Household size and poverty i

Transcription

1 Household size and poverty i Alessio Fusco and Nizamul Islam LISER (Formerly CEPS/INSTEAD) Luxembourg) May 2017 Abstract: We analyse the effect of household size, and in particular of the number of children of different age groups, on poverty, defined as being in a situation of low income. Identification of this relationship is complicated by endogeneity problems due to reverse causality and different forms of state dependence in low income. Therefore, using longitudinal data, we estimate static and dynamic probit models with alternative specifications, which allow us to control for the endogeneity of the variables of interest to be controlled for and to account for unobserved heterogeneity, first-order state dependence and serially correlated error components. Using data from the Luxembourg socioeconomic panel Liewen zu Lëtzebuerg and standard European Union definitions of poverty, we find that the number of children of different age groups significantly affects the probability of being poor. However, the magnitude of the effect varies across different specifications. For example, the increase of the likelihood of being poor due to a birth varies between 3.7% and 6.7% (1% and 2.1%) in the static (dynamic) case. In addition, we find that poverty is affected by significant true state dependence, unobserved heterogeneity and negative serial correlation in the error component. Keywords: poverty, household size, longitudinal data, state dependence, endogeneity, serial correlation, Luxembourg JEL: D10, D31, I32 i This research is part of the PersiPov project supported by the Luxembourg Fonds National de la Recherche (contract C10/LM/783502) and by core funding for LISER (Formerly CEPS/INSTEAD) from the Ministry of Higher Education and Research of Luxembourg. Comments by Francesco Andreoli, Lennart Flood, Federico Perali, Anne Reinstadler, Philippe Van Kerm, Bertrand Verheyden and Don Williams on previous versions are gratefully acknowledged. None of those mentioned should however be held responsible for the present contents. Alessio.Fusco@liser.lu, Tel: Nizamul.Islam@liser.lu, Tel:

2 1. Introduction The effect of having children is ubiquitous as it can affect many microeconomic behaviour, such as labour supply or expenditure decisions (Browning, 1992). With regard to poverty, having children is usually found to increase the propensity of being poor, which can be explained by a higher dependency ratio resulting in a dilution of household economic resources (Musgrove, 1980; Schultz, 2006). In this paper, this question is revisited and we assess whether the positive effect of the number of children on poverty still holds when taking into account two important confounding factors: endogeneity due to (i) reverse causality and (ii) various forms of state dependence in low income. (i) According to Browning (1992: ), one of the difficulties arising for all modelling of the effects of children [...] is how to take account of the fact that children may be endogenous to whatever it is that we are interested in modelling. This endogeneity may arise from reverse causality given that household size may affect poverty, but that the reverse is also possible. The latter can be due to the fact that households may choose not to have children to avoid being poor or because fertility choices and labour supply are simultaneously determined. This joint determination induces dependence between the unobservables affecting each process and suggests that the potential endogeneity of the number of children to the poverty status of a household should be considered (Schultz, 2006; Biewen, 2009). In literature on labour supply, there is a long tradition of identifying the effect of fertility on female labour supply using instrumental variables (IV). This strategy, which consists in finding a variable that influences the decision of having children without directly affecting the outcome of interest, has also been used in literature focusing on the effect of fertility on economic wellbeing and poverty (see Arpino and Aassve, 2013 for a review). The typical IV used are variables built on the basis of the composition of existing children, such as siblings sex composition (Angrist and Evans, 1998) or twins at first birth (Rosenzweig and Wolpin, 1980). 2 Compared to the case where fertility is assumed exogenous, the use of these instruments leads Mussa (2010) to find that the effect of fertility on poverty increases in Malawi while Datta Gupta and Dubey (2006) finds 2 Regarding sibling sex composition, the a priori expectation is that in developed countries, parents prefer to have mixed sibling sex composition so that parents who have two boys or two girls are more likely to have a third child than parents with one boy and one girl (in some, but not all, developing countries, parents display a strong preference for sons, which suggests that parents are more likely to have another child if the first two children are girls this is a slightly different IV). 2

3 that the effect disappears when fertility is treated as an endogenous variable. 3 A limit of using IV based on sibling composition is that the sample is restricted to women who already have at least two children and cannot extend to childless households. To tackle this problem, Agüero and Marks (2008, 2011) propose using infertility reported by women as an instrument, which leads them to the finding that endogenous fertility does not influence female labour participation, contrary to what OLS estimates were showing. (ii) Many social phenomena are affected by a considerable degree of state dependence (Heckman 2001; Skrondal and Rabe-Hesketh, 2014). For example, state dependence has been found to be an important determinant of the current poverty status (see e.g. Cappellari and Jenkins, 2004 or Ayllón, 2013). State dependence refers to the serial persistence often observed when experiencing an event in the past increases the probability of experiencing the same event in the present, in our case, the event is being in a situation of low income. State dependence can be spurious when it is the result of individual heterogeneity or genuine when it is the result of a behavioural effect of past poverty on current poverty. It can also be affected by time persistent effects of transitory errors. This framework helps to explain the reason why individuals at risk of poverty may have difficulty in exiting poverty in the future. The first explanation, linked to individual heterogeneity, suggests that individuals that were poor in the past might possess adverse observed or unobserved characteristics that increase their probability of being poor in the present. In this case, the persistence into low income is due to the persistence of adverse characteristics and not the previous experience of poverty. The second explanation refers to genuine state dependence: an individual who has experienced poverty in the past will behave differently compared with an otherwise identical individual who has not experienced poverty. For example, individuals at risk of poverty may become demoralized or have their human capital depreciated because of this situation, which prevents them from exiting poverty; the experience of poverty per se then increases the probability of being poor in the future (Jenkins, 2011, 2013). The third explanation lies in the possibility that a transitory shock such as an accident or sickness may lead to withdrawal from the labour market and persistently affect income-generating ability, leaving an individual behind on the income ladder. Identifying the 3 The findings of literature that does not take into account the endogeneity of fertility are also mixed (see e.g. Aassve et al, 2006).. In some countries the link between poverty and fertility is J-shaped implying that low income and high income have lower rates of fertility. 3

4 latter explanation is a complex challenge that has not yet been done in literature on poverty it constitutes one of the contributions of this paper. The identification of the effect of the number of children on poverty with an IV strategy is confronted with various challenges and limits. First, the conclusions that one can draw from this approach are based on strong assumptions as suggested by Rosenzweig and Wolpin (2000:864) who consider that the restrictions required for identifying the fertility effect on labour supply using either a twins-based or child-gender-based natural experiment involve strong (and similar) assumptions about preferences and household technology (see also Arpino and Aassve, 2013). Second, most of the literature using IV is based on cross-sectional data, which does not allow the issue of state dependence to be taken into account. In the current paper, the use of panel data allows the correlation of the variable of interest with the error term, due to reverse causality or state dependence, to be tackled in a more readable way. The random effects approach used, referred to as the correlated random effects approach (CRE), takes into account biases arising from reverse causality, omitted variable or unobserved heterogeneity and allows the correlation between fertility variables and unobservables to be taken into account. The current approach also allows for state dependence to be taken into account in terms of lagged dependent variable and the autocorrelation in the error term due to random shocks. A salient fact of the Luxembourg poverty profile is that the presence of children in a household increases the cross-sectional risk of poverty. Indeed, in 2009, the risk of being income poor for an individual living in a household with children was more than twice as high (21.1%) as for an individual living in a childless household (8.9%). In addition, in Luxembourg, as elsewhere, the risk of being poor increases with the number of children. For example, STATEC (2008) reports that in 2007, the risk of poverty of a couple (less than 65) without children was 8%, and increased to 10% with the presence of one child, 14% when there were two children and 25% if there were three or more children. This means that the increase in needs induced by the presence of children, but also the potential loss of labour income, is not fully compensated by family benefits provided by the state. These figures show that household size is correlated with poverty in Luxembourg, suggesting that this country constitutes a relevant case study for answering the present research question, and in particular for examining whether the effect of household size changes when endogeneity is taken into account. 4

5 The originality of this paper lies precisely in the use of longitudinal data and appropriate econometric methods to control for potential sources of state dependence and for the endogeneity of the variables of interest to evaluate the relationship under scrutiny. To our knowledge, this is the most comprehensive treatment of the effect of the number of children on the probability of being poor, for any country previously studied. In addition, since having a young child in the household is clearly different from having a teenager, this analysis focuses on the number of children of different age groups. 4 The estimation of reduced-form, static and dynamic, probit models using various specifications allows the study to control for individual differences in permanent observed and unobserved heterogeneity or transitory differences linked to serial correlation (Hyslop, 1999). To our knowledge, this paper is the first in the low income dynamics literature accounting for the possibility of transitory shocks in error components. 5 This estimation strategy enables this paper to robustly answer the following questions: does the number of children in a household increase the probability of being poor? Is this effect different for children of different age groups? This study analyses Luxembourg using data from the Panel Socio-Economique Liewen zu Lëtzebuerg (PSELL3) from 2003 to We find that the number of children of different age groups significantly affects the probability of becoming poor, even when controlling for the endogeneity of these variables. In addition, poverty is affected by significant true state dependence, unobserved heterogeneity and negative serial correlation in the error component. The paper is organised as follows. Section 2 reviews the literature establishing the link between poverty and household size. Section 3 presents the data of the Luxembourg Socio-economic panel Liewen zu Lëtzebuerg (PSELL3) and Section 4 presents the econometric model that will be used. Section 5 presents the results while Section 6 documents the magnitude of the effect through simulations and Section 7 concludes. 4 The current focus is on the effect of having children on poverty rather than on the effect of the life event of giving birth to a child on poverty. This is an important distinction as, for example, Pedersen and Schmidt (2012:4) report that in the case of subjective wellbeing there is clear evidence of differences in the results depending on whether the issue is the impact from the birth of a child, especially birth of a first child, or the eventual impact from the number of children in the family. 5 Islam and Shimeles (2007) or Bigsten and Shimeles (2008) account for this issue in the context of consumption poverty in a developing country and Hyslop (1999), Michaud and Tatsiramos (2011) or Okamura and Islam (2011) in the context of female labour supply. 5

6 2. Poverty and household size: the effect of having children Household size and composition can have an important impact on the incidence of income poverty (see e.g. Jenkins, 2000 or Jenkins and Rigg, 2001). For example, poverty literature often stresses the result that people living in larger and (generally) younger households are typically poorer (Lanjouw and Ravallion, 1995:1415). 6 This result suggests a positive association between poverty and having children. The poverty status of large households also depends on their composition: additional children generally increase the risk of being poor, which can be explained by a lower amount of resources per capita and a higher dependency ratio, while additional adults usually reduce the risk (Musgrove, 1980; Kuepie and Saïdou, 2013). 7 The presence of children may also affect poverty through a lower labour supply or human capital investment by the mother, which will reduce a mother s productivity and her family s income (Aassve et al, 2006, Datta Gupta and Dubey, 2006). This effect might also cumulate and perpetuate over generations since growing up poor has been found to have adverse consequences on a child s future outcomes in terms of health, school performance, socialization, ability to enter the labour market and welfare dependence, and hence future poverty status (e.g. Duncan and Brooks-Gunn, 1997). The number of children from different age groups may differently affect the status of poverty of a household. Young children imply the need to find a way to conciliate private and professional life: a parent might stop working because public transfers are not sufficient to cover childcare costs. An older child in the public education system decreases the cost of childcare however, other expenses in education and lower public transfers might mitigate this lower cost. Overall, the expected effect of having children on poverty is positive (unless social transfers compensate the additional costs linked with additional children), while it is unclear how this expected effect evolves with the age of the children. 6 They continue stressing that there has been much debate on which is the cause and which is the effect in this correlation. The position one takes in that debate can have implications for policy, including the role of population policy in development, and the scope for fighting poverty using demographically contingent transfers. 7 Other microeconomic arguments apply in developing countries where poorer households have a higher demand for children to contribute to the household economy (Martin-Guzman, 2005). However, the more children there are in a household, the less possibility there is to invest in each child s human capital, so that the situation of poverty of the household is perpetuated. 6

7 Causality might however run on the opposite side from poverty to the decision of having children. Indeed, individuals may decide not to have children simply to avoid being poor. This suggests that the potential endogeneity of the presence of children with respect to poverty status should be considered. The channels explaining this might be found on the labour market since labour market decisions, and hence poverty, are likely to be jointly determined by the decision to have a child (Aguëro and Marks, 2008, 2011; Fitzenberger et al, 2013). 8 Households with higher incomes tend to have fewer children because of a higher opportunity cost for the mother women with higher salaries have a higher opportunity cost of having children, which has a negative impact on their fertility decision - or for the trade-off between quality and quantity rich families invest more in children s education, which increases the cost of an additional child and has a negative impact on the fertility decision of a high salary-earning woman (Reinstadler, 2011). Therefore, the cost of having a child may be higher for high income households (Datta Gupta and Dubey, 2006). In addition, low income households may disproportionately see having children as a security or insurance for old age. In other words, there may be factors, both observed and unobserved, which drive both processes, poverty status and fertility decision, so that their relationship is circular and the direction of causality unclear (Schultz, 2006). This is well summarized by Brown (2012:54) who argues that "family structure and poverty are closely intertwined. In fact, researchers continue to debate the causal relationship between family structure and poverty. Some scholars are adamant that poverty is the cause of family structure, particularly unmarried childbearing, while others maintain that family structure leads to poverty, and still others find a middle ground" (see also Peichl et al. 2012).. In order to identify a causal effect of the number of children of different age groups on poverty, the endogeneity due to the reverse causality needs to be taken into account. In the same vein, the importance of tackling the different sources of state dependence mentioned in the introduction is a key issue. This is why this paper suggests 8 Here again, in developing countries, other reasons might be advanced to explain the link between poverty and fertility. For example, Datta Gupta and Dubey (2006:111) mention, among other reasons that poor households in developing countries may be more likely to invest in children as a source of support in old age, to compensate for missing markets in life insurance and social security. Infant mortality is another factor, in that families that expect higher mortality rates (such as the poor) may choose to have more children to compensate for this possibility (...). Also, poorer families may be slower to respond to a fall in child death rates, as they base their expectations of infant mortality rates on the experiences of their parents and others in their parent s generations, that is, there could be imperfect information. Poor families may also tend to have more children because they are more likely to be located in poorer regions where the probability is greater that a single child will not earn enough in adulthood to support his parents. 7

8 using correlated random effect panels to tackle the endogeneity of the presence of children as well as the state dependence issue. 3. Data and descriptive statistics The following empirical analysis is based on the Socio-Economic Panel Liewen zu Lëtzebuerg (PSELL3), which is the Luxembourgish component of the European Union - Statistics on Income and Living Conditions (EU-SILC). The first wave of PSELL3 collected information pertaining to around 3500 households and 10,000 individuals. The initial sample was representative of the resident population living in private households. Household members aged at least 16 answered a personal questionnaire and a reference person answered a household questionnaire. When children turn 16 they are asked to answer the personal questionnaire. Original sample members are followed over time and interviewed at intervals of approximately one year. In case of split-offs, new households, as well as all new co-residents, are followed. To account for the evolving characteristics of the population, due to the high level of migration and turnover in the resident population of Luxembourg, every year new individuals are included in the sample. The survey collects information about the incomes, living conditions and other personal and household characteristics of the interviewed so that it can provide repeated annual observations since 2003 on the same individuals allowing changes in poverty status to be linked with changes in household circumstances such as family arrangements or labour market situations. This paper utilises seven waves of the PSELL3 data covering the years 2003 to The research relies on a concept of poverty based on a lack of equivalent disposable income. Equivalent income is constructed by dividing the household total net income by an equivalence scale, which allows for the comparison of households of different size and composition. The choice of the equivalence scale is key in identifying the link between household size and poverty. In this paper, we chose to follow closely European standard practice (Atkinson et al, 2002) and use the modified OECD equivalence scale, which assigns a value of 1 to the first adult in the household, 0.5 to each additional adult and 0.3 to each child under 14. The equivalent income variable, and hence the low income status, is defined at the household level so that all household members are assumed to share the same status. The unit of analysis is the individual as individuals can be followed over time, even in the case of household splitoffs. As is standard in the European Union, an individual is considered poor if his equivalent income is lower than 60% of the annual median equivalent income. Figure 1 displays the 8

9 income distribution for individuals living in households with and without children in 2003 and These figures confirm that in Luxembourg the presence of children in a household increases the cross-sectional risk of poverty. Indeed, as already mentioned, in 2009, the unconditional risk of being income poor for an individual living in a household with children was more than twice as high (21.1%) as for an individual living in a childless household (8.9%), a relative risk of In 2003, the relative risk was 1.85; the main difference is due to the increase of the poverty rate of individuals living in a household with children (15.4% in 2003), as the poverty rates of the counterpart were stable over the period (8.2% in 2003). Figure 1: Equivalent income distribution, Density Density without children with children Source: PSELL3, ; authors computation. From now on, we restrict our sample to individuals, men and women, aged between 20 and 44 years old in 2003 and present in all waves. The working sample is a balanced panel which consists of N=918 individuals followed over T=7 periods providing 6426 person-wave observations. Table 1 presents descriptive statistics about the estimation sample. In the full sample, 76% of the individuals are never poor while 6.4% are poor only once during the period and 2.7% are always poor. The proportion of individuals remaining poor throughout the period is quite low in comparison with the annual average proportion of being poor, which amounts to 11.5% in the estimation sample. However, despite the low sample size, these proportions, which are similar in magnitude to those reported by STATEC (2010), suggest a significant persistence 9

10 in poverty. If the poverty status were following a binomial distribution of probability (the annual average proportion of non-poor), each year being independent, the probability to be never poor would be 42.5% (against 76%) and the probability to be always poor would be null (2.66e-0.7 against 2.7%). Differences in characteristics about individuals having experienced different patterns of poverty over time may arise from different sources. Heterogeneity in observable characteristics is one of them. This is why Table 1 presents the characteristics for the full estimation sample but also for the subset of individuals that are (i) never poor, (ii) poor between one and three times and (ii) at least four times poor. Table 1: descriptive statistics variable full sample never poor poor 1 to 3 at least 4 times times poor individual characteristics female age head of household characteristics female age bad or very bad health Luxembourg Portuguese other nationality married single divorced tertiary education lower education secondary education full time not full time household characteristics number of children less than number of children less between 6 and number of children less between 12 and number of adults lone parent number of individuals at work outright owner acceding to property tenant or rent free head of the household's father in high skilled job? number of times poor (column %) n Source: PSELL3, ; authors computation. Balanced sample of 6426 person-wave observations (individuals with no missing values in the covariates and aged between 20 and 44 in 2003). Compared to the full sample, individuals that are never poor live in households whose head is in better health, more likely to be Luxembourgish, better educated, working full time and in a 10

11 household with fewer children less than 6 years old, and with more individuals at work. They are also rarely renting their accommodation. Individuals who have experienced poverty at least four times live in households that are more likely to display the opposite characteristics, but also to have more children of different age categories and to live in a household where the head is a lone parent. Henceforth, employment protects from being poor while several characteristics of the head of the household are associated with poverty: lower education, citizenship, bad health and marital status (see also Fusco and Islam, 2012). Having children of different age groups increases the length of time spent in poverty. The difference is more important for the individuals at least four times poor. The difference between the never poor and the between 1 and 3 times poor are mainly found in employment and citizenship issues. 4. Econometric model This section defines the econometric model to look at the dynamics of an individual s i s poverty status, focusing on the effect of household composition particularly on the number of children of different age groups. It estimates a dynamic, discrete choice model combining the methods of finite mixture and simulated maximum likelihood. A dynamic reduced form model (Heckman 1981a, b, c; Hyslop, 1999) is adopted: = >0 (1) = + ~0, =1,2,,;=1,2,, Where P it is a binary response denoting the poverty status of an individual i at time t; Xit is a vector of exogenous variables, including individual characteristics, main income earners characteristics, household characteristics, and time dummies. The parameter γ represents true state dependence; captures the effects of time invariant unobserved factors such as intelligence, ability, motivation or general attitude of individuals that may influence the chance of being poor. The main focus is on the identification of the effects of fertility variables - that is the number of children of different age categories. As mentioned in the previous section, these variables may be endogenous with respect to poverty, and correlated with unobserved heterogeneity. The correlated random effect (CRE) approach first proposed by Mundlak (1978) or Chamberlain 11

12 (1984) allows this issue to be taken into account by redefining the unobservable factors as follow: = #!" %%%%%%%%%%+ #$ #!" %%%%%%%%%%%+ & ' #!" %%%%%%%%%%%%+) ( (2) Where #!" %%%%%%%%%% *+ is the time-averaged number of children aged between a and b. Following Heckman and Singer (1984), it is assumed that the uncorrelated unobserved factors η i follow a discrete, non-parametric distribution, with a finite number of mass points. A test of exogeneity of fertility to poverty is given by testing = = ' =0 In dynamic settings, the initial condition of an individual may be endogenous due to correlation with unobserved factors. This issue is addressed following Heckman (1981a, b, c) who suggests a method that accounts for the fact that the dynamic process may have begun before individuals are observed in the data. The model specifies a linearized reduced form equation for the initial period as: # =1 #, # +) # + # >0 (3) # =) # + # # ~-0,. / Where # is independent of unobservable factors for the initial period ) # and other exogenous variables. The set of covariates, # includes all the variables in plus an additional variable as an instrument for the initial conditions (see following section). It is assumed that the unobserved factor ) # satisfies the same discrete non-parametric distributional assumptions as ). The likelihood contribution of individual i is then defined as: > ; = : 6; ; /< < 1 # = #, # +) # 2 # 1/ ! +) 2 1/ Where δ is a vector of parameters of three additional variables related to the period under study: 1. average number of children aged between 0 and 5 in the household, 2. average number of children aged between 6 and 11 in the household, and 3. average number of children aged between 12 and 17 in the household. Equation 4 also allows for arbitrary correlation between the unobserved effect of the initial period and unobserved effects of other periods with the probability distribution of initial and other period support points. The approach proposed by Lee (1997) and recently applied in many other works in labour supply literature (see for example Hyslop, 1999, Okamura and Islam, 2011) is followed for 12 (4)

13 models with serial correlation in error terms. Following them a simulation based estimation method MSL is used (See for details Lerman and Manski, 1981, McFadden, 1989 or Pakes and Pollard, 1989) and it is assumed that the error terms are correlated over time, reflecting the correlation between transitory shocks, so that =? +@ ~0, A. For each individual i, with R independently generated vectors from random draws the simulated likelihood is then = C; 6; ; /< < < > 1 = 3 B : C ; 3 5 B #, # +) # 2 # 1/ ! +) +? 2 1/ In this specification the distribution of η is taken to have mass points j (5) η (j=1,2,...,j) with corresponding probabilities π j satisfying 0 <= π j <= 1 and π j = 1. To be specific, it is J j= 1 assumed that there are J types of individuals and that each individual is endowed with a set of unobserved characteristics, (j=1,2,...,j). Estimates based on this model are reported where J= Results The covariates reflect the demographic and working characteristics of the household where an individual lives and refer to the individual, the head of the household and the household. The individual level controls for age, age squared and gender. 10 The household level variables of the current model refer to household composition (as measured by the number of children aged less than 6, between 6 and 11 and between 12 and 17, number of adults and a dummy for lone parents), the attachment to the labour market (number of a household s members at work other than the household head) and the tenure status of the accommodation (outright owner, acceding to property, tenant or rent free). The set of covariates used to describe heads of the households includes their citizenship, employment status, health status, marital status, education, age, age squared and gender. 11 Dummy variables for each year are also included (table A1 provides some descriptive statistics). 9 The choice of J = 3 was made after comparing the likelihood of different options (see Chay and Hyslop, 1998). 10 When estimating the current models, the age variables were rescaled (divided by 10). 11 In the PSELL3 data, the head of the household is defined as the person in charge of the accommodation. If two individuals are co-responsible (e.g. a couple co-owning a house), the head of the household is the older. This last case was modified, and when two persons are in charge of the accommodation, the main income recipient among them is considered the head of the household. The hypothesis is that the household member with the highest personal income among the responsible of the accommodation has the highest influence on the household s standard of living. If they both have the same personal income, the older is deigned as the head of the household. 13

14 As mentioned in the previous section, an exclusion restriction is needed to account for the initial conditions problem using the approach proposed by Heckman. The exclusion restriction used for initial poverty status is a dummy variable indicating whether the head of the household's father was in a high skilled job when the head of the household was between 12 and 16 years old. As displayed in Table 1, for the full sample, 33% of the individuals had a father in a high skilled job. While this percentage was higher for individuals never poor (39%) it was lower for individuals poor between 1 and 3 times (16%) and much lower for those poor at least 4 times (4%). Using PSELL3, Fusco and Islam (2012) demonstrated the validity of this exclusion restriction when modelling the validity of initial poverty. Table 2 displays the result of various static models (simple pooled probit, random effect latent class probit and correlated random effect latent class probit). The first two columns present the results of the standard probit. This model does not allow for unobserved heterogeneity, state dependence or serially correlated errors. The three fertility variables number of children below 6, between 6 and 11, and between 12 and 17 have a significantly positive impact on the poverty status. An additional child from each of these age categories increases the likelihood of being poor. It is noted that having an additional young child has a lower effect than having an additional older child. Other characteristics of the head of the household have a stronger impact than demographic variables: it is especially the case when living in a household where the head followed only lower or secondary levels of education, is not in full time work, is not Luxembourgish or in bad health. An additional wage earner in the household reduces the probability of being poor. 14

15 Table 2: Estimated parameters of various static probit models Simple probit Random effect (latent class) (1) (2) (3) (4) (5) (6) estimates SE estimates SE estimates SE Correlated random effect (latent class) Individual characteristics female age/ age squared/ Main income earner characteristics female age/ age squared/ bad or very bad health Portuguese other nationality Single separated/divorced/widow lower education secondary education not full time workers Household characteristics number of children less than number of children less between 6 and number of children less between 12 and number of adults lone parent number of individuals at work acceding to property tenant or rent free Year dummies wave wave wave wave wave wave Correlated variables Mean_#ch age< Mean_#ch 5<=age< Mean_#ch 12<=age< Unobserved heterogeneity Mass point Mass point Mass point Prob. of mass point Prob. of mass point Prob. of mass point intercept Log likelihood No. of observations Source: PSELL3, ; authors computation. Balanced sample restricted to individuals with no missing values in the covariates and aged between 20 and 44 in

16 Columns (3) and (4) of Table 2 contain the results of the random effect latent class probit. It is assumed that persistence into low income may be due to the persistence of unobserved adverse individual characteristics that will increase the probability of being poor in the future. Therefore, in this model allowance is made for these adverse characteristics, which are assumed to have a common discrete distribution with a finite mixture of mass points. Results show that when controlling for unobserved heterogeneity, the three fertility variables still have a positive and significant impact on poverty, but the size of the effect is higher especially for children less than six years old, for whom the estimated coefficient almost doubles. This result shows a strong omitted variable bias and confirms that a large amount of latent error variance exists in the model and this variation can be explained by the unobserved heterogeneity in the individual risk of being poor. Furthermore, the estimated support points and accompanying probabilities for this model indicate that there are three types of risk. The first estimated support point (θ1= ) with corresponding probability π1 = indicates that 76% of individuals have a lower risk of being poor. The higher the value of the mass point, the higher the probability of being poor. This figure can be compared to the fact that 76% of the sample was found to be never poor (see Table 1). The second estimated support point (θ2=4.59) with corresponding probability π2 = indicates that the proportion of individuals with a high risk of being poor is very low. On the other hand, the third estimated support point (θ3=-1.203) with corresponding probability π3 = indicates that 23% of the individuals have a medium risk of being poor. As mentioned earlier, the main focus of this study relates to the identification of the effects of the number of children of different age categories. These variables may be endogenous, i.e. correlated with individual unobserved heterogeneity. In order to take this issue into account the static correlated random effect probit (see columns (5) and (6) of table 2) model is estimated. The results (separate Wald test) do not reject the null hypothesis that the number of younger children is endogenous, in the sense that the number of children below 6 and between 6 and 12 are correlated with unobserved heterogeneity. However, the null hypothesis of the endogeneity of the older children (between 13 and 18) is rejected. The simultaneous test of endogeneity of the three variables through the likelihood ratio test is not rejected (LR statistics=10.60 with 3 degrees of freedom) highlighting the importance of its modelling. While controlling for this endogeneity, the three fertility variables still have a positive and significant impact on poverty. The size of the effect increased by more than 60% for the two younger groups of children. This 16

17 implies that an estimation ignoring the endogeneity of fertility potentially leads to downward biased results. In this respect the results are similar to those obtained by Mussa (2010). The static models presented in model 2 allow endogeneity due to reverse causality to be taken into account, but not the various forms of state dependence. For this purpose Table 3 displays the result of the dynamics models presented in the previous section. First focus is placed on the issue of state dependence and then on the effect of the variables of interest in the dynamic context. In the dynamic model, the status of poverty is modelled as a function of lagged poverty and by using the Heckman approach to control for the initial conditions problem (see Table A2 and A3 for the initial conditions equations). 12 To determine whether there is genuine state dependence, the coefficient of the lagged poverty status needs to be examined. A satisfactory condition for the presence of genuine state dependence is the rejection of the null hypothesis that this coefficient is equal to zero. Columns (1) and (2) of table 3 present the estimated parameters of a correlated random effect dynamic model on the Heckman correction for initial conditions. This model suggests that there is genuine state dependence, as can be seen from the positive impact of the lagged status of poverty (γ = 0.975). Contrary to the static case, the separate Wald test rejects the exogeneity of the number of children between 6 and 12 and between 12 and 18, but not the exogeneity of the number of children less than 6. However, a simultaneous test of exogeneity of the three variables through the likelihood ratio test between this model and a dynamic uncorrelated random effect (not shown in the table) is rejected. The three fertility variables still significantly and positively impact on poverty, but it is interesting to note that contrary to the static case, younger children have a stronger impact than older ones. Table 3: Estimated parameters of Correlated Random Effect (CRE) dynamic models 12 To check the robustness of this modelling strategy, the model is estimated using the Wooldridge (2005) approach with initial conditions. Results (presented in annex table A4) show that using the Wooldridge initial conditions approach produces almost similar effects of the three fertility variables, as was the case with the Heckman initial condition approach. However, a slightly larger effect of state dependence is found in the Heckman approach compared to the Wooldridge approach. 17

18 CRE Heckman initial conditions CRE Heckman initial conditions and AR(1) (1) (2) (3) (4) estimates SE estimates SE Individual characteristics female age/ age squared/ Main income earner characteristics female age/ age squared/ bad or very bad health Portuguese other nationality single separated/divorced/widow lower education secondary education not full time workers Household characteristics number of children less than number of children less between 6 and number of children less between 12 and number of adults lone parent number of individuals at work acceding to property tenant or rent free Year dummies wave wave wave wave wave Correlated variables Mean_#ch age< Mean_#ch 5<=age< Mean_#ch 12<=age< lag poverty status in t initial period poverty status AR(1) Unobserved heterogeneity Mass point Mass point Mass point Prob. of mass point Prob. of mass point Prob. of mass point Log likelihood No. of observations Source: PSELL3, ; authors computation. Balanced sample restricted to individuals with no missing values in the covariates and aged between 20 and 44 in the first wave. 18

19 Finally, it is assumed that the time varying unobservable errors ) are serially correlated (first order autocorrelation AR(1)) with parameter ρ. The CRE Heckman initial conditions with AR(1) model (equation 5) involves identifying the effect of random shock that refers to autocorrelation in the error term. Columns (3) and (4) present the results of a correlated random effects dynamic model with a stationary AR(1) error component. The AR(1) error component is found to have a significant negative effect on poverty status ( ρ =-0.601). The log-likelihood of this model is better for this model than for the previous ones. Regarding the main research question, the results are similar to those obtained from the previous model: the variable number of children less than 6 is endogenous while the two other fertility variables are exogenous. The three fertility variables still significantly and positively impact on poverty. There is true state dependence as can be seen from the positive impact of the lagged status of poverty. 6. Simulations Coefficient estimates of models with limited dependent variables do not convey the magnitude of the effects. Simulations of the response to an event can be used to capture this magnitude. Our simulation strategy is very similar to Hyslop (1999), Islam (2006) or Okamura and Islam (2012) where they simulate the effect of birth during 1st year and follow the response of the birth on mother participation decision over 20 years. In this paper we simulate the similar event on poverty over the 16 years of age of the child. For this we simulate two events: first, we calculate the probability of being poor over the 16 years using the estimated parameter for various specifications reported in Tables 2 and 3 with full sample keeping all other variables constant; second; second we simulate an event (adding a child during 1st year) and calculate the probability of being poor over the 16 years with the same sample. To assess the effect of a birth we see differences of these two events. Indeed this is the marginal effect of a birth on poverty status. Figure 1 compares these marginal effects for simple probit (Simple), random effect probit (RE), correlated random effect probit (CRE), correlated random effect dynamic probit with Heckman initial condition (Dynamic), and correlated random effect dynamic probit with Heckman initial condition and with 1st order auto correlation in the error term (Dynamic-AR (1)) specifications presented in the previous section. 19

20 Figure 1: Simulated response of being poor to a birth during 1 st year Source: PSELL3, ; authors computation. Balanced sample restricted to individuals with no missing values in the covariates and aged between 20 and 44 in the first wave. Reading guide: The curve of the simple probit reports the change of probability due to the birth of a child in t=0 and then to the presence of one child of age equal to 1 through 16 according to the parameter estimated in Table 2 column (1). Before turning 6, the increase of probability of being poor due to the presence of this child is equal to 3.7% (which corresponds to the estimated parameter of 0.140); when the child is between 6 and 11, the value is 4.5% (corresponding to a parameter of 0.169); when the child is between 12 and 16, the value is 6.9% (corresponding to the parameter of 0.256). This confirms that in the simple probit, an additional older child in the household has a stronger effect than an additional younger child. In the first year, an additional child increases the probability of being poor by 3.7 percentage points in the simple model, 6.7 in the RE model, 4.8 in the CRE model, 1.00 in the dynamic model, and finally 2.1 in the dynamic-ar(1) model. The almost 3% difference between the simple and RE model shows that heterogeneity-bias arise from the individual specific unobserved characteristics while the difference (1.9%) between RE and CRE model shows that endogeneity-bias arise from the correlation between individual specific unobserved characteristics (such as motivation, ability to work, preferences) and the fertility behaviour (for example having a certain number of children or not). Next, the dynamic model with Heckman-type initial conditions is considered. Allowing for initial condition and true state dependence, we find a stronger effect of a birth on poverty: the distance between the CRE and Dynamic model. However, this effect is noticeably different to the simulated effect from the Dynamic-AR(1) model: when the serial correlation in the error term is taken into account. 20