Rural–urban differences in parental spending on children's primary education in Malawi

Abstract

Using Malawian data, this paper answers two interrelated questions: are there rural–urban differences in the factors that influence the probability that a household spends or does not spend on own children's education; and are there rural–urban differences in the factors that affect educational expenditure if a household decides to spend? Computed elasticities indicate that spending on education by rural households is more sensitive to changes in income compared with urban households, suggesting that spending on education in rural areas is a luxury good. In both areas, a mother's employment and education has a larger impact on spending compared with those of a father. Urban households compared with their rural counterparts are more sensitive to the quality of access to primary schools. We find no evidence of gender bias in school spending in urban areas, but rural households exhibit bias in favour of boys.

Keywords:

• education
• excess zeros
• double hurdle
• Malawi

1. Introduction

One of the costs of raising children that must be incurred by parents is investing in their education. There are two major players in investments in human capital of children, namely the household and the government. Household and government expenditure on education is both an end in itself and a means for achieving other goals of development, such as economic growth, poverty reduction, improved health status, greater equity and reduced fertility (Glewwe & Ilias, 1996). The low level of human capital development in most African countries is considered an obstacle of economic growth as well as in the alleviation of poverty (Glick & Sahn, 2000).

The Malawi government, in recognition of the crucial role that human capital accumulation and development plays in fostering economic growth, among other benefits introduced free primary education in 1994. Under free primary education, parents no longer pay tuition fees, but they still have to pay for other educational expenses including books, uniforms, transport, contributions for school building and maintenance, among other expenses. This means that households still have to play a role in investing in the primary education of their children. Besides, they also have to pay for the education of their children when they go to secondary school.

In this study, we focus on investment in education by families and not government. Economists have long been concerned with modelling decisions that parents make regarding investments in the education of their children (for a review, see Haveman & Wolfe, 1995). They have investigated the time parents allocate to their children (e.g., Lazear & Michael, 1988; Leibowitz, 1974, 1977; van der Gaag, 1982). They have focused on the factors that influence enrolment in primary and secondary schools (e.g., Glewwe & Ilias, 1996; Kabubo-Mariara & Mwabu, 2007). Others have looked at household willingness to pay for the education of children (e.g., Gertler & Glewwe, 1990). Other studies have looked at the factors that influence direct education expenditures which parents make on their children. Here, there are two strands of literature; those that use aggregated expenditure where expenditure on education is combined with other items (e.g., Lazear & Michael, 1988), and another strand that uses education expenditure as a stand-alone item (e.g., Beneito et al., 2001; Mauldin et al., 2001; Kingdon, 2005; Song et al., 2006; Yueh, 2006). In this study, we look at education expenditure as a stand-alone item.

While focusing on household expenditure on primary education as a separate item, this study advances the understanding of the direct expenditures that parents make on their children in two ways. First, we make a distinction between households by whether they reside in rural or urban areas. Most studies looking at spending on education of children either pool the rural and urban samples or just look at one sample – for example, Mauldin et al. (2001) focus on a pooled sample, while Yueh (2006), Song et al. (2006), and Kingdon (2005) look at rural households only. Al-Samarrai & Reilly (2000) contend that the perceived expected rate of return to education may not be the same between rural and urban areas, due to differences in returns between the formal sector (mostly urban) and the agricultural sector (mostly rural). The implication of this is that a household's expected return to investing in education may be different between the two areas, and hence the spending would also reflect this. The characteristics between the two areas can be dissimilar in the sense that, for example, access to schools in terms of distance would be poorer in rural areas, reflecting an urban bias in terms of developmental projects. The rural–urban divide is also interesting in that most poor people live in rural areas. One can therefore loosely look at the spatial demarcation as a poor–rich one.

A second novelty of the paper is that with this rural–urban distinction in mind, the study looks at factors that influence a family's decision to spend on their own children's primary education in rural and urban Malawi while accounting for two things. First, the study directly models the presence of excess zeros, which is a common feature of expenditure data, and second, it takes due cognisance of the fact that households make two decisions with regard to spending. Specifically, the study answers two interrelated questions: are there rural–urban differences in the factors that influence the probability that a household spends or does not spend on own children's education? This is a difference at the participation decision level. Also, are there rural–urban differences in the factors that affect educational expenditure if a household decides to spend? This is a difference at the expenditure decision level.

The rest of the paper proceeds as follows. Section 2 looks at model specification, variables used, estimation issues, and data and descriptives. Econometric results are the focus of Section 3. We finally conclude in Section 4.

2. Methodology

2.1 Model specification

This study is based on direct expenditures that households make on the primary education of their children. One underlying feature of expenditure data is that they contain excess zeros, and the choice of a statistical technique used to deal with the zeros is important, as an inappropriate treatment of zeros can lead to biased and inconsistent estimates (Greene, 1981). The Tobit model (Tobin, 1958) has been widely used to model outcomes that have excess zeros. The Tobit model is derived from an individual optimisation problem and views zeros as corner solution outcomes. The major drawback of the Tobit model is that it assumes that the same stochastic process determines both the extensive and intensive margins; that is, the decision whether or not to spend (participation decision) and how much (expenditure decision) are treated as the same. This assumption is restrictive. A model that corrects this limitation of the Tobit model is the Double Hurdle (DH) model.

The DH model, originally formulated by Cragg (1971), assumes that households make two decisions with regard to spending, each of which is determined by a different underlying stochastic process. Following Jones (1989), the DH is formally specified as follows.

The participation equation (the first hurdle) is given as:

The expenditure equation (the second hurdle) is given as follows:

Observed expenditure is as follows:

where is a latent variable describing the household's decision to participate (spend or not) on children's education, is a latent variable describing household expenditure on children's education, is a vector of variables explaining the participation decision, and is a vector of variables explaining the expenditure decision. The parameter vectors α and β are assumed to be linear. ϵ_i and ν_i are independent random errors with the following properties: and , and i denotes a household. The assumption of independence between and is quite common when using the DH model. The alternative would be to assume that the errors are dependent. However, Smith (2003) shows that there is little statistical information to support the estimation of a DH model with dependent errors even when dependence exists. The model assumes that the variance of the error term of the expenditure equation is homoskedastic. A failure of this assumption can affect the efficiency of estimated parameters. In order to address this possibility we use Huber–White heteroskedasticity robust standard errors.

2.2 Variables used

The DH model is estimated separately by area of residence (rural and urban). The dependent variable is the share of total annual household expenditure on the education of primary school children in total annual consumption expenditure. In order to account for price variability across areas and time, both expenditure items are deflated using the Malawi National Statistical Office's spatial and temporal deflator with base national and February/March 2004 data . The expenditure items include fees (tuition and boarding), books and other materials, school uniform, contributions to school building and maintenance, parental association fees, and other school-related expenses.

We include the age of the youngest primary school-going child in the household; this is motivated by the fact that as children get older, education expenditures increase. One can alternatively include the average age of primary school-going children in a household. Results based on the average age were qualitatively similar to those based on the age of the youngest child. We therefore report results based on the age of the youngest child. Age of the child may also reflect the opportunity cost of home production, which increases with age. We include the square of age of the youngest child to measure possible non-linearities. Household permanent income as proxied by the log of total household per-capita expenditure has been found to affect spending on education (e.g., Song et al., 2006; Yueh, 2006). The expectation is that poor households may be unable to afford the direct or indirect costs of schooling and may also be credit-constrained to cover the costs. Wealthier households are more likely to pay for schooling out of current income or savings or credit.

We also include a variable that captures the proportion of children who go to government schools in a household. This variable is defined as the number of government school scholars divided by the number of children in the household.

The number of children in a household may also affect whether or not a household spends on their education; and if so, how much. In the literature there are basically two opposite findings regarding the impact of number of children on investment in human capital. The first finding that confirms the quantity–quality trade-off is that having more children negatively impacts on investment in human capital (Gertler & Glewwe, 1990). The other finding is that having more children actually increases human capital formation as it ensures that each child requires less time for home production (Al-Samarrai & Reilly, 2000). Additionally, we include the square of number children in the household to measure the possibility that marginal expenditures diminish with more children.

Employment status of parents may be positively related to expenditures on a child's primary education as it may influence their perception of the relationship between human capital investments and returns on those investments. Studies by Haveman et al. (1991) and Ribar (1993) in the United States find a significant and positive relationship between mother's employment during a child's teenage years and high school completion, but find no significant effect on the same for the father's employment. In this study, we measure the employment status of both parents by whether they work for a wage or not. We use wage employment here because, unlike self-employment, for example, it better captures the perceptions of returns to education. The educational level of parents is expected to have a positive effect on investment in education. The theoretical explanation of this expectation is that parents with higher levels of education are more likely to perceive greater future benefits or returns on investing in their children's education, and thus may be willing to sacrifice more for these future returns. More educated parents expect that their children will exhibit greater promise and thus will be more willing to invest in their child's education (Becker & Tomes, 1976; Becker, 1981). At the empirical level, several studies that look at the relationship between attainment and parental education support this human capital perspective (e.g., Song et al. 2006; Kabubo-Mariara & Mwabu, 2007).

Parental age may influence expenditures on children's primary education. Age reflects experience, and the expectation is that with age comes the ability to appreciate the benefits and returns on investments in education. As argued by Mauldin et al. (2001), if parents are older at the time their children are in primary and secondary schools, they will be more financially secure as well and be more willing to sacrifice a larger proportion of income for their children's education. We thus include the age of the mother and father as well as the square of ages for both parents to measure the possibility of non-linearities. Studies by Case & Deaton (1999), and Al-Samarrai & Reilly (2000) have found significant negative effects of distance to the nearest primary school. Distance to the nearest primary school can be a measure of the quality of access to primary schools; it can also reflect the direct cost of primary education. Households are less likely to invest in the education of their children if, for example, schools are very far. In this study, distance to nearest primary school measured in kilometres is set equal to zero if there is a primary school in the community.

There may be bias in spending against a particular sex. Besides, some empirical studies have found evidence of son preference in spending; for example, Song et al. (2006) and Yueh (2006) for China, and Kingdon (2005) for India. In order to capture the possibility of gender bias in spending, we construct a variable defined as:

where is the number of household members in age–gender group g and H is the household size. We distinguish 10 age and gender categories: ages 0 to 6, 7 to 15, 16 to 19, 20 to 55, and over 55 for each gender. Since we are using aggregate household education expenditure data, this variable can give an indirect test of gender bias in spending. In particular, to check for evidence of differences in spending between primary school-going boys and girls, we are concerned with the coefficients of the age–gender variable for the ages 7 to 15 for both sexes. If the coefficients are significant and different that is evidence of preference for a particular sex in spending. We control for regional fixed effects by including a three-class regional dummy for the north, centre, and south.

2.3 Estimation issues

The log of per-capita expenditure is potentially endogenous, and this may lead to biased and inconsistent results. One possible channel of endogeneity is that the log of per-capita expenditure and spending on education can be jointly determined through labour supply decisions in the sense that a decision to send children to school may be jointly determined with a decision to send the children to work to supplement household income. Another route for endogeneity would be that parents with a good taste for the education of their children may work harder so they are able to pay for their schooling (Kingdon, 2005).

We address this problem in both the participation and expenditure decision equations. In the participation equation we use the Rivers & Vuong (1988) procedure for discrete choice models, and in the expenditure equation we use the Smith & Blundell (1986) procedure for limited dependent variable models. The two procedures are analogous and they are done in two stages. In the first stage, a reduced form regression of an endogenous variable is regressed using ordinary least squares on exogenous variables including instruments, and residuals are predicted. In the second stage, the predicted residuals are included in the participation equation (the Rivers and Vuong procedure) and the expenditure equation (the Smith and Blundell procedure) including the endogenous variable. A simple t-test of the coefficient on the residual tests the null hypothesis of exogeneity. We use household assets, namely hectares of land and its square, as instrumental variables for log of per-capita expenditure. Similar instruments are used by Glewwe & Jacoby (1994), Glewwe & Ilias (1996), and Kingdon (2005).

An instrumental variable must be correlated with the endogenous variable (log of per-capita expenditure in our case), but uncorrelated with the error term for the participation equation or the expenditure equation; that is, the instrumental variable must be redundant in the participation equation or the expenditure equation once log of per-capita expenditure is included. Thus, the effect of the instrumental variable on school spending must work through the log of per-capita expenditure only. As is shown later, land and its square are correlated with log of per-capita expenditure. Land is an illiquid asset, and therefore is unlikely to be sold in the short term to cover schooling expenses (Kingdon, 2005).

2.4 Data and descriptives

The data used in the study come from the Second Malawi Integrated Household Survey. This is a nationally representative sample survey designed to provide information on the various aspects of household welfare in Malawi. The survey was conducted by the National Statistical Office from March 2004 to April 2005. The survey collects information from a nationally representative sample of 11 280 households. These data contain detailed information on socio-economic and demographic characteristics of the households. The survey also collects annualised household education information, which includes household expenditure on primary, secondary, and tertiary education, for household members aged five and above. The expenditure items are school fees (tuition and boarding), books and other materials, school uniform, contributions to school building and maintenance, parental association fees, and other school-related expenses. In this study, we use husband–wife and single-parent families with at least one child in primary school. We do this for two reasons. Firstly, the survey does not record the parental characteristics of children who do not live with their parents, thus this restriction allows us to examine the impact of parental characteristics as discussed in Section 2.2. Secondly, schooling decisions are cumulative in nature such that the circumstances in which a person was raised as a child are more relevant than current ones (Glick & Sahn, 2000). This restriction may potentially lead to a non-random sample (i.e. a selected sample), which may bias our results. Specifically, if children are fostered out or older children leave the house to marry or work, this may lead to a selected sample of children who are different from those that have left. Since fostering increases with age and the likelihood of children leaving to marry or work also increases with age, by focusing on primary education, we somewhat mitigate the fears of selection bias.

 Table 1 provides the context in terms of enrolment status of boys and girls by age and location. As would be expected, urban areas have higher enrolment rates than the rural areas. The results indicate that in rural areas boys' enrolments are consistently higher than girls' and the gap widens with age, a reflection of girls' dropping out of school. This is more noticeable over the age range 14 to 15; here, 91.8% of boys are in school compared with only 80.5% of girls. For urban areas, no consistent discernible pattern is observed in terms gender gaps in enrolment.

Table 1: Enrolment rates by age, sex, and location

Age category	Rural		Urban
	Males	Females	Males	Females
6 to 7	98.2	96.0	99.0	99.2
8 to 9	96.4	94.8	98.9	99.2
10 to 11	95.4	91.3	98.7	97.9
12 to 13	94.8	85.7	96.8	93.5
14 to 15	91.8	80.5	91.4	92.4

Descriptive statistics of all the variables used in the analysis for families with non-zero expenditures and for the full sample by area of residence are presented in Tables 2 and 3. The full sample comprises households with primary school-going children, with zero expenditures and non-zero expenditures on education. In Table 2, we report sample means of annual household expenditure on primary education (absolute expenditure) and the share of annual expenditure on primary education in total household consumption expenditure; our dependent variable.

Table 2: Annual primary education expenditure

Expenditure	Rural		Urban		Gap 1	Gap 2
	Full sample (1)	Spending sample (2)	Full sample (3)	Spending sample (4)	(3) – (1)	(4) – (2)
Absolute	379.97	510.68	4696	6863.38	6352.70***	4316.03***
Share	0.004	0.005	0.014	0.022	0.01***	0.017***
Disaggregated absolute expenditure of full sample
Tuition	35.48		2945.85		2910.27***
Books	74.81		250.63		175.82***
Uniform	160.64		343.62		182.98***
Boarding	13.05		124.06		111.01***
Building	53.78		82.78		28.89*
PTA	10.55		233.23		222.68***
Other	31.46		715.83		684.37***

Notes: The full sample is made up of all households with school-going children, and the spending sample is made of households with non-zero expenditure on education. Absolute is the absolute expenditure while share is absolute expenditure divided by household annual consumption expenditure. We use two-tailed tests to test the significance of the differences (gaps) in expenditure between rural and urban. Significance: *p < 0.10, **p < 0.05, ***p < 0.01. Expenditure is measured in Malawi Kwacha.

Table 3: Sample descriptives of explanatory variables

Variable	Rural		Urban		Gap 1	Gap 2
	Full sample (1)	Spending sample (2)	Full sample (3)	Spending sample (4)	(3) – (1)	(4) – (2)
Household characteristics
Last child's age	7.97	7.65	9.3	8.57	1.3***	0.92**
Consumption expenditure	9.64	9.65	10.07	10.19	0.43***	0.53***
Government scholars	0.79	0.8	0.69	0.7	–0.10***	–0.10**
Children	3.52	3.68	3.59	3.71	0.04	0.07
Parental characteristics
Father works	0.71	0.72	0.82	0.81	0.10**	0.11***
Mother works	0.23	0.24	0.3	0.3	0.05	0.07*
Father's education	2.02	2.01	5.4	5.75	3.74***	3.38***
Mother's education	0.79	0.76	2.9	3.31	2.55***	2.11***
Father's age	47.77	47.78	47.88	47.87	0.09	0.11
Mother's age	43.62	43.23	43.11	42.13	–1.1	–0.51
School characteristics
Distance primary	2.75	2.95	1.99	1.3	–1.65	–0.76
Age–gender composition of household
Males aged 0 to 6	0.11	0.11	0.09	0.09	–0.02*	–0.02
Males aged 7 to 15	0.16	0.16	0.13	0.13	–0.03**	–0.03**
Males aged 16 to 19	0.05	0.05	0.05	0.04	–0.003	0.0006
Males aged 20 to 55	0.15	0.15	0.18	0.18	0.03***	0.02**
Males above 55	0.03	0.03	0.04	0.04	0.007	0.01
Females aged 0 to 6	0.11	0.11	0.09	0.1	–0.005	–0.03
Females aged 7 to 15	0.15	0.16	0.16	0.15	–0.008	0.002
Females aged 16 to 19	0.03	0.03	0.04	0.04	0.01	0.01
Females aged 20 to 55	0.18	0.18	0.2	0.21	0.03***	0.02**
Females above 55	0.03	0.02	0.02	0.01	–0.01	–0.01
Region
North	0.18	0.16	0.29	0.19	0.02	0.12
Centre	0.4	0.46	0.44	0.51	0.05	0.04
South	0.42	0.38	0.27	0.31	–0.07	–0.15***
Sample size	3739	2782	676	548

Notes: The full sample is made up of all households with school-going children, and the spending sample is made of households with non-zero expenditure on education. We use two-tailed tests to test the significance of the differences (gaps) in regressors between rural and urban. For continuous regressors we use mean differences, and for dummies we use proportional differences. Significance: *p < 0.10, **p < 0.05, ***p < 0.01.

The table also presents results of tests for statistical significance of the differences in expenditure between rural and urban households. The results show that there are differences between rural and urban households. In terms of absolute expenditure, rural households spend less on average compared with urban households. The share of education spending out of total household consumption expenditure for rural households is lower than that of urban households. These differences hold for both the full and spending samples. Additionally, the differentials are statistically significant. Looking at the various components of expenditure on education, we notice that urban spending on all items is significantly higher than that of rural households. We also observe that for urban households tuition takes up a big part of spending, whereas for rural households most of the spending is done on uniforms.

Table 3 presents results of summary statistics of explanatory variables used in the study by area of residence for the full sample and the sample of households that actually spend on education. The table also reports whether the differences in the variables are statistically significant. With the rural–urban demarcation of the sample, we have 3739 rural households and 676 urban households with primary school-going children. Of these full samples, 2782 rural households (74.4% of sample) and 548 urban households (81.1% of sample) have non-zero expenditures on primary school children. This suggests that compared with rural areas, there are more households in urban areas with positive expenditures on education. In terms of the proportion of children going to government schools, the results show that rural households have a higher number (79%) compared with 69% for urban households. The difference is statistically significant. In urban areas a significantly higher proportion of both mothers and fathers work for a wage and have more years of schooling compared with their rural counterparts. The results show that the urban households have significantly nearer schools compared with rural ones. Looking at the age–gender demographics for the primary school-going age (7 to 15 years), the results suggest that there are differences between the two areas with rural households having a significantly higher proportion of boys (16%) compared with 13% for urban households. In terms of the proportion of girls of school-going age, we find no significant difference between the two areas. Essentially, we observe that, just like expenditure on education discussed earlier, there are differences in the characteristics across area of residence. We discuss the econometric results in the next section.

3. Econometric results

The descriptive statistics show that there are differences in expenditure on primary education as well as characteristics between rural and urban households. In light of this, we formally tested the hypothesis that households in rural and urban areas are not different with respect to their investment in children's education. We essentially seek to investigate whether or not coefficients for the different variables are the same for rural and urban households. This is done by conducting a pooling test; a failure of pooling between the two groups would indicate that they are different. To conduct the pooling test, we use the likelihood ratio (LR) test. For comparison, the hypothesis is tested using both the DH and the Tobit models. The unrestricted regression is estimated with separate urban and rural households, and the restricted regression with the pooled sample using an area of residence dummy variable ‘rural’. If we denote the log-likelihoods for the urban, rural and pooled samples respectively as with the corresponding number of parameters , then the LR statistic that follows a chi-square distribution with degrees of freedom is given by:

Results of the pooling tests are presented in Table 4. The results for both the DH and Tobit models show that rural and urban households are different, and thus pooling the rural and urban households is inappropriate.

Table 4: LR test of differences in expenditure on education

	Log likelihood value (number of parameters)
Model	Pooled	Rural	Urban	LR statistic	Degrees of freedom	p value
DH	–8 306.19(66)	–6 167.27(64)	–2 075.03(64)	127.78	62	0.00
Tobit	–8 398.78(33)	–6 211.47(32)	–2 107.53(32)	159.56	31	0.00

This means that the DH model or the Tobit model should be estimated separately for the two areas. The next issue that we address is whether the DH model or the Tobit model is the right model for our data. Basically, we seek to ascertain using the LR test whether there is another censoring mechanism as represented by the participation equation. Results of the tests are reported in Table 5. The LR test results favour the use of the independent DH model as opposed to the Tobit model. This implies that there are two decision processes underlying spending on education: households decide whether or not to spend; and if yes, how much. We therefore discuss results of the DH model for the two groups of households.

Table 5: LR test of the Tobit model against the independent DH model

Group	Independent DH model	Tobit model	LR statistic	Degrees of freedom	p value
Rural	–6 167.27	–6 211.47	88.4	32	0.00
Urban	–2 075.03	–2 107.53	65	32	0.00

As discussed earlier, the log of per-capita expenditure is potentially endogenous; we tested for this using the Rivers and Vuong procedure for the participation equation and the Smith and Blundell procedure for the expenditure equation as outlined earlier. We find that the log of per-capita expenditure is endogenous in the expenditure equation only for rural households. To ensure comparability in terms of number of variables, we included residuals from the reduced form regression for urban households in the urban expenditure equation as well. The reduced form regressions of log of per-capita expenditure for both areas reported in Table A1 of Appendix A show that the instrumental variables land and its square perform reasonably well as they are significantly correlated with the log of per-capita expenditure.

The final maximum likelihood results of the DH model are presented in Table 6. Since the Tobit model has been rejected in favour of the DH model, our discussion of the results is based on the DH model but we show results of the Tobit model (Table A2 in Appendix A) for comparison.

Table 6: Results of the independent DH model by area of residence

Variable	Rural		Urban
	Participation	Level	Participation	Level
Household characteristics
Last child's age	–0.05488***	–0.01060	0.30450	0.00072
	(0.01614)	(0.00883)	(0.23719)	(0.00365)
Last child's age^2	0.00104***	0.00022	–0.00767	–0.00009
	(0.00038)	(0.00021)	(0.00710)	(0.00009)
Consumption expenditure	0.23207***	0.05227***	0.56821***	0.03576***
	(0.05461)	(0.00355)	(0.01981)	(0.01283)
Government scholars	0.76890***	–0.11241**	–2.86960**	0.02045
	(0.10820)	(0.04691)	(1.34249)	(0.01268)
Children	0.03128	0.04425***	1.63650**	–0.00016
	(0.04129)	(0.01411)	(0.64050)	(0.00804)
Children^2	–0.00132	–0.00132**	–0.14069**	0.00046
	(0.00398)	(0.00056)	(0.07013)	(0.00084)
Parental characteristics
Father works	0.00650***	0.00756***	0.04989***	0.02324***
	(0.00138)	(0.00155)	(0.00224)	(0.00296)
Mother works	0.20134***	0.02023***	0.64032***	0.02352***
	(0.05835)	(0.00219)	(0.07506)	(0.00132)
Father's education	0.00677***	0.01142***	0.02940***	0.00121***
	(0.00170)	(0.00259)	(0.00354)	(0.00019)
Mother's education	0.00683***	0.00865***	0.03234***	0.00231***
	(0.00101)	(0.00148)	(0.00609)	(0.00026)
Father's age	0.03908	0.01789	0.90438**	–0.01001
	(0.03091)	(0.01648)	(0.37120)	(0.00628)
Father's age^2	–0.00019	–0.00018	–0.00825**	0.00010
	(0.00027)	(0.00015)	(0.00341)	(0.00006)
Mother's age	0.04274	0.05428***	–0.51033**	–0.01090
	(0.03055)	(0.01915)	(0.21431)	(0.01311)
Mother's age^2	–0.00045	–0.00048***	0.00328*	0.00015
	(0.00028)	(0.00018)	(0.00181)	(0.00014)
School characteristics
Distance primary	–0.00699***	–0.00908***		–0.02440***
	(0.00024)	(0.00084)		(0.00158)
Age–gender composition of household
Males aged 0 to 6	1.11652**	–0.27137	–8.03960	0.20918*
	(0.55346)	(0.21291)	(5.46235)	(0.11936)
Males aged 7 to 15	1.94601***	0.23238***	6.16139***	0.18465***
	(0.54091)	(0.00950)	(0.09781)	(0.00321)
Males aged 16 to 19	1.05852*	0.30828	–11.41691*	0.26668*
	(0.57515)	(0.22514)	(6.57410)	(0.14466)
Males aged 20 to 55	0.43034	0.14724	–12.28649**	0.17875*
	(0.50640)	(0.18605)	(5.65072)	(0.10662)
Females aged 0 to 6	0.87586	–0.58748**	7.37600	0.26562**
	(0.54953)	(0.25236)	(5.68817)	(0.12612)
Females aged 7 to 15	1.82512***	0.25020***	7.70956***	0.29012**
	(0.23620)	(0.00930)	(0.40535)	(0.12162)
Females aged 16 to 19	0.33254	0.36888*	–8.92036	0.31863***
	(0.59034)	(0.22344)	(5.63699)	(0.12218)
Females aged 20 to 55	0.63089	0.30406	–3.77753	0.12265
	(0.59596)	(0.23380)	(4.96818)	(0.10029)
Females above 55	1.47903**	0.51368*	–4.29883	0.41458**
	(0.71350)	(0.28441)	(6.11054)	(0.18104)
Region
North	0.17206***	0.13929*	–1.56052*	0.04564
	(0.06414)	(0.07396)	(0.87341)	(0.03108)
Centre	0.70344***	0.01791	–0.73286	–0.02001*
	(0.05767)	(0.02882)	(0.61972)	(0.01063)
Controls for endogeneity
Residualcons		–0.19670**		(0.02123)
		(0.08155)		(0.01426)
Constant	–5.71966***	–1.95478*	(9.54081)	(0.12453)
	(1.40696)	(1.16150)	(12.48037)	(0.33370)
Sigma		0.01358***		0.01182***
		(0.00258)		(0.00160)
Log-likelihood	–6 167.27		–2 075.03
p values of equality of coefficients of males aged 7 to 15 and females aged 7 to 15	0.007	0.002	0.52	0.36

Notes: Significance: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are standard errors. Residualcons is the residual from the reduced form of log per-capita consumption expenditure.

The results generally show that some variables are significant for one group but insignificant for another; an indication of the rural–urban differences alluded to earlier. The age of the youngest child is significant and negative only in the participation equation for rural households. This suggests that parents in rural areas are less likely to spend on the education of children as they get older. This perhaps reflects the opportunity cost of sending children to school; that is, as they get older they can be a source of labour for agriculture and other income-generating activities to supplement parental income. This opportunity cost may not be as high in urban areas. The level of income as proxied by the log of per-capita expenditure significantly increases the likelihood of spending on education and how much is spent for both rural and urban households. The results therefore suggest that income matters at both the extensive and intensive margins for the two groups of households. Mauldin et al. (2001) also find that income has a positive and significant effect on household spending on education at both decision levels in the United States. We cannot compare the magnitudes of these coefficients of income in the two areas, but later in the next section we compare the magnitudes of the coefficients by computing elasticities. Suffice to say that the positive and significant effect of income indicates that spending on education is considered a normal consumption good. It may also indicate the presence of credit constraints in both areas.

For rural households, having a higher proportion of children going to government schools significantly increases the probability of spending on them but lowers the share of education expenditure. For urban households, having more government scholars lowers the chance of spending on primary education but has no impact on the share of education expenditure in total expenditure. We find that the number of children influences positively and significantly the share of education expenditure for rural households, but does not significantly affect the likelihood of spending on education. For urban households, having more children increases the likelihood that a household will spend on their education but does not affect the share of expenditure. This positive effect conforms with the argument by Al-Samarrai & Reilly (2000) that the more children a household has, the less time is needed for household production activities, and hence the higher will be the investment in their education. This however, contradicts an argument by Gertler & Glewwe (1990) that larger families may derive less utility from sending an additional child to school if some are already enrolled. This lower enrolment resulting from having many children could be reflected in lower spending. This also runs counter to the expectation that with more children there is more competition for resources.

In terms of parental employment, the results show that for rural and urban households a father's and a mother's employment significantly increases the share of expenditure on education as well as the chance that they will spend on children. This suggests that, holding other things constant, employed parents will invest more in their children. With respect to education, we find that the education of both the mother and the father positively and significantly affects the decision whether or not to spend as well as how much to spend on the primary education of their children in both rural and urban areas. Thus, ceteris paribus the higher the parental human capital, the higher will be the investment in schooling of children. These results are in line with findings by Song et al. (2006) for rural China, where they found that the educational level of both parents positively impacts household spending on education. We cannot compare the magnitudes of the DH coefficients of the employment and education for parents in the two areas, but this issue is taken up later in the next section where we compute elasticities. These comparisons allow us to say something about the possible differences in the impact of the two variables between parents and between the two areas.

The quality of access to primary schools as proxied by distance to the nearest primary school has a negative impact on the participation and the expenditure decisions of both rural and urban households. This suggests that households will be less likely to spend on primary education if the schools are far away and if they do actually decide to spend, the amount spent will be lower. In terms of the age–gender demographics, the results suggest that having more primary school-going boys (i.e. proportion of males aged 7 to 15) and girls (i.e. proportion of females aged 7 to 15) significantly and positively impacts on the participation and the expenditure decision levels of rural households. The same is true for urban households. We investigate further to check evidence of gender bias against girls by conducting Wald tests for the equality of the coefficients for the proportion of males and females aged 7 to 15 in the two areas. Results of the tests are shown at the bottom of Table 6. The test results indicate that for rural households there is gender bias against girls at both the participation and expenditure decision levels. For urban households, the Wald test results indicate that there are no statistically significant gender differences at both the intensive and extensive margins. Thus, the Wald tests show evidence of gender bias in favour of boys in rural areas only. The finding that there are gender gaps in education access in favour of boys is consistent with other studies on the African continent. Glick & Sahn (2000) find significant enrolment gaps in favour of boys in Guinea, while Kabubo-Mariara & Mwabu (2007) find that boys are more likely to move to higher school levels than girls in Kenya. Interestingly, we observe that when the Tobit model is used (see Table A2 in Appendix A), there is no evidence of gender bias in both areas. This is in conformity with a finding by Kingdon (2005), who shows that when a variant of the DH model is used more evidence of gender bias in school spending is found in India as compared with using a single equation model. This underlines the importance of the participation decision when modelling a dependent variable with excess zeros.

We complement the Wald tests results by comparing the magnitude of elasticities for the proportion of males and females aged 7 to 15 in the next sub-section. We have assessed the impact of different regressors on expenditure, and found some to be significant in the levels equation only while others are significant in the participation equation only or in both the levels and participation equations. Further to that, some variables have been found to have opposite signs in the two decision levels. As noted by Yen (2005), when examining the impact of explanatory variables, the presence of parameter estimates with opposite signs in the participation and level equations complicate the interpretation of the estimated effects. Thus, the impact of explanatory variables can be better explored by computing elasticities. It is worth noting that the elasticities, unlike the coefficients we have just discussed, also allow us to talk about the economic significance of the variables used.

3.1 Elasticities in the independent Double Hurdle model

The interpretation of coefficients in limited dependent-variable models is complicated, and to overcome this the effect of explanatory variables on the unconditional expectation of the dependent variable as measured by elasticities is decomposed into an effect on the probability of a positive expenditure and an effect on conditional expenditure (Yen, 2005).

The unconditional expectation of in the independent DH model is given as:

where the probability of expenditure is given by:

The conditional expectation of is expressed as:

The elasticities of the unconditional expectation of with respect to the continuous regressors are computed by differentiating Equations (6) and (7), and using the adding up property (Equation (5)). Formally, the elasticity of a continuous variable j that appears in both the participation and the expenditure equations is written as follows:

Equation (8) shows that the elasticity of the unconditional expectation of with respect to a continuous variable j, which appears in both the participation and the expenditure equations is simply a sum of the elasticity of the probability of observing a positive expenditure and the elasticity of conditional expenditure .

These elasticities of the probability, conditional level and unconditional level for continuous variables are computed at the sample means of the regressors. Table 7 reports the elasticities for the probability, conditional and unconditional levels of some selected variables for the DH model.

Table 7: Elasticities with respect to selected regressors for the DH model

Variable	Rural			Urban
	Probability	Conditional	Unconditional	Probability	Conditional	Unconditional
Consumption expenditure	1.889***	1.145***	2.33***	0.154***	0.177***	0.331***
	(0.209)	(0.055)	(0.264)	(0.083)	(0.120)	(0.095)
Father works	0.164***	0.143***	0.307***	0.124***	0.132***	0.256***
	(0.006)	(0.007)	(0.013)	(0.003)	(0.025)	(0.028)
Mother works	0.272***	0.312***	0.584***	0.205***	0.206***	0.411***
	(0.003)	(0.004)	(0.007)	(0.064)	(0.114)	(0.178)
Father's education	0.174***	0.137***	0.311***	0.114***	0.0856***	0.1996***
	(0.007)	(0.032)	(0.039)	(0.014)	(0.002)	(0.016)
Mother's education	0.441	0.318***	0.759***	0.166***	0.224***	0.390***
	(0.030)	(0.073)	(0.030)	(0.017)	(0.023)	(0.040)
Distance primary	–0.018***	–0.047***	–0.065***	–0.296**	0.854***	–1.15***
	(0.002)	(0.005)	(0.007)	(0.115)	(0.268)	(0.383)
Males aged 7 to 15	0.120***	0.66***	0.780***	0.314***	0.320***	0.634***
	(0.033)	(0.055)	(0.088)	(0.077)	(0.036)	(0.113)
Females aged 7 to 15	0.014***	0.070***	0.084***	0.317***	0.321***	0.638***
	(0.003)	(0.004)	(0.007)	(0.024)	(0.013)	(0.037)

Notes: Significance: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are bootstrapped (1000 replications) standard errors.

For comparison, we present the elasticities for the probability, conditional and unconditional levels of some selected variables for the Tobit model in Table A3 of Appendix A. The elasticity of probability for both rural and urban households with respect to the log of per-capita expenditure that proxies permanent income is positive and significant, implying that spending on education is considered a normal item. The same holds true for the elasticity of conditional and unconditional levels for the log of per-capita expenditure. It is worth noting that rural households have greater than one elasticities of the probability, conditional level and unconditional level compared with urban households. We test whether the income elasticities are statistically greater than one for rural areas and less than one for urban areas. For rural areas with t-statistics of 4.25, 2.64, and 5.04 respectively for probability, conditional level and unconditional level, we reject the null that the elasticities are equal to one and conclude that they are greater than one. For urban areas with t-statistics of –10.2, –6.9, and –7 respectively for probability, conditional level and unconditional level, we reject the null that the elasticities are equal to one and conclude that they are less than one. This means that, for rural households, spending on the schooling of children is more sensitive to income compared with urban households, and thus schooling is a luxury good in rural areas. Policies that aim to further reduce the costs associated with attending school may lead to improved education outcomes. Since in rural households most of the spending goes on uniforms (see Table 1), reducing the cost of uniforms is a possible cost item to be targeted.

The elasticities of probability, conditional level and unconditional level with respect to parental employment and education are positive and significant in both areas. However, we note two things: firstly, the elasticities for parental employment and education are higher for rural areas; and secondly, the elasticities for mother's employment and education are higher than those of fathers in both areas. These findings indicate that parental characteristics have a bigger impact on spending in rural areas, and that a mother's characteristics have a larger impact on spending compared with a father's. If one thinks of the employment status and education of the mother as a reflection of the bargaining power of the mother in the household, this would imply that children's education benefits from an improvement in the bargaining position of the mother. Besides, this result has intergenerational implications for human capital formation in that more female education entails more educated mothers, and hence more education for children.

The elasticities of probability, conditional level and unconditional level with respect to the distance to the nearest primary school are negative and statistically significant for both areas. We observe that the elasticities are larger for urban areas as compared with rural areas, suggesting that urban households are more sensitive to the quality of access to primary schools. The elasticities of probability, conditional level and unconditional level with respect to the proportion of primary school-going boys (proportion of males aged 7 to 15) and girls (proportion of females aged 7 to 15) are positive, statistically significant and economically substantial for rural and urban households. In addition, we also note that for rural households the elasticities of probability, conditional level and unconditional level for boys are larger than those for girls, suggesting a bias against girls. The computed elasticities for urban households are not noticeably different. These elasticities therefore reinforce evidence shown earlier using Wald tests that boys are favoured when it comes to whether or not to spend as well as how much to spend in rural households, but there is no evidence of school-spending gender bias in urban households. Just like the raw coefficients discussed earlier for the Tobit model, we find that the elasticities (see Table A3 in Appendix A) are both statistically insignificant and economically not very different from each other. Thus, when a single equation model is used we find no evidence of gender bias in spending in both rural and urban households.

4. Concluding comments

Using the Second Malawi Integrated Household Survey data, the paper has looked at household expenditure on the education of own primary school children. We make a distinction between rural and urban households. Computed elasticities have shown that spending on education by rural households is more sensitive to changes in income compared with urban households, suggesting that spending on education in rural areas is a luxury good. We have found that a father's and mother's employment has a bigger impact on spending in rural areas compared with urban areas. In the two areas, a mother's employment and education has been found to exert a bigger influence on spending compared with a father's. The study has found evidence of gender bias in school spending in rural areas only.

Our empirical analysis has a number of caveats that are worth pointing out. Firstly, we have not taken into account the possibility that sending children to school and sending them to work (i.e. child labour) are joint decisions. Secondly, the study makes the implicit assumption that more spending on education entails more schooling either in levels or in quality. However, more spending on education can translate into more schooling or more quality of schooling rather imperfectly. Finally, there may be a possibility of spatial sorting that may hold if most hard-working parents or those with the strongest taste for education are more likely to move to urban areas, which may result in urban households spending more on education. We are unable to address this selection on unobservables. Our conclusions should therefore be taken with these caveats in mind.

Appendix A. Reduced form and Tobit results

Table A1: Reduced form regressions of log per-capita consumption

Variable	Rural	Urban
Last child's age	0.090***	0.121***
	(0.005)	(0.045)
Last child's age^2	–0.002***	0.002
	(0.000)	(0.001)
Father's age	–0.143***	–0.007
	(0.009)	(0.081)
Father's age^2	0.001***	0.002
	(0.000)	(0.001)
Mother's age	–0.084***	–0.071
	(0.010)	(0.047)
Mother's age^2	0.01***	0.010
	(0.002)	(0.050)
North	–0.001	–0.120
	(0.022)	(0.158)
Centre	0.214***	0.159
	(0.017)	(0.149)
Land	0.023***	0.036***
	(0.003)	(0.001)
Land^2	–0.12***	–0.24***
	(0.002)	(0.014)
Constant	14.815***	10.741***
	(0.263)	(2.211)
F-test of joint significance of instruments
F-stat	111.000	9.640
Prob > F-stat	0.000	0.000
F-test of overall significance
F-stat	122.000	19.680
Prob > F-stat	0.000	0.000
R-squared	0.299	0.456

Notes: The instruments for per-capita consumption expenditure are land and its square. Significance: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are standard errors.

Table A2: Results of the Tobit by area of residence

Variable	Rural	Urban
Household characteristics
Last child's age	–0.00044***	0.00191
	(0.00016)	(0.00176)
Last child's age^2	0.00001**	–0.00008
	(0.00000)	(0.00005)
Consumption expenditure	0.00171***	0.01259**
	(0.00018)	(0.00611)
Government scholars	0.00337***	0.01023
	(0.00072)	(0.00670)
Children	–0.00009	0.00293
	(0.00025)	(0.00351)
Children^2	0.00006**	0.00009
	(0.00002)	(0.00040)
Parental characteristics
Father works	0.00134***	0.0164***
	(0.00032)	(0.00368)
Mother works	0.02277**	0.01213***
	(0.00034)	(0.00129)
Father's education	0.00151***	0.01206***
	(0.00004)	(0.00037)
Mother's education	0.00431***	0.01074***
	(0.00007)	(0.00049)
Father's age	0.00059*	–0.00024
	(0.00030)	(0.00216)
Father's age^2	–0.00000*	0.00000
	0.00000	(0.00002)
Mother's age	0.00077***	–0.00259*
	(0.00023)	(0.00144)
Mother's age^2	–0.00001***	0.00002*
	(0.00000)	(0.00001)
School characteristics
Distance primary	–0.00042*	–0.01039***
	(0.00022)	(0.00295)
Males aged 0 to 6	0.00150	–0.02059
	(0.00346)	(0.03275)
Males aged 7 to 15	0.00871	0.01916
	(0.33700)	(0.23000)
Males aged 16 to 19	0.00763**	–0.02771
	(0.00361)	(0.03614)
Males aged 20 to 55	0.00291	–0.04197
	(0.00316)	(0.02973)
Females aged 0 to 6	–0.00124	–0.00743
	(0.00345)	(0.03255)
Females aged 7 to 15	0.00867	0.07097
	(0.33400)	(0.97700)
Females aged 16 to 19	0.00640*	–0.00056
	(0.00374)	(0.02995)
Females aged 20 to 55	0.00419	–0.00840
	(0.00378)	(0.03112)
Females above 55	0.00874*	0.05879
	(0.00448)	(0.04469)
Region
North	0.00097	0.01347
	(0.00125)	(0.01054)
Centre	0.00266***	–0.00272
	(0.00050)	(0.00388)
Residualcons	–0.00246*	–0.00538
	(0.00132)	(0.00683)
Constant	–0.04727**	–0.05142
	(0.02112)	(0.11718)
Sigma	0.00813***	0.01340***
	(0.00011)	(0.00102)
Log-likelihood	(6211.47)	(2107.53)
p-values for equality of coefficients of males aged 7 to 15 and females aged 7 to 15	0.2315	0.5768

Notes: Significance: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are standard errors. Residualcons is the residual from the reduced form of log per-capita consumption expenditure.

Table A3: Elasticities with respect to selected regressors for the Tobit

Variable	Rural			Urban
	Probability	Conditional	Unconditional	Probability	Conditional	Unconditional
Consumption expenditure	1.524***	1.399***	2.923***	0.450***	0.461***	0.911***
	(0.043)	(0.071)	(0.114)	(0.098)	(0.020)	(0.120)
Father works	0.23***	0.17***	0.40***	0.16***	0.12***	0.28***
	(0.007)	(0.005)	(0.001)	(0.015)	(0.001)	(0.016)
Mother works	0.713***	0.64***	1.35***	0.449**	0.412**	0.861***
	(0.004)	(0.003)	(0.007)	(0.070)	(0.051)	(0.120)
Father's education	0.431***	0.532***	0.963***	0.252***	0.407***	0.659***
	(0.046)	(0.034)	(0.080)	(0.033)	(0.064)	(0.097)
Mother's education	0.869***	0.761***	1.630***	0.785***	0.658***	1.443
	(0.068)	(0.056)	(0.124)	(0.025)	(0.066)	(0.091)
Distance primary	–0.089*	–0.068*	–0.157*	–0.988***	–0.728***	–1.716***
	(0.046)	(0.035)	(0.080)	(0.303)	(0.211)	(0.504)
Males aged 7 to 15	0.104	0.079	0.182	–0.116	–0.086	–0.202
	(0.400)	(0.300)	(0.710)	(0.186)	(0.136)	(0.322)
Females aged 7 to 15	0.102	0.078	0.181	–0.082	–0.061	–0.143
	(0.040)	(0.030)	(0.070)	(0.223)	(0.164)	(0.388)

Notes: Significance: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are standard errors.