolensky and Taussig1982) and Robb and Burbidge (Reference Robb and Burbidge1989) who document that consumption demand decreases with age in the late stages of the life cycle, we expect the sign of the coefficient associated with the main respondent's age to be negative. Compared with singles, married people face less uncertainty in their income and consumption as their partners will support them when they encounter financial problems. Thus, marriage can be regarded as a form of insurance against income and health risks (Yang & De Nardi, Reference Yang and De Nardi2016). We therefore expect a positive association between the dummy variable indicating that the respondent is married and household consumption. Furthermore, considering the low level of social welfare benefits in China (Cheng et al., Reference Cheng, Liu, Zhang and Zhao2018b), we expect people with poorer health to incur higher out-of-pocket medical expenditures and hence to exhibit higher consumption. In line with Gan et al. (Reference Gan, Yin and Zang2010), we expect homeownership to be associated with a higher consumption. Finally, according to the wealth and income effect, people tend to spend more as their income and/or the value of their assets increase. We therefore anticipate a positive sign on the coefficients associated with total household financial wealth, income, and home ownership (Paiella and Pistaferri, Reference Paiella and Pistaferri2017).

It is particularly important to include income in our equation as the departure of older offspring may affect household consumption indirectly by affecting household income. Specifically, such departures would reduce the leavers' financial contributions to the household, which may, in turn, affect household consumption. Similarly, children who migrate may send remittances back home, which have been found to supplement income in rural China and increase per capita consumption (Démurger & Wang, Reference Démurger and Wang2016). Parents who leave their children behind typically also send remittances back home to help grandparents with the education and upbringing of the children (Secondi, Reference Secondi1997). When they take their children back, they may stop these transfers. All these effects are captured by our household income variable, which includes the salaries of all household members as well as remittances from non-resident household members. As a result, all the effects of the departure of members of the younger generation on the consumption of the remaining household members that we discuss hereafter are net of these changes in income.

The error term in Equation (1) is made up of the following components: u _j, which is a household-specific time-invariant effect often referred to as unobserved heterogeneity; u _t, which accounts for business cycle effects; the interaction between provincial fixed effects (u _p) and time fixed effects (u _t), which is aimed at capturing province-specific business cycle effects; and $\varepsilon _{jt}$, which represents an idiosyncratic error term. To account for the u _j component of the error term, we use a fixed-effects estimator.Footnote ¹⁷ We report robust standard errors rather than the conventional standard errors to account for potential heteroskedasticity and within-group correlation.

In order to assess how the remaining household members allocate the resources freed up by the leaver, it is necessary to estimate Equation (1) both for household consumption and per capita consumption. Table 3 shows how different coefficients associated with the YoungMove _j,t variable in the two equations translate in the freed-up resources being saved and/or consumed.

Table 3. Conceptual framework

Note: This table reports possible signs of the coefficients associated with number of leavers in the models aimed at explaining total consumption (column 1) and per capita consumption (column 2). Column 3 describes whether according to the combinations of signs in columns 1 and 2, the resources freed up by the leaver are consumed and/or saved.

In a nutshell, if the coefficient associated with YoungMove _j,t in the model for per capita consumption is positive, there are three possible scenarios. If the corresponding coefficient in the model for total consumption is also positive, then all the resources freed up by the leaver are consumed and, after the departure, the remaining household members even increase their consumption further compared to the pre-departure period. If the corresponding coefficient in the model for total consumption is not statistically significant, then all freed-up resources are consumed. If it is negative, then part of the freed-up resources is consumed and part is saved.

If the coefficient associated with YoungMove _j,t in the model for per capita consumption is negative and the corresponding coefficient in the model for total consumption is also negative, then the freed-up resources are saved and the remaining household members even decrease their overall consumption after the departure compared to the pre-departure period. Finally, if the coefficient associated with YoungMove _j,t in the model for per capita consumption is not statistically significant and the corresponding coefficient in the model for total consumption is negative, then all freed-up resources are saved.Footnote ¹⁸

4.2 Differentiating leavers by age

We next examine the extent to which consumption changes according to the age of the leavers. To this end, we estimate the following equation:

(2)$$\eqalign{\log C_{\,j, t} = \;& \partial + \gamma _1YoungMove0\_16_{\,j, t} + \gamma _2YoungMove17\_24_{\,j, t} + \gamma _3YoungMove25\_30_{\,j, t} \cr & \;\;+ \gamma _4YoungMove31\!+_{j, t} + \;\delta ^{\prime}Controls_{\,j, t} + u_j + u_t + ( u_p\,\ast\, u_t) + \varepsilon _{\,j, t}} $$

YoungMove0_16_j,t, YoungMove17_24_j,t, YoungMove25_30_j,t, and YoungMove31+_j,t represent the number of young leavers in each age group in household j in year t.Footnote ^19, Footnote ²⁰ The control variables and components of the error term are the same as in Equation (1). Once again, we estimate Equation (2) both for household consumption and per capita consumption, using a fixed-effects estimator. As in the previous sub-section, in order to assess whether the remaining household members save or consume the resources freed up by the leavers, the coefficients associated with the YoungMove variables in the models for per capita consumption need to be interpreted together with those in the models for total consumption.

6.1 Robustness tests

We conduct a set of robustness tests. First, Appendix Table A5 shows that our baseline results are robust to using a weighted fixed-effects estimator. Second, Appendix Table A6 shows that they hold when using a balanced panel.Footnote ²⁵ Both these exercises enable us to conclude that our main findings are not driven by attrition. Third, Appendix Table A7 shows that our results are robust to dropping members of the younger generation who passed away or left the household for reasons other than moving out.

Fourth, so far we have looked at the determinants of total, non-durable, and non-education consumption. One may wonder whether the results also hold for specific consumption categories. However, as durable and education consumption are respectively characterized by 61.05 and 72.39% zero values, we are not able to estimate their determinants using a fixed-effects linear estimator. A Tobit estimator should be used in this case, but fixed effects cannot be accounted for due to the incidental parameter problem. In Appendix Table A8, we therefore verify whether our results are robust to focusing on two other consumption aggregates, namely out-of-pocket medical expenditure and “other” expenditure, which either have few or no zero values. The former represents an important share (13.44%) of the total consumption of the respondents in our dataset, is essential expenditure, and closely depends on household composition. The latter is a miscellaneous category which includes diverse items such as local transportation; fees for matrons, housekeepers, and servants; taxes and fees turned over to the government; donations and so on. We can see that our main results hold for these two sub-categories of consumption, with one exception: neither total nor adult-equivalent out-of-pocket medical expenditure are affected by movers aged 25–30. This can be explained bearing in mind that respondents in this age group are generally healthy and may only free up a small amount of resources.Footnote ²⁶

6.2 Differentiating households based in rural and urban areas

As households living in rural areas may be very different from households based in urban areas, we have conducted separate analyses for households based in the two areas. The results are presented in Tables 6 and 7. In both Tables, the dependent variables in columns 1–3 are the logarithms of total household consumption, non-durable consumption, and non-education consumption, respectively. The dependent variables in columns 4 to 6 are the logarithms of total, non-durable and non-education adult-equivalent consumption.

Table 6. Young leavers and household consumption differentiating leavers by age; urban sample

Note: All models are estimated using a fixed-effects estimator. See Appendix Table A1 for definitions of all variables. The dependent variables in columns 1–3 are the logarithms of total, non-durable, and non-education household consumption, respectively. The dependent variables in columns 4–6 are the logarithms of adult-equivalent total, non-durable, and non-education consumption, respectively, which are calculated by dividing consumption by the equivalence scale (n^0.8). Year dummies and the interactions between provincial and year dummies are included in all models, but their estimates are not reported for brevity. Robust standard errors are in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

Table 7. Young leavers and household consumption differentiating leavers by age; rural sample

Note: All models are estimated using a fixed-effects estimator. See Appendix Table A1 for definitions of all variables. The dependent variables in columns 1–3 are the logarithms of total, non-durable, and non-education household consumption, respectively. The dependent variables in columns 4–6 are the logarithms of adult-equivalent total, non-durable, and non-education consumption, respectively, which are calculated by dividing consumption by the equivalence scale (n^0.8). Year dummies and the interactions between provincial and year dummies are included in all models, but their estimates are not reported for brevity. Robust standard errors are in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

For movers aged 0–30, these Tables show broadly similar results in urban and rural areas, which are also very similar to the baseline results. Specifically, we observe negative coefficients associated with the number of leavers aged 0–24 in the models for total, non-durable, and non-education consumption, coupled with insignificant coefficients in the corresponding regressions for adult-equivalent consumption. This suggests that the remaining household members save the resources freed up by the leavers. Focusing on the leavers aged 25–30, we observe positive coefficients associated with the adult-equivalent consumption aggregates and insignificant coefficients associated with the total aggregates. This suggests that the remaining household members consume the resources freed up by these leavers.

The Tables highlight, however, one difference between rural and urban areas. In rural areas, leavers aged 31 or more are associated with a higher adult-equivalent consumption of the left-behind household members (columns 4–6), coupled with an unchanged total consumption (columns 1–3). This suggests that regardless of the consumption aggregate considered, the remaining household members consume the resources freed up by the leaver. Yet, in urban areas, the results show negative (albeit only marginally significant) coefficients associated with these same leavers in columns 1–3, coupled with positive coefficients for the adult-equivalent aggregates (columns 4–6), which indicates that the remaining household members consume only part of the resources freed up by the leaver and save the rest. This difference between rural and urban areas could be explained bearing in mind that parents with leavers aged 31 and above are typically older and realize that they may need more help and support both financially and in-kind going forward. Whilst in rural areas, due to tighter social networks, support can be more easily obtained from friends, neighbors, and relatives living outside the household, this may be more difficult in big cities, which could then trigger a tendency of left-behind household members to save part of the resources freed up by the leaver for precautionary reasons. Another reason why households with leavers aged 31 or above may save part of the resources freed up by the leaver in urban areas, but not in rural areas may be that pension payments are a larger concern for urban households due to persistent increases in living expenses. By contrast, they are less of an issue in rural areas where many residents rely on self-sufficient agriculture (Zhang et al., Reference Zhang, Brooks, Ding, Ding, He, Lu and Mano2018).

6.3 Propensity score matching (PSM)

The key challenge of evaluating the causal link between the departure of offspring and the consumption of the left-behind household members is to make sure any changes in consumption are due to the departure of the offspring and would not have occurred without that departure. However, in real life, it is impossible to observe the outcome in the absence of the event. Hence, although we make use of panel estimators and control for a wide variety of individual- and household-specific characteristics in our models, which help alleviate the endogeneity concerns arising from omitted variable bias, our findings so far do not necessarily reflect causal relationships between leavers and household consumption.Footnote ²⁷

To better understand the links between the departure of members of the younger generation and consumption of the remaining household members, we make use of PSM (Rosenbaum & Rubin, Reference Rosenbaum and Rubin1983). PSM is a technique that mimics randomization in an observational data set by creating two groups (a treatment and a control group) that are comparable on observed characteristics. As a result, bias attributable to confounding is significantly reduced and selection bias is alleviated.

6.3.1 Methodological considerations

We first estimate Probit regressions to assess the probability of having at least one young leaver in a given age range (i.e., the probability of being treated) as a function of all control variables used in the baseline models evaluated in 2011. Fitted values from these regressions give the propensity scores, which are used to identify households in the control group (i.e., households who share the same characteristics as the treated households, but do not have young leavers) and form the basis of our matching.

Second, we use the one-to-one nearest neighbor matching with replacement, which matches each treated household with the control unit which is closest in terms of propensity score (Rosenbaum & Rubin, Reference Rosenbaum and Rubin1983). When matching with replacement, comparison units can be used as matches more than once if necessary.Footnote ²⁸ We use the caliper matching method, in which caliper refers to the difference in the predicted probabilities between the treated and control households. We match within a caliper of 1%.

Third, following Rottke and Klos (Reference Rottke and Klos2016), we define the average treatment effect of the treated (ATT) as follows:

(3)$$ATT = E( {Y_1-Y_0\vert D = 1} ) = E( {Y_1\vert D = 1} ) - E( {Y_0\vert D = 1} ) $$

where Y represents changes in adult-equivalent consumption between 2011 and 2013; the subscripts 1 and 0 refer to households with and without leavers in the age group considered, respectively; and D = 1 denotes the presence of leavers in that age group. At the household level, the first term on the right-hand side of Equation (3) represents the change in adult-equivalent consumption of household X, which has young leavers in the given age range. The second term represents the counterfactual: it measures what the change in adult-equivalent consumption of a household with young leavers in a given age bracket would have been had this household not had leavers. As this counterfactual is unobservable for household X, we seek an alternative household, Z (taken from the control group), with the same characteristics as household X, and observe their change in adult-equivalent consumption. In other words, we use this as a surrogate outcome for household X's counterfactual outcome. Extending this to a group level enables us to calculate the ATTs.Footnote ²⁹

In our context, the ATTs are defined as the expected differences in changes in adult-equivalent consumption over the period 2011–2013 between the treated and the control group.Footnote ³⁰ Any observed difference can be attributed to the departure of offspring in the age range considered. In other words, the ATTs represent the effect of experiencing the departure of a member of the younger generation in a given age range on changes in adult-equivalent consumption for households who actually experienced the departure.Footnote ³¹

6.3.3 Results

We report the ATTs for households with leavers in various age groups in Table 8. Columns 1–3 respectively refer to changes in adult-equivalent total, non-durable, and non-education consumption. All results are broadly consistent with our previous findings. They suggest that only households with leavers aged 25 and above show statistically significant and positive ATTs. In other words, regardless of how consumption is measured, compared to similar households with no leavers, only households with leavers aged 25–30 and above 30 show a statistically significant premium in adult-equivalent consumption growth, which is likely due to the departure of the offspring(s). In all specifications, the latter households always show the highest ATTs. By contrast, households with leavers younger than 25 show statistically insignificant ATTs.

Table 8. Average treatment effects on the treated (ATTs)

Note: This table reports the ATTs together with their standard errors. These are obtained using PSM with one-to-one nearest-neighbor matching and caliper of 1%. Columns 1–3 respectively refer to changes in adult-equivalent total, non-durable, and non-education consumption, calculated by dividing total, non-durable, and non-education consumption by the equivalence scale (n^0.8). See Appendix Table A1 for definitions of all variables. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.