Social Pensions, Migration and the Anticipation E ect

Transcription

1 Social Pensions, Migration and the Anticipation E ect Mark N. Harris y, Brett Inder z and Pushkar Maitra x June 2007 Abstract In this paper we examine intra-household decisions surrounding the relationship between migration of working-age adults and the provision of aged pension. The empirical analysis exploits the structure of the social pension program in South Africa, where for most black households age-eligibility is su cient to ensure pension receipt. We allow for the possibility of an anticipation e ect, where as some members of the household approach the of- cial age of eligibility for pension receipt, households adjust their behaviour with migration of working-age adults becoming more likely. The estimation methodology allows the data to endogenously determine the ages at which the pension anticipation e ect takes e ect and any subsequent ages at which the e ect changes. The empirical results suggest that households with pension recipients are more likely to send migrants in search of work. Households do not seem to wait for the members to become actually eligible to receive social pension. Furthermore, this forward-looking behaviour appears to become stronger as we move closer to the o cial age of pension eligibility. It appears that the program has created economic opportunity, in allowing working-age adults to migrate in pursuit of better employment possibilities. JEL Classi cation: O15, I38, C25, C15 Keywords: Migration, Household Behaviour, Anticipation E ect, Social Pension, South Africa Funding provided by the Faculty Research Grant Scheme, Faculty of Business and Economics, Monash University. We would like to thank Asadul Islam, seminar participants at CSSS, Kolkata, Monash University and the Australian National University for their comments and suggestions. The usual caveat applies. y Mark N. Harris, Department of Econometrics and Business Statistics, Monash University, Clayton Campus, VIC Mark.Harris@Buseco.monash.edu.au z Brett Inder, Department of Econometrics and Business Statistics, Monash University, Clayton Campus, VIC Brett.Inder@Buseco.monash.edu.au x Pushkar Maitra, Department of Economics, Monash University, Clayton Campus, VIC Pushkar.Maitra@Buseco.monash.edu.au 1

2 1 Introduction Rural-urban migration is a pervasive fact of life in developing countries. Typically a working age adult member of the household will respond to earning opportunity di erentials by migrating to the city and remitting a portion of his/her income back home to support the parent household. It is typically assumed that co-residence in the village is the preferred option and migration happens only if co-residence is no longer a ordable and the main driver of rural-urban migration is the income di erential in the two locations. In this context consider the introduction of a social protection program, which increases household income and directly bene ts the parent household. What happens to migration as a result of this income shock? On the one hand, given that co-residence is now more a ordable, we might see a reduction in migration. On the other hand, remember that migration is a risky decision it is not certain that the migrant will get a job on migrating and poor households might be less willing and less able to bear this risk. The introduction of the social protection program, by reducing the income constraint, increases the ability of the household to bear risk. As a consequence we might observe more migration. Which of the two e ects dominates is an empirical question. In this paper we examine the relationship between a social protection program and migration in a developing country. The speci c social protection program is aged pension in South Africa. While a social pension program aimed at maintaining the standard of living of the elderly and unemployed white South Africans has been in existence since the 1940 s, universal coverage of this program is a relatively recent phenomenon: it is only with the recent eradication of apartheid and the demand for equal coverage and racial parity that coverage was extended to include the nonwhites. The structure of this social pension program makes it an ideal one to analyse the e ects of a social protection program on migration. For rural black South Africans, income from this program depends primarily on age-eligibility: men become eligible at age 65 and women at age There is a means test although 1 During the apartheid era, all South Africans were categorised into one of the following four 2

3 it is not binding for most rural black South African households (Alderman 1999). Typically there are a number of identi cation and endogeneity problems that make it di cult to analyse the e ect of pension income on migration (for example pension income typically depends on past decisions, which in turn might have a direct e ect on migration decisions). However the structure of this particular program allows us to address these issues. The program is discontinuous in nature (de ned by the age-eligibility criterion for receiving pension income) and we explicitly use this discontinuity to identify the e ect of pension receipt on migration. We initially assume a continuous e ect of the ageing of members on the household s migration behaviour. We then allow for a jump (or a break) in this relationship at (or around) the o cial age of pension eligibility. However, is it rational to expect that household behaviour changes abruptly as members of the household become age quali ed? After all, if households are aware of this age-eligibility e ect, should they not incorporate this into their behaviour? In other words, as households members approach age-eligibility, forward looking households can alter their behaviour even before the household becomes age-eligible. An obvious discontinuity is at the point at which family members become age quali ed. The discontinuity might not however occur (only) at this age: perfect knowledge and foresight might push it forwards, while imperfect knowledge and issues of pension take-up rates might push it backwards. It would therefore appear more appropriate to let the data endogenously determine such a break point rather than imposing it a priori. We then take this approach further by ascertaining whether, apart from this initial discontinuity there are any secondary break points. That is, we allow the model to capture di erent degrees of response of the migration decision depending on the speci c age(s) of the elderly in the household. The results reported in this paper con rm that households with pension recipients are more likely to send migrants in search of work, suggesting that the universalisation of the pension program reduced the income constraint on the parent households, allowing working age households to migrate in pursuit of better employment categories: black (or African); coloured (or mixed race); Indian (or Asian); and white (or caucasian). To maintain consistency with the data and the existing literature, we stick to this categorisation. 3

4 opportunities. Often (though interestingly not always), households appear to exhibit forward looking behaviour: as some members of the household approach the o cial age of eligibility, households appear to adjust their behaviour rather than waiting for the members to actually become age eligible. Additionally this forward looking behaviour actually becomes stronger as we move closer to the o cial age of eligibility. It is also important to note that we nd signi cant gender di erentials in terms of the impact of pension receipts on migration. 2 The Social Pension Program in South Africa and its E ects on Household Behaviour Before going into the details of the modelling approach and the results, it is worthwhile presenting some contextual background. Despite its relatively short history, the e ect of social pensions on black South African households cannot be underestimated. The pension makes an important contribution to the income of black South African households: Vorster, Rossouw, Raubenheimer, and Muller (1996) nd that if pension income is excluded from household income, all households without a wage income drop below the subsistence level and 60% of households with one earner drop below the subsistence level. What were the bene ts like? In 1993 the maximum bene t was R370, increasing to R520 by In recent years there has been quite a large amount of work on the South African social pension program. Di erent researchers have examined di erent aspects of the program: see, for example, Lund (1994), Case and Deaton (1998), Maitra and Ray (2003), Du o (2003), Bertrand, Mullainathan, and Miller (2003), Jensen (2004) and Edmonds, Mammen, and Miller (2005). In this paper we will examine the potential connection between access to the social pension and internal migration. In doing so we address the broader question of how a social protection program of this sort a ects household composition and household formation. The issue of endogenous household formation is an important one in the development of social policy. The recent South African experience provides an excellent 2 As of 1999 the exchange rate was 1USD = 6 Rands. 4

5 opportunity to examine the e ects of various social policies, as the dismantling of apartheid brought with it a number of drastic changes, particularly with respect to legal rights and social protection. One particular issue centres on the mobility of working-age adults. There is a belief that the changing legal, social and economic circumstances in post apartheid South Africa have resulted in increased child fostering among black households. 3 After the dismantling of apartheid and the repealing of the dreaded pass laws, black women now have the legal freedom to migrate to the cities in search of employment. However, because of the poor living conditions in South African cities, adults often prefer not to bring their children with them to the cities, instead leaving them with their grandparents and/or other relatives in the villages. 4 Black South Africans also often prefer their children to grow up in the villages so as to maintain historical, social and tribal ties with the land. Edmonds, Mammen, and Miller (2005), using census data, nd that pension-receiving households have fewer prime working age adult females but have more resident children below the age of 5 and more young women of childbearing age. They argue that this changing structure of the black South African household is the result of the increase in the coverage of the social pension program. Maitra and Ray (2004), using panel data from the Kwazulu-Natal province in South Africa, nd no evidence to support the hypothesis that an increase in pension amount, or an extension of the pensions program to a wider group of households, leads to an increase in household size (due to more working age adults and children residing in pensioner households). The evidence overall suggests that an increase in pension amount and/or coverage, leads to a reduction in the number of working age adults in the household. They were, however, unable to nd an explanation for this phenomenon. The possible explanation that we wish to explore in more detail in this paper is whether the expanding social pensions program in South Africa encourages working 3 See Zimmerman (2003) for a discussion of child fostering in South Africa. 4 Maluccio, Thomas, and Haddad (2003) provide evidence of a signi cant increase in the number of children residing away from their mothers in 1998 compared to 1993, when the apartheid system had only just been abandoned. On the other hand, they found no signi cant change in the proportion of children living away from their fathers in 1998 compared to The much greater access to the social pensions scheme may well have encouraged households to have children and other dependents live with the pensioners. 5

6 age adults to leave the villages in search of employment in the city, with their elderly parents left to care for the children. It is well documented that pensioners have a propensity towards sharing their pensions with others 5 and it is plausible that this extends as far as allowing working-age adults being mobile in search of employment. 3 Data, Descriptive Statistics and Econometric Speci cation 3.1 Data and Descriptive Statistics We use two di erent cross-sectional data sets for our analyses. The rst is the South African Integrated Household (SIHS) data set, which was collected in 1993 as a part of the World Bank s Living Standard Measurement Surveys undertaken in a number of developing countries. This data was collected in the nine months prior to the rst democratic elections in South Africa that brought Nelson Mandela to power. The survey was conducted jointly by the World Bank and the South Africa Labour and Development Research Unit (SALDRU) at the University of Cape Town. This cross-sectional data set is unique because it is the rst survey that covers the entire South African population including those in the predominantly Black homelands. The sample consists of approximately 9,000 households drawn randomly from 360 geographical districts/clusters. The questionnaire and summary statistics are contained in SALDRU (1994). We will henceforth refer to this as the SIHS93 data. The second data set that we use is the October Household Survey (OHS) data set from 1998 (OHS98 data). The OHS is an annual survey, based on a probability sample of a large number of households. The data sets cover a range of development indicators that include: demographic factors (such as age, gender, level of education, marital status, migration, use of health services and internal migration); economic variables (such as employment, unemployment and informal sector employment); and social and well being measures (access to health and social services, safety of 5 Evidence on this is contained in Ardington and Lund (1995), McKendrick and Shingwenyana (1995), Moller and Devey (1995), Moller and Sotshongaye (1996). 6

7 household, average household size, type of dwelling, level of education, quality of life, health statistics and vital statistics). Though the OHS has been conducted every year from 1993 onwards, we use data from the 1998 survey only, primarily because of data comparability. Comparison of the results that we obtain using the data sets from 1993 and 1998 could throw light on the changes that happened in South Africa in the 5 years following the o cial end of apartheid. Table 1 presents a selection of descriptive statistics for the data. Recall that the estimation sample is restricted to black households as pension uptake for white, Indian and coloured households could be endogenous as the income means test applies to a higher proportion of these population groups. Not surprisingly the period has witnessed signi cant changes in a number of the broad aggregates. In the most striking example, on average there were migrants per household in 1993, while this rose to in There has been a sharp increase in the average number of both male and female migrants. Average household size has fallen over the period, from 5.38 members in 1993 to 4.55 members in 1998 and this decrease is uniformly distributed across all age categories. The maximum number of age quali ed elderly in any household is 3 (the minimum being 0); the maximum number of age quali ed males is 2 and the maximum number of age quali ed females is again 3. There has been a drastic increase in the proportion of households where the highest education attained by the household head is more than high school, from 2.60% in 1993 to 23.8% in An appropriate measure for pension receipt would appear to be the actual amount of pension received by members of the household. However, this data appears to contain a number of errors often the amount of pension received takes quite implausible values. Consequently, we use the more indirect, but more reliably measured, variable representing the number of adults who are age-quali ed to receive the pension (AGEQUAL), de ned as the number of males aged 65 and over and females aged 60 and over. This variable should (theoretically) provide a good indication of the amount received: the pension is a xed amount per eligible recipient as the income means test, which could lead to a reduced pension receipt, applies to 7

8 very few rural, black South African households. 3.2 Econometric Methodology The simplest way of examining how pension receipts a ects migration would be to estimate a standard binary probit, or logit, regression where the dependent variable is whether the household has a migrant or not (m i ), regressed on a number of household and community characteristics, including AGEQUAL. 6 If the coe cient estimate of AGEQU AL is positive and statistically signi cant, this suggests that as the number of age pension quali ed household members increases, so does the probability the household has a migrant. Not surprisingly the results from such an analysis (presented in Table A1 in the appendix) show that this coe cient is indeed positive and statistically signi cant. We call these the baseline results. 7 However, there is no reason to expect that the discontinuity will coincide exactly with the actual age at which individuals become age-eligible: rational individuals should make decisions based on all available information and therefore if households know of this age quali cation e ect, they should incorporate this into their behaviour. Our hypothesis is that the marginal e ect of the number of persons falling into various age categories (in the vicinity of the age of eligibility) on the probability of observing a migrant in the household is not constant. We start by assuming that in the absence of the program, changes in migration behaviour associated with the ageing of members of the household are smooth: there are no jumps or discontinuities. We then look at discontinuous changes in migration behaviour that occur as a result of the age eligibility condition and explicitly allow the data to choose the point(s) of discontinuity. We make certain assumptions about the nature of the relationship between pension receipt and the probability of migration. In particular we assume that within the relevant age range, the e ect of age on the probability of migration is a constant. For example, in the baseline regression we assume that having an 6 The precise wording of the relevant question in the surveys is: Are there any persons who are usually regarded as members of this household, but who were away for a month or more in the last year because they are migrant workers? A migrant worker is someone who is absent from home for more than a month each year to work or seek work. 7 Bertrand, Mullainathan, and Miller (2003) use a similar speci cation in analysing the e ect of pension receipts on employment status of working age adults in the household. 8

9 additional age-quali ed pensioner in the household (on the probability of migration) is invariant to the actual age of this additional member. There is another issue worth noting. In certain areas of the country, authorities deviated from the rule that men become pension eligible at a later age compared to women. As Case and Deaton (1998) report, the age di erential in pension eligibility is technically unconstitutional and certain local authorities might have gone ahead with age equalization as far back as Therefore assuming that the discontinuity will coincide exactly at the actual age at which individuals become pension eligible could make the model mis-speci ed. Let Q i[j;k] be the number of individuals in household i who are aged between j and k years from the age of o cial pension eligibility. For example, Q i[ 10;2] would be the number of males aged between 55 and 67, plus the number of females aged between 50 and 62. Under this notation, the number of age-quali ed individuals in the household (AGEQUAL) would be given by Q i[0;1]. The baseline model can then be speci ed as m i = Q i[0;1] + x 0 i + e i ; (1) where x i is a vector of other household controls, is a set of parameters to be estimated and e i is a standard normally distributed error term; m i = 1 if the household has a migrant and zero otherwise. We present a range of variations on this speci cation that capture di erent possible pension e ects. In each case, nested simpler models are obtained via parameter restrictions, allowing us to perform tests to see whether a particular speci cation can be rejected in favour of others. The rst e ect we consider is whether there is a di ering pension e ect once a person is more than 10 years past eligibility age. The argument here is that as elderly members of the household reach more advanced years, their physical capabilities may diminish and the potential of death and loss of pension increases. These factors could imply possible changes in the e ect on the migration decision. To capture this e ect we estimate m i = Q i[0;10] 1 + Q i[11;1] 2 + x 0 i + e i (2) 9

10 Note that Q i[0;1] = Q i[0;10] + Q i[11;1], so equation (1) is a special case of (2) with the linear restriction 1 = 2 = : We refer to the speci cation in equation (2) as the extended baseline speci cation. Next, we want to capture the possibility of an anticipation e ect. In this case we could use the following model speci cations: m i = Q i[ 10;10] 1 + Q i[11;1] 2 + x 0 i + e i (3) and m i = Q i[ 10; 1] 11 + Q i[0;10] 12 + Q i[11;1] 2 + x 0 i + e i (4) Imposing the restriction that 11 = 12 in (4) gives the speci cation in (3), exploiting the fact that Q i[ 10;10] = Q i[ 10; 1] + Q i[0;10]. In addition, if 11 = 0; then (4) reduces to the model in (2). Inability to reject the null hypothesis 11 = 12 in (4) implies that migration behaviour is not a ected by the age composition of the household (conditional on di erential behaviour for individuals more than 10 years past eligibility). If the null hypothesis is rejected against the alternative 11 6= 12, we conclude that there is a discontinuity in migration behaviour that arises at the point of pension eligibility. In this case (in equation (4)) remember that we are imposing the restriction that the discontinuity happens exactly at the age of quali cation. Also remember that here we are assuming that the marginal e ect of an additional member in the age range [ 10; 1] is constant, as is the marginal e ect of an additional member in the age range [0; 10]. The next level of complexity allows the data to endogenously determine the point of discontinuity, rather than imposing that break exactly at the age of pension eligibility. In other words, we estimate the following set of models m i = Q i[ 10;j 1] 11 + Q i[j;10] 12 + Q i[11;1] 2 + x 0 i + e i (5) where j 2 ( 8; 9). We estimate equation (5) for each value of j in the speci ed range, and then choose the model (value of j) which maximises the likelihood function. We call this the maximum likelihood estimator (MLE) of j. For example, when j = 8, we construct Q i[ 10; 9] and Q i[ 8;10] and estimate the model obtaining the 10

11 maximised likelihood function conditional on j = 8. We repeat this for each value of j between 8 and +9, obtaining a maximised likelihood function in each case. The MLE of j is obtained as the value of j, which yields the maximum of these conditional likelihoods. Another level of generalisation is possible if we allow the anticipation or pension e ects to vary by specifying for further breaks in the coe cients. Suppose the maximum likelihood estimator for j is given by j. We can then estimate the following models, conditional on the rst e ect: m i = Q i[ 10;k 1] Q i[k;;j 1] Q i[j ;10] 12 + Q i[11;1] 2 + x 0 i + e i (6) where k varies between 8 and j 2. If a maximum likelihood estimate of k is given by k, we then estimate m i = Q i[ 10;k 1] 111 +Q i[k ;j 1] 112 +Q i[j ;` 1] 121 +Q i[`;10] 122 +Q i[11;1] 2 +x 0 i +e i for ` varying between j + 2 and 9. The optimal version of equation (7) would be found by using the maximum likelihood estimate of ` (`). One can decide on an appropriate model speci cation by performing a range of tests of the restrictions on the more general models to see whether the restricted models are valid. One complication with this approach is that, under the null, one, or more, breakpoint parameters is (are) not identi ed. For example, when equation (5) is estimated over the range of j values and the MLE j found, the model can be written as m i = Q i[ 10;j 1] 11 + Q i[j ;10] 12 + Q i[11;1] 2 + x 0 i + e i (8) If 11 = 12 in (8), this equation is equivalent to (3), and we can easily compute a Wald, Likelihood Ratio or Lagrange Multiplier test statistic to tell us whether the generalisation to allow for a break in the magnitude of the pension anticipation e ect is justi ed or not. However, under the null hypothesis that 11 = 12, the parameter j is not identi ed. This problem is similar to that found in the time series literature when testing for structural breaks with unknown change points. 11 (7)

12 Asymptotic results for the distribution of the W ald statistic in this case were obtained by Andrews (1993): the distributions are not standard 2 because of this unidenti ed nuisance parameter. Andrews (1993) tabulates critical values based on the asymptotic distribution results presented in that paper. Unfortunately we are not able to utilise Andrews s (1993) critical values, as his asymptotic results are speci c to the assumed properties of the regressors and the nature of the structural change, and they do not apply to the type of models we are analysing. That is, here we are dealing with models with discrete dependent variables and regressors whose asymptotic moments would not satisfy the required properties. However, we can draw on Andrews s (1993) general approach to devise a procedure for simulating critical values for our situation. We illustrate the methodology with reference to testing the simpler model (3) against the more general model (8). As noted, for a given value of j, equation (3) is obtained by imposing the restriction that 11 = 12 and a standard W ald statistic for testing a linear restriction can be calculated. Refer to this test as W ald(j). This can be repeated for each value of j in the range 8 to 9: We de ne the test statistic is the maximum of these statistics sup W = sup W ald(j): While the distribution of each individual W ald(j) statistic is a standard 2 under the null hypothesis, the distribution of sup W, given by the sup of all these asymptotic 2 distributions, will be very complex, as it will be dependent on the speci c dependence structure between the separate W ald(j) tests, which in turn will depend on the asymptotic behaviour of standardised moments of the explanatory variables in the model, particularly the Q i[j;k] variables. In other words, the asymptotic distribution depends on the speci c asymptotic properties of the explanatory variables in the model. We will outline the theoretical issue in a more general context here, before moving to a practical solution to performing the required tests in the above cases. First, consider the more general model y i = Q 0 i(j) (j) + x 0 i + e i (9) 12

13 where y i is a dependent variable of interest, x i is a vector of explanatory variables, and Q i(j) is a vector of explanatory variables where the exact composition of the Q i(j) vector can vary across J di erent cases (J being a nite constant). That is, there are J possible sets of Q i(j) vectors, each with coe cient vector (j). Equation (9) encompasses the various models described above, plus other cases where one might wish to consider a range of possible explanatory variables. For example, Q i(j) may represent a set of possible standardised indices proxying for some unobserved latent variable presumed to in uence y i. 8 The maximum likelihood estimator for j, denoted j, and for (j), can be obtained by estimating (9) using maximum likelihood for each value of j = 1; :::; J and choosing the value of j which maximises the likelihood function. We are interested in testing hypotheses about (j): consider the general linear restriction R (j) r = 0. In general, the Wald statistic for this testing problem for a given j can be written as W ald(j) = (R(j) r) 0 [RV (j) R 0 ] 1 (R(j) r) (10) (j) is the estimate of obtained when Q i(j) is included in the estimated model, and V (j) is the estimated variance-covariance matrix of (j) : The optimal test is the J th order statistic of this vector of Wald statistics sup W = sup W ald(j). distribution function of sup W is given by David and Nagaraja (2003) The Pr(sup W < w) = Pr(W ald(1) < w; W ald(2) < w; :::; W ald(j) < w): (11) Importantly, this distribution depends on the joint distribution of the W ald statistics. It is clear from (10) that the W ald statistics will be correlated with each other, so there is no obvious or general means of simplifying their joint distribution to obtain a closed form for the desired distribution function. This leaves no practical choice but to obtain critical values by simulation for any given case. In the present context, we proceed in this direction by generating repeated samples under the null hypothesis, using the estimated parameter values from the null model 8 We should point out that this framework is similar, but conceptually di erent to that considered in threshold regression models. With threshold models, the set of explanatory variables is xed, and the coe cient vector varies, depending on whether a chosen indicator variable crosses some threshold value, which might be estimated from the data. So while there are analogies here, the speci c context is quite di erent. 13

14 and the actual x i data to generate the arti cial data. For each sample, we construct the W ald(j) statistics and the sup W statistic. After repeated samples, we have an empirical null distribution for sup W. This can be used to calculate an appropriate test critical value or to obtain the empirical p value for the actual test statistic. This process can be applied to test the model of (3) against (8), and then (8) against the more general model given by: m i = Q i[ 10;k 1] Q i[k ;;j 1] Q i[j ;10] 12 + Q i[11;1] 2 + x 0 i + e i (12) and then (12) against the even more general model: m i = Q i[ 10;k 1] 111 +Q i[k ;j 1] 112 +Q i[j ;` 1] 121 +Q i[`;10] 122 +Q i[11;1] 2 +x 0 i+e i : (13) The estimation and testing methodology adopted here can be adapted to di erentiate migrants by gender, as well as for varying e ects by gender of the pension recipient. This contrasts with Edmonds, Mammen, and Miller (2005) and others, who focus on female pension recipients alone. Arguments have been made in support of capturing only the e ects of female pension receipt. First, Edmonds, Mammen, and Miller (2005) argue that the identifying assumptions would be more suspect in the case of men: for example men are more likely to face retirement incentives at the age of pension eligibility, while this is likely to be less of an issue for women. Second, Bertrand, Mullainathan, and Miller (2003) argue that in some provinces in South Africa, men report pension take-up on turning 60 and not on turning 65. Third, Du o (2003) and Bertrand, Mullainathan, and Miller (2003) argue that women s pension receipts are more likely to have a (stronger) e ect on household behaviour as female pensioners are more likely to share their pension income with other household members. Because our methodology involves searching over a range of ages (age of pension eligibility 10 years), this can address the rst two concerns relating to potential incentive e ects and the measurement error associated with pension uptake. As far as the third issue is concerned, we argue that di erential gender e ects are an empirical question, which needs to be tested using available data. Accordingly in this paper we take into account both male and female pension e ects and allow for possible di erences in e ects across gender. 14

15 4 Estimation Results Due to space constraints the discussion of results focuses on those using the OHS98 data. We present the marginal e ects (and not the actual coe cient estimates) as they are more easily interpreted; standard errors are computed robustly to account for arbitrary heteroskedasticity. Each estimated model includes a range of other variables designed to capture household characteristics, demographics and economic status (x i ). These variables include: the number of resident children; age, sex and highest level of education attained by the head of the household (primary, high and more than high school; the reference category is that the head of the household has no formal education); a dummy variable for rural residence; a set of province dummies; and a set of household asset variables (including the main source of energy for heating, lighting and cooking; main wall and roof material for the house; and the number of rooms in the house). 4.1 Extended Baseline Results Table 2 presents the extended baseline probit regression results for the presence of a migrant in the household. These results all represent variations on equation (2), where we allow for separate e ects for age-quali ed adults up to 10 years past age-eligibility and adults more than 10 years past eligibility. 9 The results presented in column (1) do not distinguish between male and female age-quali ed pensioners while those in columns (2) (4) do. The results in columns (1) and (2) do not identify the gender of the migrant in the household, while in columns (3) and (4) we present the marginal e ects from the probit estimation for the presence of male and female migrants in the household, respectively. The marginal e ects associated with the pension variable imply that the number of age-quali ed elderly in the household has a positive and highly statistically signi cant e ect on the probability of migration. An increase in the number of male age-quali ed pensioners generally has a stronger e ect on the probability of migration; an increase in the number of female age-quali ed pensioners has a statistically signi cant e ect on the presence 9 See Table A1 in the appendix for the baseline regression results (corresponding to the speci - cation in equation (1)). 15

16 of a female migrant in the household, but not on migration of males. 4.2 Optimally Chosen Break Points, No Gender Di erentiation of Pension Recipient The rest of the results that we present are the estimated marginal e ects for the presence of a migrant in the household when we allow the data to endogenously determine the age(s) at which marginal e ects vary. The rst set of results (Tables 3 and 4) do not allow male and female pension receipt to have di ering e ects; later results will relax this restriction. Table 3 gives results using the OHS98 data. The rst column shows the estimates of equation (5) where we allow for separate anticipation, and then actual, pension receipt e ects. That is, we estimate via maximum likelihood the point at which there is a switch from anticipation to receipt e ect. It turns out that the optimal point is actually at j = 0. Remember this optimal break point corresponds to the j for which the likelihood function is maximized. This is interesting because this implies that the rst, and the strongest, break is attained exactly at the o cial age-quali cation for pension. The estimated coe cients imply that an increase in the number of males aged and the number of females aged in the household Q i[ 10; 1] is associated with a 6.5 percentage point increase in the probability of having a migrant but this increases to 9.7 percentage points when there is an increase the number of males aged 65 of females aged and the number 70 Q i[0;10]. The sup W statistic for testing the restriction that these coe cients are equal takes the value 12:04: The simulated p value for this test is small (at 0.005), indicating that the more general model is supported by the data. When the same analysis is undertaken using the SIHS93 data set (see Table 4), while the maximum likelihood estimate of the location of the break is at j = an increase in the number of males aged 55 7, neither 58 and the number of females aged in the household Q i[ 10; 7] nor an increase the number of males aged and the number of females aged Q i[ 6;10] have a statistically signi cant e ect on the probability of there being a migrant in the household. Moreover the null hypothesis of equality of the coe cient estimates cannot be rejected. This may 16

17 in part be due to the smaller sample and the much lower pension take-up in these transitional years after the demise of the apartheid regime. Given these results, we do not proceed any further with this data set. Returning to the OHS98 data, once we have obtained the rst break, we hold this break point as given and then undertake a grid search to examine if there are any subsequent breaks. Recall the rst break was obtained at j = 0. We now estimate the model with further breaks in the rst sub-sample; that is, we include Q i[ 10;k 1] and Q i[k; 1] (as well as Q i[0;10] and Q i[11;1] ) in the model, where k takes values between 8 and 2: Maximising the likelihood for each value of k and then choosing the value of k which produces the maximum of these likelihoods yields a maximum likelihood estimate of the second break point at k = 7: In other words, we allow separately for di ering e ects for the number of males aged and females aged Q i[ 10; 8], compared to the number of males aged and females aged Q i[ 7; 1] : Recall that we still include the actual pension-e ect variables: the number of males aged and the number of females aged The marginal e ects (and robust standard errors) of this model are presented in column (2) of Table 3. They show that an increase in the number of adults in the rst category (number of males aged 55 aged and females 52) is associated with a 5 percentage point increase in the probability of there being a migrant in the household, while an increase in the second category (number of males aged and females aged 53 59) is associated with a 7.1 percentage point increase in the probability of there being a migrant in the household. The null hypothesis that these two estimates are the same cannot be rejected (sup W = 2:12; p value = 0:407) : To reiterate, in computing this second break, we take the rst break as given. However the test results suggest that the additional complexity of allowing for the second break is not rewarded in a signi cant improvement in model t, so the preferred model would have the one break at j = 0 (column (1)) We also estimated an alternative generalisation of the model in column (1) where we search for two further breaks in the pension e ects: we take the rst break point (j = 0 for the OHS data set) as given, and search for a further break in each of the subsamples before and after this break point. To operationalise this, we consider every possible combination of pairs of breaks at 17

18 We brie y summarise the results related to the other control variables (these are presented in the appendix, Tables A3 and A4). For the OHS98 data (Table A3), we nd that an increase in the number of resident children in the household, having a female head and having a rural residence all increase the probability of having a migrant. On the other hand an increase in the age of the head of the household and having a household head with more than high school as the highest level of educational attainment signi cantly reduces the probability of having a migrant in the household. Several of the household asset variables have a statistically signi cant e ect on the probability of having a migrant in the household. Regressions using the SIHS93 data (Table A4) show that very few of the additional control variables have a statistically signi cant e ect on the probability of the household having a migrant, Of the ones that do, we nd that the probability of having a migrant is signi cantly lower in a female-headed household (the opposite of what we saw in the regressions using the OHS data) and the higher the level of educational attained by the household head, the stronger e ect is the e ect on the probability of the household having a migrant. 4.3 Optimally Chosen Break Points, Pension Recipient by Gender Table 5 repeats the analysis using the OHS98 data set, but here we allow age eligibility to be separately classi ed by the gender of the recipient. Column (1) presents the results for the case where the break is restricted at the point of o cial age eligibility. While an increase in the number of males in the household aged and both signi cantly increase the probability that there is a migrant in the household the e ect is signi cantly stronger for the latter age group ( 2 (1) = 18:75; p value = 0:00). In other words, actual receipt of pension has a stronger positive e ect on migration than anticipation of future pension eligibility. points between 8 and 2, and in the range 2 to 9. For each of these pairs of values, we calculate the likelihood function, and choose the combination of break points that maximises the overall likelihood function. This produces two futher potential break points at j = 5 and j = 2 (in addition to the break point at j = 0). However the evidence using the sup W tests suggests that the preferred model continues to be the one presented in column (1), where there is only one break point, at j = 0. These results are not presented, but are available on request. 18

19 For females, an increase in the number of females in the household aged and both signi cantly increase the probability that there is a migrant in the household, with both age groups having quite similar marginal e ects: the di erence between them is not statistically signi cant ( 2 (1) = 0:22; p value = 0:63). The marginal e ects are noticeably weaker for females than males. In column (2) we present the results for the case where we optimally choose the (single) break point. For each age for the males in the range we choose the value of the age for the female (in the range 50 70) that gives the largest value for the likelihood function, and then the optimal break (one for males and one for females) is obtained by choosing the maximum of these likelihood values. The optimally chosen breaks (at age 59 for males and at age 63 for females) do not correspond to the o cial age of quali cation. The results presented in column (2) also show that gender of the pension recipient has very di erent implications for the migrant status of the household: and the e ect of a male who is a pensioner or close to becoming a pensioner has a signi - cantly higher e ect compared to that of a female pensioner or a female member of the household who is close to becoming a pensioner. An increase in the number of males aged is associated with a 8.5 percentage point increase in the probability that there is a migrant in the household, whilst an increase in the number of males aged is associated with a percentage point increase. An increase in the number of females aged is associated with a 2.6 percentage point increase in migrant probability, whereas an increase in the number of females aged is associated with a 4.8 percentage point increase in the same probability. Remember that the breaks are jointly estimated and the null hypothesis that there is no break at age 59 for males and at age 63 for females is rejected (sup W = 21:10; p value = 0:0000). To examine whether there are any additional break points we again hold the rst set of break points (at age 59 for males and age 63 for females) as given and search over the age range for males and for females. The corresponding results are presented in column (3). For males we nd a second break at age 61 while for females 19

20 we nd an additional break at age 56: both four years before they become pension eligible. However, the null hypothesis that there is no additional break at age 61 for males and age 56 for females cannot be rejected (sup W = 2:51; p value = 0:972). The test results therefore suggest that the additional complexity through allowing for the second break is not rewarded in the form of a signi cant improvement in model t. Turning to the results for the other control variables (presented in Table A5), we nd that the results are qualitatively very similar to those presented in Table A3. The only exception is that now primary schooling attained by the head of the household has a statistically signi cant e ect on the probability of having a migrant in the household, though the e ect is quite weak. 4.4 Optimally Chosen Break Points, Migrant and Pension Recipient by Gender Traditionally migrants in South Africa have been males. The restrictions on movement and the pass laws imposed by the apartheid regime restricted the migration of women to urban areas (either in search of jobs or to live with their partners). Following the dismantling of apartheid and the repealing of the pass laws, it has been claimed that Black women in South Africa are increasingly migrating to the cities in search of employment. To explore this claim, we next classify migrants by gender and estimate the migration decision separately for males and females. Table 6 presents (using the OHS98 data set) marginal e ects (and robust standard errors) for the models explaining the presence of male migrants in the household, and Table 7 presents the corresponding results for female migrants. 11 As before column (1) presents the results corresponding to the speci cation where the break is restricted to the point of o cial age eligibility. A comparison of the results presented in column (1) of Tables 6 and 7 indicate signi cant gender di erences in the e ect of pension receipts within the household. Male pension receipts have signi cantly stronger e ects on male migration; female pension receipts, on the other hand, have 11 Again the corresponding results for the SIHS93 data set are available on request. 20

21 strong e fects on female migration but not on male migration. We will come back to this issue of gender speci c e ects below. In column (2) of Tables 6 and 7 we present the results for the case where we endogenously estimate the break point. Here again for each age for the males in the range we choose the value of the age for the female (in the range 50 70) that gives the biggest value for the likelihood function, and then the optimal break (one for males and one for females) is obtained by choosing the maximum of these likelihoods. The rst break for males is attained at age 61; whilst that for women is at age 56, with regard to the regressions for the presence of a male migrant in the household (Table 6). For the presence of a female migrant in the household, the rst break is attained at age 58 for males and at age 65 for females (Table 7). Again it is important to note that the optimally chosen breaks do not correspond to the o cial age quali cation. It is clear that in the case of male pension receipts, the anticipation e ect is very strong: the probability of having a male or a female migrant in the household doubles as a male member of the household comes closer to becoming age-quali ed. The e ect of female pension receipts on female migration is quite signi cant. What is interesting though is that we do not nd any anticipation e ect to speak of: the big jump in e ect happens at age 65, past the o cial age of quali cation. We next examine whether there are any additional breaks. The results are presented in column (3), Tables 6 and 7. However, in each case the sup W test lends support to the model in column (2) against this more general case. 12 Finally turning to the results for the other control variables (presented in Tables A6 and A7), we again nd that the results are qualitatively very similar to those presented in Tables A3 and A5. The only di erence worth noting is that the region of residence (rural/urban) does not have a statistically signi cant e ect on the probability of having a male migrant. However, the probability of having a female migrant is signi cantly higher in a rural household. 12 For the male migrant sup W = 3:29; p value = 0:970. For the female migrant sup W = 9:37; p value = 0:

22 4.5 Robustness Checks Are there any other explanations for this observed relationship between the age of residents and presence of migrants in the household? For example one could argue that these results essentially capture demographic e ects. Consider the results presented in Table 5, column (2). The preferred speci cation had optimally chosen breaks at age 59 for males and age 63 for females. Focusing on males, the estimated marginal e ect on the probability of migration for males in the age-range is , while for those in the age range the estimate is We argue that this discontinuity can be attributed to the anticipated pension e ect. However, one could also argue that the jump in the marginal e ect is due to demographic di erences in the make-up of households and be unrelated to the aged pension. At the extreme, a household where the oldest male is aged 55 could be very di erent to one where the age of the oldest male close to 75. For example, it could be argued that the latter household is more likely to have a working-age adult in the household, and thus more likely to have a migrant. To investigate this possibility, we ran a further set of models where we rst set a break at the pension-eligibility age of 65, and then searched for a break in the rst sub-sample. In other words, we estimated a restricted version of (5) as follows: m i = Q i[ 10;j 1] Q i[j; 1] Q i[0;10] 12 + Q i[11;1] 2 + x 0 i + e i (14) across a range of j = ( 9; 2). We found an optimal break at the same points as the breaks reported in Table As a typical result, the marginal e ects for males in the age ranges 55 58, and were , , and respectively. Note the big increase in the marginal e ect between the and age categories. The marginal e ect for the latter category is more akin to that of the age group. There is little demographic di erence between the and categories of ages, so it is unlikely the jump can be attributed to demographic e ects. Our explanation is that those in this near-eligible age category are indeed exhibiting anticipatory behaviour and acting more like pension recipients. 13 The results are available on request. 22