Monazza Aslam
email: monazza.aslam@wolfson.ox.ac.uk

Geeta Gandhi Kingdon

Jean Drèze

Marcel Fafchamps

Demographic Economics, J16 -Economics of Gender < J1 -Demographic

Keywords: gender bias, educational expenditure, engel curve, pakistan JEL Classification Number: I21, J16, J71 Gender bias, educational expenditure, Engel curve, Pakistan

Note 1: M denotes 'male' and F denotes 'female'; t depicts the t value. All cells where the gender difference is significant at the 10% level or better are shaded. Note 2: FATA contains no observations for enrolled girls in the 15-19 and 20-24 age categories.

1 Despite Table 1 revealing a current enrolment of 2 per cent for females in FATA, the 3 observations on currently enrolled females in the FATA sub-samples reported educational expenditures of 0 in the 10-14 age group.

F o r P e e r R e v i e w

Note:

The figures in parentheses are p-values of the t-test of the DME and the shaded cells represent significance at 5%. The DME in the conditional OLS equation in Column (b) were transformed as the dependent variable of the conditional OLS equation is the natural log of the budget share of education for the household while the dependent variable in (d) is the budget share of education. Column (b) reports results after transforming the dependent variable of the conditional into absolute terms. The DME have been multiplied by 100. The standard errors of the t-test in column (c) were obtained using bootstrapping in STATA. 5A. * t-values in parentheses and shaded cells denote significance at the 5 % level or more.

F o r P e e r R e v i e w

Age5-9

Age10-14 Age15-19

Probit ANY-EDEXP

Conditional

OLS of LNTOTAL_ EDU

Unconditional

OLS of TOTAL_EDU

Probit

ANY-EDEXP

Conditional

OLS of LNTOTAL_ EDU

Unconditional

OLS of TOTAL_EDU

Probit

ANY-EDEXP

Conditional

OLS of LNTOTAL_ EDU

Unconditional

OLS of TOTAL_EDU

Note:

Coefficients have been multiplied by 100 in column (a).The dependent variables are EDU_SHARE (budget share of education), ANYEDEXP equals 1 if household spends anything on education and 0 otherwise and the natural log of EDU_SHARE. Base dummy for Head's education is HEAD_,MATRICMORE =1 if head has more than 10 years of education 0 otherwise. The last 4 rows represent the p-values of the F test that the male and female genderage coefficients in that column are equal. PUNJAB is the excluded province and rural is the base category for the URBAN dummy. Head's education takes form as five dummy variables: (i) dummy capturing missing values for head's education, (ii) with head's education less than or equal to Primary (Grade 'katchi' 1 to 5) (iii) education at least equal to Middle (grades 6, 7 and 8) and (iii) education at least equal to Matric (grades 9 and 10). The base category is head's education more than Matric (including F.A., B.A., Masters etc.). Marital status of the household head takes on various values such as married, widowed, etc. Gender of the head is a dummy variable, equals 1 if head is female. Head's occupation is defined in four occupational dummies: (i) missing (ii) 'white collar workers' include managers, professionals, technicians or clerks, (iii) machine operators and assemblers or belonging to the services or trades industry are grouped into 'HEAD_SERVICE'. Individuals in elementary occupations or skilled agricultural workers are the omitted category. The detection of gender bias in intra-household allocation of consumption has relied on two approaches: 1) the direct comparison of expenditure by gender, contingent on availability of individual level data and 2) the indirect Engel curve methodology which utilises household level expenditure data to infer differential treatment, by analysing how changes in household gender composition lead to changes in household consumption or expenditure patterns. Much of the extant literature has, due to lack of individual-level data, relied on the indirect approach. This large literature investigating gender biases in household consumption patterns has raised numerous questions. In particular, the conventional Engel curve approach has failed to detect gender differentiated treatment in household allocations even where outcomes bespeak large pro-male differences. Deaton (1997, pp. 239-241) remarks 'It is a puzzle that expenditure patterns so consistently fail to show strong gender effects even when measures of outcomes show differences between boys and girls. ' Ahmad and Morduch (2002, p. 17) say "coupled with evidence on [significant gender differences in] mortality and health outcomes, the results on household expenditures pose a challenge in understanding consumer behavior". [START_REF] Case | Consumption, health, gender and poverty[END_REF] say "it is not clear whether there really is no discrimination or whether, for some reason that is unclear, the method simply does not work".

Several explanations have been advanced for explaining this puzzle. One explanation is by [START_REF] Jensen | Equal Treatment, Unequal Outcomes? Generating Sex Inequality Through Fertility Behaviour[END_REF] who argues that parents' fertility behaviour can lead to girls' educational (and other) outcomes being inferior to boys' without there being any parental discrimination in the within-household allocation of educational (or other) resources1 . Another explanation, [START_REF] Rose | Consumption Smoothing and Excess Female Mortality in Rural India[END_REF], is that households' inability to smooth consumption in the face of shocks leads to parents sacrificing daughters so that only the wanted girls survive; thus any lack of gender bias in current allocations masks prior gender bias in mortality selection. Yet another explanation by [START_REF] Ahmad | Identifying Sex Bias in the Allocation of Household Resources: Evidence from Linked Household Surveys from Bangladesh[END_REF] suggests two-stage budgeting, namely that parents' choices about aggregate expenditures is separable from their choices about how those expenditures are allocated. In other words, budget share on a commodity might remain unchanged with a change in gender composition of the household but parents might allot different portions of a commodity to sons than daughters. This will not show up in investigations of aggregate expenditures but it will show up in examination of individual outcomes.

Testing these explanations for the failure of the Engel curve method to detect bias requires the availability of individual level data on expenditures. For instance, Jensen's point implies that any observed gender differences in educational expenditure at the individual level could be across-household differences due to endogenously differing household sizes for girls and boys, rather than being due to within-household pro-male parental bias in education expenditure allocations. However, with individual level data on expenditure, a family fixed effects model becomes possible which is a powerful way of purging endogeneity bias and examining whether the gender gaps are a within-or across-household phenomenon. We have individual level data on educational expenditures to permit the estimation of such models.

The paper has two objectives. Firstly, we test the hypothesis that, in Pakistan, the allocation of household educational resources favours males over females. Secondly, we investigate possible reasons for the failure of extant studies to detect gender bias in contexts where it is expected to exist. Data from the Pakistan Integrated Household Survey (PIHS, 2001(PIHS, -2002) ) are utilised to address both questions.

Although a large literature documents gender biases in food consumption, only a few studies investigate differential treatments in educational expenditure, all these being for India [START_REF] Subramanian | Gender Discrimination in Intra-Household Allocation in India[END_REF][START_REF] Subramanian | Gender Effects in Indian Consumption Patterns[END_REF][START_REF] Coale | Excess Female Mortality and the Balance of the Sexes in the Population: An estimate of the number of "Missing Females[END_REF][START_REF] Subramanian | Gender Discrimination in Intra-Household Allocation in India[END_REF][START_REF] Lancaster | Endogenous Power, Household Expenditure Patterns and New Tests of Gender Bias: Evidence from India[END_REF]and Kingdon, 2005). On Pakistan, to our knowledge, no study analyses gender biases in educational allocations 2 .

As mentioned above, the reliability of the Engel curve approach has been questioned in recent years due to its failure to detect gender-differentiated treatment even where it is population having more siblings, higher average household size and lower per capita resources than boys. Lower per capita resources due to larger household size imply that girls' outcomes will be worse than boys' even in the absence of any within-household differential treatment of sons and daughters. 2 Studies by [START_REF] Deaton | The Analysis of Household Surveys: A Microeconometric Approach to Development Policy[END_REF] and [START_REF] Bhalotra | Intrahousehold Resource Allocation in Rural Pakistan: A Semiparametric Analysis[END_REF] focus on food consumption. Averaging across the two (as is implicit in the Engel curve technique) may dilute biases if gender bias occurs through only one channel rather than both, or if the biases in the two channels are in opposite directions. For example, suppose a pro-male bias exists in households' first decision -i.e. a boy is associated with a larger probability of positive spending on education (i.e. of enrolment). Suppose also that, conditional on enrolment, households spend more on daughters' than sons' education either because they belong to a select (e.g. more enlightened) group or because it is genuinely costlier to educate daughters, e.g. more expenditure may need to be incurred for transport and school clothing for girls for safety and modesty concerns. In this case, there will be pro-female expenditure allocation in the second mechanism. Averaging across these two divergent mechanisms may mute gender effects even if there is be pro-male bias in the former mechanism. The researcher would be interested in knowing whether significant bias occurs via either of the two mechanisms separately and whether it is the averaging across the two mechanisms that leads to the conclusion of non-bias. In other words, one would be interested not only in the average unconditional expenditure on girls and boys but also in the distribution of the expenditure 3 .

To examine this first ('averaging') explanation of the failure of Engel Curve methods, we will estimate Hurdle Models to analyse the two household decisions separately, i.e. the binary and conditional expenditure decisions. This will highlight the two possible mechanisms of bias in intra-household allocations of educational expenditure. 3 The conventional application of the Engel curve technique may fail to pick up bias against girls for another reason as well, namely if the distributional assumptions about the dependant variable and thus the specification of the budget-share equation are wrong. For instance, if the education budget-share for households with positive education spending is distributed log-normally but, because the budget-share equation is fitted on all (zero and non-zero education budget-share) households, the researcher has to use absolute budget-share rather than the log budget-share as the dependant variable, leading to incorrect standard errors. However, in large samples such as ours, this is not a particularly important worry. The second potential explanation for the failure of the Engel curve approach has to do with the nature of the data. Previous studies have, perforce, used aggregated household data to infer discrimination. Typically, expenditure data on food, education and health in household surveys is available for the entire household rather than separately for each individual member. The Engel curve technique attempts to deduce differential treatment from household-level aggregated data. It is possible that using household level data somehow makes it more difficult to detect gender biases in intra-household allocations.

To examine this second (aggregation) explanation, we exploit the fact that we have data on educational expenditure of each individual child in a given household. This allows us to test whether data aggregation is responsible for the failure of previous studies to detect gender biases. A few recent studies have attempted to analyse individual-level outcomes to investigate differential treatment by gender in different country environments [START_REF] Hazarika | Gender Differences in Children's Nutrition and Access to Health Care in Pakistan[END_REF] for Pakistan, [START_REF] Quisumbing | Intrahousehold Allocation and Gender Relations: New Empirical Evidence from Four Developing Countries[END_REF] for Bangladesh, Indonesia, Ethiopia and South Africa, and [START_REF] Kingdon | Where Has All the Bias Gone? Detecting Gender Bias in the Intrahousehold Allocation of Educational Expenditure[END_REF] for India, with only the latter study focusing on educational expenditure allocations and the issues mentioned above.

The paper proceeds as follows. Section 2 describes the models and empirical strategies adopted while section 3 discusses the data and descriptive statistics. The empirical results are discussed in Section 4 and the final section concludes.

Model and Empirical Strategy

We begin the analysis with the estimation of a standard Engel curve linking budget shares on educational expenditure with total household expenditure and the demographic composition of the household. We use the Working-Leser specification as follows:

w i = + ln (x i / n i ) + ln n i + k ( n ki / n i ) + z i + µ i (1)
where w i is the budget share of education of the ith household. It is = (Exp_edu / Total exp);

x i is the total expenditure of the household; is the error term.

n i is the household size; ln (x i / n i )
, , , k and are the parameters to be estimated. The Working-Leser specification will be relaxed to allow for non-linearity in log per capita expenditure (LNPCE). The term n i allows for an independent scale effect of household size. Since the n ki / n i fractions add up to unity, one of them has to be omitted from the regression. We allow for 14 age-gender groups:

males and females aged 0-4, 5-9, 10-14, 15-19, 20-24, 25-60 and 61 and above (omitting the fraction of women aged 61 and above in the regression analysis) 4 . The age categories 5-9, 10-14 and the 15-19 were chosen to correspond roughly with primary, middle and secondaryschool-ages respectively 5 . The remaining age categories represent the infants and young children (0-4), prime-aged adults (25-60) and the elderly (61 and above). The k coefficients capture the effect of household composition on household budgetary allocations. These coefficients tell us what the effect of changing household composition is while holding household size constant, for example by replacing a child aged 5-9 by a child aged 10-14 or by replacing a male with a female in a given age category. The difference across gender can be easily tested using a F-test under the following null hypothesis:

km = kf (2)
where m denotes males and f denotes females and k refers to a given age-category. Testing, for example, whether boys aged 10-14 are treated differently from girls aged 10-14, we simply seek whether the coefficient on M10TO14 (proportion of males aged 10 to 14 years in the household) is significantly different from the coefficient on F10TO14 (proportion of females aged 10 to 14 years in the household).

Existing applications of the Engel curve approach fit OLS equations of the absolute education budget share on the sample of all households (including those with zero education 4 These age-gender categories are defined as M0TO4, F0TO4, M5TO9, F5TO9, M10TO14, F10TO14 etc. and are the proportion of males (M) and (F) aged 0-4, 5-19, 10-14 and so in a given household. 5 These age-groupings are the same as those used in [START_REF] Subramanian | Gender Effects in Indian Consumption Patterns[END_REF] and in [START_REF] Kingdon | Where Has All the Bias Gone? Detecting Gender Bias in the Intrahousehold Allocation of Educational Expenditure[END_REF] for India. While regressions were also estimated for the 20-24 age category (corresponding with higher education ages), we do not report the detailed findings for this age group here (see [START_REF] Aslam | Gender and Household Education Expenditure in Pakistan[END_REF] expenditure). In so doing, they implicitly assume that dependent variable -the budget share of education (EDU_SHARE) -is normally rather than log-normally distributed. The reason for including all households in the estimation is that some or much of the bias against girls may occur in the decision of whether to enrol a child in school, i.e. in the zero-versus-positive spending decision, w i = 0 vs. w i >0, rather than only in the decision of how much to spend conditional on enrolment.

In much of the existing literature, equation (1) has been estimated using OLS with household budget share of food, education or health regressed on the independent variables.

Given the large proportion of households reporting zero education expenditure and the resulting censoring of the dependent variable, OLS is not the appropriate model to apply in the analysis of the education budget share. A simple application of the OLS model to data that is censored yields parameter estimates which are biased downwards (Deaton, 1997) 6 .

Although the Tobit model is a suggested alternative, it is identified only if the assumptions of normality and homoskedasticity are fulfilled [START_REF] Deaton | The Analysis of Household Surveys: A Microeconometric Approach to Development Policy[END_REF]. Moreover, it assumes that a single mechanism determines the choice between w =0 versus w > 0 and the amount of w given w >0. In particular, P (w > 0 x) / x j and E (w > 0 x, w > 0) / x j are constrained to have the same sign. An alternative to Tobit is the Hurdle model (Wooldridge, 2002, p536-38) which allows the initial decision of w = 0 to be separate from the decision of how much w is, given positive w.

'Hurdle Models' are two-tier models because the 'hurdle' or first tier is the decision of whether to choose a positive w or not ( w = 0 versus w > 0) and the second tier the decision of how much to spend conditional on spending a positive amount (w w >0). A simple Hurdle model can be written as follows:

P ( w = 0 x) = 1 -(x ) (2) log (w) (x, w > 0) ~ Normal (x , 2 ) ( 3
)
where w is the share of family budget spent on education, x is a vector of explanatory variables, and are parameters to be estimated while is the standard deviation of w.

Equation, (2) shows the probability that w is positive or zero, while the equation (3) stipulates that conditional on w >0, w x follows a lognormal distribution. In our data, the conditional education budget share is indeed lognormally distributed. The MLE of is the probit estimator using w = 0 versus w > 0 as the binary response.

The MLE of is just the OLS estimator of which is obtained from the regression of log (w) on x using only those observations for which budget share is positive i.e. w > 0. The consistent estimator of ˆ is just the usual standard error from this latter regression. Because of the assumption that conditional on w > 0, log (w) follows a classical linear model, estimation is fairly straightforward. Using the following properties of a lognormal distribution, it is easy to obtain the conditional expectation of E (w x, w > 0) and the unconditional expectation E (w x ):

E (w x, w > 0) = exp(x + 2 /2) (4) E (w x) = (x ) exp(x + 2 /2) (5)
which can be easily estimated given ˆ , 2 ˆ and ˆ . One can obtain the marginal effect of x on w by transforming the marginal effect of log (w) and using the exponent. Taking the derivative of the conditional expectation of w with respect to x, we can obtain the marginal effect of x on w in the OLS regression of log (w) conditional on w > 0. This is as follows:

E(w x, w > 0)/ x = . exp (x + 2 /2) (6)
The combined marginal effect of x on w, i.e. taking account of the effect of x on the probability that w > 0 and on the size of w w > 0, can be obtained by taking the derivative of the unconditional expectation of w with respect to x. We can use the product rule and take the derivative of the unconditional expectation in ( 7) to obtain the combined marginal effect as follows:

E (w x ) / x = (x ) exp(x + 2 /2) + (x ) . exp(x + 2 /2) = { (x ) + (x ) }. exp (x + 2 /2) (7)
In the analysis that follows, we estimate three equations for each province of Pakistan: Lastly, we also estimate all three individual-level equations with family fixed effects.

This deals with the potential endogeneity of variables included in all our other equations, i.e.

of variables such as household per capita expenditure, household size and household head's occupation. It provides a convincing way of examining whether differential educational expenditures on girls and boys are within-or across-household phenomena in Pakistan.

Data and descriptive statistics

We use data from the fourth round of the The dependent variable in the conventional Engel curve analysis is the share of educational expenditure in total household expenditure. The PIHS reports individual-level expenditure on each child currently enrolled in school as well as total household level expenditure on various items of consumption including food, leisure, health and education.

The education budget share (EDU_SHARE) variable was created as the fraction of educational expenditure in total household expenditure.

In the first instance, we regress the household budget share of education on the log of household per capita expenditure (LNPCE) and its square (LNPCE2), log of household size (LNHHSIZE), the age-gender composition variables, and the z-vector variables including the dummy variables for head's education, marital status and gender, and regional and provincial dummies. This is the pooled sample. To further disaggregate the analysis, we estimate separate regressions for the various provinces and further sub-divide the sample into urban and rural regions to analyse whether gender differential patterns differ across the regions and across provinces, though we report only selected results here 8 .

Table 1 shows the sex-ratio in the 0-14 year age group in sample households. There is considerable variation across provinces and regions with Punjab having the highest proportion of girls (49.5 per cent) with the lowest proportions in FATA, followed by Balochistan and AJK. This suggests, a priori, that gender biases in household expenditure allocation are likely to be the highest in these three regions and the least in Punjab. Table 1 also divides households with children aged 0-14 into 'girls only' households and 'boys only' households.

There is a statistically very significant difference in mean budget share on education in girlsonly and boys-only households. Finally, Table 1 computes average household size by gender and province. Average household size is significantly different for boys and girls in Balochistan and Northern Areas. These statistics give some credence to [START_REF] Jensen | Equal Treatment, Unequal Outcomes? Generating Sex Inequality Through Fertility Behaviour[END_REF] argument that due to parents' fertility behaviour female children will have a larger number of siblings and larger household size than male children, suggesting that girls may get less 7 The total educational expenditure (TOTAL_EDU) variable was truncated at Rs. 25,000 to exclude outliers Only 0.6 per cent of the sample reported expenditures greater than Rs. 25,000. 8 See [START_REF] Aslam | Gender and Household Education Expenditure in Pakistan[END_REF] for all the disaggregated results. 2 and3 suggests that much of the gender differentiated treatment occurs in terms of parents' decision whether or not to enrol/keep boys and girls in school i.e. in girls' significantly lower probability of positive education expenditure, rather than in lower expenditures conditional on enrolment.

Empirical Results

The results of the empirical analysis are divided into two sub-sections. In the first, household level analysis is conducted to explore two main questions: 1) using the conventional Engel curve approach, is there any evidence that the allocation of household educational expenditure favours males over females? And 2) does incorrect functional form explain failure of the conventional Engel curve method in picking up gender bias? This analysis is based on a comparison of the conventional Engel curves with Hurdle Models using household level data. The second sub-section explores whether aggregation of data at the household level can explain failure to detect gender bias where it is expected. To this end, we estimate unconditional OLS and the Hurdle models using individual-level data, which are compared to the results from the household-level analysis.

In the first instance we discuss the main findings on the Pakistan sample as a whole.

This is disaggregated by region (urban and rural). The main results in Tables 4, 5 and education with urban areas spending a larger share (6.7 per cent) as compared to the rural regions (3.5 per cent). This national average masks large differences across provinces and regions. The regional variation is not unexpected given that average incomes and possibly educational preferences vary across provinces.

In column (a), per capita expenditure and its square are significant. The coefficient on household size is highly significant and positive and this was also so across all provinces and regions. This could be evidence of economies of scale but an alternative explanation is that larger households are more likely to have children of school-going age which is why they spend a greater budget share on education 10 . Female headed households (HEAD_FEMALE) have significantly higher education budget shares in Pakistan as a whole. As compared to households with more educated heads (in the base category, HEAD_FAMORE), those with heads with primary, middle and matric education have significantly lower education budget 9 The provinces were also disaggregated by region (urban and rural). A total of 54 equations have been estimated. There are 4 provinces and 3 territories in Pakistan. We also wish to present results for Pakistan as a whole, thus making 8 geographical units. For 5 of these units, we have broken the unit up into three samples: rural, urban and whole (rural + urban). Thus, in total we have (5x3) + 3 = 18 separate samples. For each of these samples 3 different equations have been fitted, implying a total of 18x3=54 equations using household level data. Appendix 1 does not report results by province due to space constraints. Tables 4 and 5 also do not report results by regional categorisation for the different provinces. Disaggregated results are available in [START_REF] Aslam | Gender and Household Education Expenditure in Pakistan[END_REF]. 10 The theoretical literature suggests that at any given level of per capita resources, larger households will be better off because they share household public goods, such as housing, consumer durables etc. Larger households should, therefore, be able to allocate larger shares to private goods such as education provided they do not substitute towards the 'cheaper' public goods. In Pakistani households, economies of scale could be especially important given the norm of a 'joint family' system. [START_REF] Deaton | Economies of Scale, Household Size, and the Demand for Food[END_REF] did not find evidence of such economies of scale across 7 high and low income countries, though they examined food budget shares. As mentioned before, the conditional budget share equation could suffer from sample selectivity bias due to being estimated only for a sub-sample (households with positive education budget share, i.e. with currently enrolled children), which could be non-randomly selected from the population. We attempted to control for selectivity by using the Heckman two-step approach but in the absence of convincing exclusion restrictions, we have not proceeded with this route 11 . We recognise the possible downward selectivity bias in the coefficients of the gender-age composition variables. However, if selectivity bias affects the male and female demographic variables equally, then we need not worry since our interest is in the difference in the coefficients of the male and female demographic variables 12 .

F

In Appendix Table 1, the effect of LNPCE is concave and significant in the probit of ANYEDEXP and also in the conditional OLS equation in the full sample and in urban and rural regions of Pakistan. An increase in household size (LNHHSIZE) also has a positive and very significant coefficient in both the probit and conditional OLS equations. In Pakistan as a whole and in rural Pakistan, female-headed households have both a greater probability of spending a positive amount on education and higher conditional education budget shares.

Since our key objective is an analysis of gender bias, our main interest lies in the effect of the demographic variables on the two outcomes (ANYEDEXP and LNEDU_SHARE) in columns (b) and (c), and on the unconditional budget share outcome (EDU_SHARE) in column (a) in Appendix 1. Table 4 presents the difference in marginal effects (DME) of the demographic variables in the three age categories (ages 5-9, 10-14 and 15-19) calculated from the results in Appendix Table 1. The province values have been calculated similarly but the underlying equations are not reported to conserve space. In keeping with our previous analysis, we disaggregate the results by region.

To see how the DME has been calculated, consider the DME of the demographic variables M5TO9 and F5TO9 for Pakistan as a whole, reported in the probit equation in column 1 in Table 4A. For the full sample, in column (b) of Appendix Table 1, the marginal effect of M5TO9 in the probit equation is 1.1352. The marginal effect of F5TO9 in the same equation is 0.7617, yielding a difference of 0.3735 which is multiplied by 100 to yield a DME of 37.35. The DMEs for the unconditional OLS (conventional Engel curve equations) in column (d) of Table 4A have been calculated similarly using column (a) of Appendix Table 1.

The DMEs in columns (b) and (c) of Table 4A have been calculated somewhat differently.

11 Three exclusion restrictions were used in controlling for possible sample selectivity: LAND_OWN (whether household owns any agricultural land), LAND_ACRES (the amount of land owned by the household) and BUSINESS (whether the household is an owner/proprietor of a non-farm business). A priori, we might have expected a household owning agricultural land or a business to have a higher demand for child labour, i.e. to affect the school enrolment (or positive education expenditure) decision, but not to affect conditional educational expenditure. However, in no case were the exclusion restrictions jointly significant at the 5 per cent level. The F tests revealed that the p-values of the joint significance of the exclusion restrictions in the probit of current enrolment were: 0.14 (age 5-9), 0.53 (age 10-14) and 0.06 (age 15-19). Only in the 20-24 age-group, the exclusion restrictions were jointly significant (at 4 per cent), but the Lambda term was insignificant (t = -1.27).

12 If girls' unobserved traits are important in parents' decisions about their enrolment/education and boys' traits are not important (or less important) to parents' decisions about their schooling, then any pro-male bias will be over-estimated because the female demographic variables will suffer from greater downward bias in the conditional education budget share equation than will male demographic variables. Column (b) refers to the DME in the conditional OLS equation of the log of budget share of education (LNEDU_SHARE). Since the dependent variable in this equation was in logs, we transformed the marginal effects of the male and female variables before taking the difference between the two, so as to ensure comparison with column (d), where the dependent variable is EDU_SHARE rather than the log of EDU_SHARE 13 . Column (c) reports the results of the DME of the combined marginal effects of the probit and conditional OLS equations. The combined marginal effects were computed using STATA, in the way set out in equation ( 7) in Section 2. The p value of each DME is reported in the bracket below it. For example, the p value of the DME in column (d) for children aged 5-9 in urban Balochistan is 0.04, suggesting that the DME there is significant at the 4 per cent level. The shaded cells represent DMEs significant at the 5 per cent level or better.

The results of main interest for the Pakistan sample as a whole are in the top panel of Table 4. Several interesting results emerge from an analysis of the DME at the household level. Firstly, looking at Table 4A, the conventional Engel curve results in column (d) shows that in the 5-9 age-group, while conventional Engel curve results suggest a pro-male bias in the full and rural samples only, the results reported in columns (a) and (b) demonstrate differently. In both rural and urban areas, the DME in the probit equation is positive and highly significant: an additional boy in the household has a larger impact on the probability of a non-zero education budget share (ANYEDEXP) as compared to an additional girl, i.e. there is strong pro-male bias in the binary decision of allocating positive educational expenditure.

However, the story is somewhat different in column (b): the DME of the gender variables in the conditional budget share equation is negative (albeit insignificant) in the urban sample and, when it is positive, it is insignificant (full and rural sample). Thus, at least in the 5-9 age group in Pakistan, much of the gender bias in household educational expenditure allocation occurs at the stage of the enrolment / drop-out decision for boys and girls, rather than in the conditional decision of how much to spend on enrolled boys and girls. It is clear that averaging the (often) oppositely signed probit and conditional expenditure DMEs -which is implicitly what the Engel curve method does -leads to the conclusion of no bias, and would 13 For example for the full sample Punjab, the coefficients on M5TO9 and F5TO9 in the conditional OLS of LNEDU_SHARE was bm = 0.9426 and bf = 0.7840 respectively. We can obtain the log transformations of these by using the property of the log normal distribution that the conditional expectation of E (w x, w >0) equals exp (x + 2 /2). The Exp (.) for this sub-sample is 0.1838. Thus the transformed marginal effect for males is bm*Exp(.) = (0.9426)*(0.0720) = 0.0679 and that for females is bf * Exp (.) = (0.7840)*(0.0720) = 0.0565. The difference between the male and female marginal effects is 0.0679 -0.0565 = 0.0114. In the table all DME are multiplied by 100 and so the reported DME is 1.14. It is also noteworthy that the Hurdle model in column (c) -which allows the binary and conditional decisions to be modelled separately -has greater power to detect bias than the conventional Engel curve method (column d) which uses a single equation to model bias:

there is significant evidence of gender bias in urban areas using the Hurdle model while the Engel curve approach is unable to detect this.

This picture changes quite a lot in the 10-14 age group (Table 4B). In this junior education age group, the Engel curve is good at picking up evidence of pro-male bias in Pakistan, see column (d). This seems to be for two reasons. Firstly the size of the DMEs is greater in the probit equation and secondly, the DMEs in the conditional OLS are almost always positive in this age group and also statistically significant in many cases, i.e. both the binary and conditional expenditure decisions work in the same direction (rather than in opposite directions, as was often the case in the 5-9 age group). Thus, here not only do households favour males in their zero-versus-positive expenditure decision (w i > 0), they also favour them in the amount spent conditional on enrolment. The findings are similar in the 15-19 age group (Table 4C).

It is not clear what explains the lack of pro-male bias in conditional education expenditure in the primary age group but its presence in the junior and secondary school age group. Simple tabulations and corresponding t-values for the different educational expenditures indicate that in no age-group is the cost of schooling significantly higher for boys than for girls such that cost-differences explain higher conditional expenditure on boys 14 . However, this doesn't entirely rule out lower conditional expenditure on girls due to other supply-side factors. For instance, lack of availability of single-sex schools in rural areas may result in lower conditional education expenditure on girls because of lack of access rather than due to parental discrimination 15 . However, there is also evidence [START_REF] Aslam | The Relative Effectiveness of Government and Private Schools in Pakistan[END_REF] to suggest that male children are more likely to be sent to more expensive private schools in Pakistan and this could be one mechanism by which pro-male biases in conditional expenditure operate.

14 For instance, tuition fees for males and females aged 5-9, 15-19 and 20-24 are statistically insignificantly different from each other (for the 10-14 age group they are significantly higher for girls). Similarly, the data suggest that expense on transport is significantly greater for girls aged 10-14, 15-19 and 20-24. 15 Alderman et al. (1996) attribute reduced availability of schools for females in rural Pakistan to lower adult cognitive achievement while [START_REF] Lloyd | The Effect of Gender Differences in Primary School Access, Choice and Quality on the Decision to Enroll in Rural Pakistan[END_REF] suggest that single-sex girls' school availability is a key determinant of parent's decision to enrol girls in school in rural Pakistan. The results for Pakistan are corroborated when we disaggregate by province in the three age-groups. For example, in the 5-9 age group, the Hurdle model detects pro-male bias in NWFP and Balochistan (and in age group 10-14 in Punjab) which the Engel curve is unable to detect. Punjab, generally known to be a more progressive province, has no significant gender bias in the 5-9 age group (although bias is present in rural Punjab even in the 5-9 age group, this is not shown in Table 4A).

The overall results suggest a number of conclusions. Firstly, typically the two 'discriminatory' processes highlighted in the probit and conditional OLS equations in the 10-14 and 15-19 age groups reinforce each other. In these age groups in almost all instances, the DMEs in columns (a) are (b) are positive suggesting a pro-male bias in the zero-versuspositive expenditure decision as well as in the conditional expenditure decision. Secondly, this explains why the Engel curve method detects pro-male bias in educational spending at least in the 10-14 and 15-19 age groups. Finally, 'unpacking' the two mechanisms of bias sheds some light on the puzzle we started with, namely the inability of the Engel curve method to detect bias even where it is strongly expected. The results above suggest that one of the reasons for the failure of the Engel curve method is its incorrect functional form. If the correct model for the binary decision of whether to make a purchase or not is non-linear and the distribution of conditional expenditure is log normally (rather than normally) distributed, it is incorrect to model these two different decisions within a single OLS budget share equation, and especially so if the effects of the age-gender variables on these two decisions are in divergent directions, as they are in Pakistan in the 5-9 age group.

'Aggregation' explanation of the Engel curve method's failure

One of the central limitations of studies investigating gender bias in intra-household allocations has been their reliance, perforce, on aggregated household level data to infer who gets what within the household. Failure of the Engel curve method in detecting differential treatment even where it is expected a priori may be attributable to data aggregation. Using individual level data on education expenditures, we investigate whether this can be a shortcoming of household allocation analyses in urban and rural Pakistan.

In this section we compare the household level Engel curve results with the estimates obtained using individual level data. However, the two sets of results are not directly comparable. Firstly, the dependent variable in the individual level analysis is the educational expenditure on the individual child (TOTAL_EDU) rather than the household's budget share of education (EDU_SHARE), as in household level analysis. Secondly, instead of using the As before with household level analysis, we estimate three equations at the individual level for each region: (1) probit of ANYEDEXP, (2) OLS of LNTOTAL_EDU (conditional OLS), and (3) unconditional OLS of TOTAL_EDU. These equations are estimated for the three age-groups separately: ages 5-9, 10-14 and 15-19 16 . We focus on the MALE gender coefficient and report the marginal effects of this variable in Table 5 17 .

In Table 5, columns (a) and (b) refer to the marginal effects of the MALE variable in the probit and the conditional OLS equations, respectively. As before, the marginal effects in The results based on individual level data confirm the findings from the descriptive analysis. There is a large and significant pro-male bias in the allocation of educational expenditure in all age groups and in both rural and urban regions in Pakistan. Comparing the results in Table 5 with those in Table 4 shows that individual level analysis is far more capable of capturing gender bias than household level analysis. In individual level analysis (Table 5), all cells in the 5-9, 10-14 and 15-19 age groups are statistically significant while in the household level analysis, fewer cells are statistically significant. This suggests that there is no substitute for individual level analysis if one wishes to reliably detect gender bias in the within household allocation of educational resources. Aggregation of data at the household 16 Although we estimated a total of 288 equations (aged 20-24 was a separate category and the results were disaggregated by region for all provinces), as before we do not report all results. More detailed results are available in [START_REF] Aslam | Gender and Household Education Expenditure in Pakistan[END_REF]. 17 The full results of the individual-level regressions are available from the authors. At the household level, much of the evidence for gender bias against girls in the 5-9 age-group had manifested itself in the probit equation of ANYEDEXP (Table 4A). There was not much evidence of pro-male bias in the conditional OLS estimates or in the conventional Engel curve estimation in this age-group. At the individual level, however, differential treatment against females aged 5-9 is apparent in both mechanisms. These findings are largely corroborated by provincial disaggregation.

Household Fixed

Effects: Gender differences within or across households? [START_REF] Jensen | Equal Treatment, Unequal Outcomes? Generating Sex Inequality Through Fertility Behaviour[END_REF] argues that in some developing countries, parents may have "son preferring, differential stopping behaviour". If parents have a strong preference for male children, they will continue child bearing until one (or their desired number of) male offspring is born. In other words, if early born children are girls, parents will be less likely to stop bearing more children than if the early borns are boys. This type of fertility behaviour will imply that, on average, female children will have a larger number of siblings and larger household size than male children. In larger households, all children (male and female) are worse off than in smaller houses, since larger family sizes result in a dilution of household resources across children. Average sibling size in Pakistan is 4.8 for girls and 4.7 for boys, which is significantly different (Table 1). This suggests that girls may get less educational resources not because they are discriminated against within their own household but rather because they are more likely than boys to live in larger households. In other words, any observed lower educational expenditures on girls than boys could be an across-household phenomenon due to differential household sizes for girls and boys in the population. If household size is endogenously chosen in the way Jensen describes then simply controlling for household size as we have done previously, will not suffice.

Introducing household fixed effects is a powerful way of controlling for unobserved parental fertility preferences and thus for the endogeneity of household size. Our household fixed effects analysis estimates three equations using individual-level data: 1) a probit equation of ANYEDEXP (whether any positive expenditure was incurred on the child's education); 2) the equation of the log of educational expenditure (LNTOTAL_EDU) conditional on positive educational expenditure; and 3) the unconditional educational expenditure (TOTAL_EDU) equation. Table 6 reports results of the household fixed effects estimation. We report the coefficient of the MALE dummy in the three equations with the t-statistic in brackets. We notice the large number of significant values in all decisions -the decision to enrol as well as the conditional and unconditional expenditure decisions -at all age groups, though there are some variations. There is pervasive evidence of significant within-household pro-male bias in the allocation of educational resources, and one cannot attribute the results of previous tables simply to differences in household size across the population. The household fixed effects estimates constitute fairly convincing evidence of strong pro-male bias in educational decisions within households in Pakistan in all school-going age-groups 18 : in the 5-9 age group, a daughter is 13.5 percentage points less likely than a son to have any education expenditure incurred on her education (i.e. to be enrolled in school); this rises to 24 percentage points in the 10-14 age group. Education expenditure allocation differs dramatically for sons and daughters within the household.

Summary and Conclusions

In this paper we have examined two questions central to the intra-household allocation literature: (i) does the allocation of household educational resources in Pakistan favour males over females and (ii) what explains the inability of the standard Engel curve approach to detect differential treatment even where discrimination is known to exist? We exploit the latest national sample survey, the Pakistan Integrated Household Survey (PIHS 2001(PIHS -2002)),

to address both concerns.

The descriptive statistics reveal large and significant gaps in schooling outcomes for males and females of school-going age in Pakistani households. These gender disparities are more strongly discernible in Balochistan, NWFP and FATA, and in rural areas. Much of the bias in educational expenditures manifests itself in significantly lower probability of girls' enrolment, and hence zero expenditure, rather than in lower expenditures conditional on enrolment.

18 As a referee of this journal points out, age gaps between siblings may differ for girls and boys within the household since a new born's gender may affect parental decisions about the spacing of the next birth [START_REF] Angrist | New Evidence on the Causal Link Between the Quantity and Quality of Children[END_REF]. The family fixed effects approach does not address this issue or the possibility of time-varying unobserved household heterogeneity. The conventional (Engel curve) approach to discovering differential treatment in intrahousehold allocations has been questioned in recent years for its inability to detect biases in allocations even when outcomes reveal differently. Two possible explanations for this puzzle were tested: 1) that the functional form adopted by the Engel approach is too restrictive and 2) that data aggregation somehow diminishes ability to detect gender biases. To explore the first issue, we estimated Hurdle Models which allow the two potentially 'discriminatory' channels of bias -the zero-versus-positive expenditure decision and the conditional spending decision -to be modelled separately, instead of constraining them to be in the same direction.

Additionally, the Hurdle Model allows the functional forms of the two decisions to be guided by the underlying distributions of the education budget share. The binary decision is modelled as a probit and the conditional expenditure decision using OLS of the log of budget share since budget share is distributed log-normally. The second explanation -which has to do with aggregation of data at the household level -is tested using unique individual-level data on educational expenditures on each child in the sample.

The results suggest several conclusions. Even using the conventional Engel curve approach, robust evidence of a pro-male bias in educational expenditure is found especially in the 10-14 and 15-19 age-groups. Much of this differential treatment manifests itself in rural areas. The lack of evidence in the 5-9 age-group is puzzling given large gender differentials in enrolment seen in Table 2. The Hurdle Models highlight why this is the case. While there is substantial evidence of strong pro-male bias in the binary decision whether to spend anything on education (the probit), there is weak pro-female bias in the conditional expenditure decision, i.e. the two potential channels of bias often go in opposite directions. In the older age groups, both channels typically work in the same direction, i.e. reinforce each other.

These results hold when using individual level data. Hurdle models are better able to detect gender bias in educational expenditure as compared to the conventional Engel curve approach, especially when using household level data. Controlling for unobserved household preferences by using household fixed effects confirms that the large and significant pro-male biases in educational expenditures in Pakistan are a within-household phenomenon. Pakistan [START_REF] Aslam | Returns to Education by Gender in Pakistan[END_REF] suggests that while returns to education for women are significantly higher than those for men, overall labour market returns are higher for men since the latter have much higher earnings than women 19 . Thus, an investment motive seems at least one plausible explanation for gender bias within the household. Even if returns to education were similar for males and females (or even higher for females), the part of the return to a child's education that accrues to the parents is likely to be higher from sons' education than from daughters' since in societies such as Pakistan sons provide old age support for parents while any economic returns to a daughter's education are reaped by her in-laws. This asymmetry in parental incentives to invest in sons' and daughters' education could well explain the observed gender gaps in education expenditure within Pakistani households and has obvious and important public policy implications. 19 An Oaxaca decomposition suggests that much of the gender earnings gap is not explained by differences in the observed characteristics between men and women, suggesting a good deal of gender discrimination in the labour market. Studies by [START_REF] Ashraf | Estimating the Gender Wage Gap in Rawalpindi City[END_REF] and [START_REF] Siddiqui | A Decomposition of Male-Female Earnings Differentials[END_REF]

  for girls' very inferior educational outcomes relative to boys in Pakistan would seem to be that girls receive less educational expenditure than boys in the within-household allocation of resources. When it has been tested for other South Asian countries, no consistent evidence of within-household gender differentials in education expenditure has been found. The objective of this study is to test whether the commonly used indirect expenditure (Engel curve) methodology is capable of discerning bias in the withinhousehold allocation of educational expenditures in Pakistan.

  [START_REF] Kingdon | Where Has All the Bias Gone? Detecting Gender Bias in the Intrahousehold Allocation of Educational Expenditure[END_REF] proposes two possible reasons for this failure: 1) the Engel curve approach uses the incorrect functional form to model the mechanisms of bias and 2) aggregated household level data mutes the detection of gender biases.On the first issue, the Engel curve technique estimates a single budget share equation encompassing two different mechanisms of bias, assigning equal weight to the two. The two potential mechanisms of bias are: a) in the household's decision of whether to spend anything on a given commodity (the zero-versus-positive expenditure decision, called the 'binary decision' in this paper) and b) in the household's decision of how much to spend conditional on spending a positive amount (called the 'conditional expenditure decision' in this paper).

  unconditional OLS equation of the budget share of education (conventional Engel curve) in the household level analysis, and OLS equation of unconditional education expenditure in the individual level analysis; (ii) Probit equation of the binary decision whether the budget share of education is positive at the household level analysis, and the probit equation of whether any positive educational expenditure is incurred on the index child in the individual level analysis; (iii) conditional OLS of log of budget share of education in the household level analysis, i.e. conditional on positive budget share of education, and OLS of log of conditional education expenditure in the individual level analysis. Equations (ii) and (iii) together are the Hurdle model estimates. In equation (iii), we attempt to allow for possible sample selectivity bias by estimating a Heckman two-step model (more details later). Each of these three equations are fitted on household and individual level data.The difference between the two lies in the level of aggregation of the data. Household level equations are fitted for households with at least one child aged 5-24 years. At the individual level we estimate the same equations but, instead of the dependent variable in the OLS equations being the budget share of education (as in household level analysis), the dependent variable is education expenditure on the individual child. Also, all the independent variables are the same in household-and individual-level equations except for gender: while household level equations include proportion of household members in 14 age-gender categories, individual level equations simply use age of child and the simple dummy variable MALE for gender.

  because they are discriminated against within their own household but rather because they are more likely than boys to live in larger households.

  that there is bias through one of the channels, namely in the enrolment (positive spending) decision.

  (b) have been transformed from logs to absolute values for comparison with (d) where the dependent variable is total educational expenditure. Column (c) reports the combined marginal effects of the probit and conditional OLS equation in the Hurdle model while (d) presents the marginal effect of MALE in the simple OLS of total educational expenditure.

  inherent feature of previous studies on intra-household resource allocation, mutes the true extent of gender bias.

Furthermore, a comparison

  of individual and household level results reveals that aggregating expenditure data across individuals within a household mutes the ability to 'pick up' gender effects. The findings suggest that individual level data are far preferable to household level data if one wishes to reliably estimate gender effects.Whether the substantial gender differences observed in within-household education expenditure allocations constitute pure discrimination remains arguable. Gender differentiated principle be attributed to an investment motive on the part of parents, reflecting differential labour market returns to education for males and females. Evidence on

Table 1 Descriptive statistics, by Province

 1

		Proportion of	Mean budget	Mean budget	Mean budget	Average	Average
	PROVINCE	'girls-only' households (age 0-14)	share of education in 'girls-only' households	share of education in 'boys-only' households	share of education in all households (age 5-24)	household size (girls)	household size (boys)	t-value of difference in (b) and (c)	t-value of difference in (e) and (f)
			(age 5-24)	(age 5-24)
		(a)	(b)	(c)	(d)	(e)	(f)	(g)	(h)
	PAKISTAN	14.5	2.0	4.1	4.6	9.4	9.3	-11.8	1.1
	PUNJAB	16.7	2.5	4.6	5.5	8.4	8.2	-7.1	1.7
	SINDH	13.6	1.9	3.8	3.8	9.8	9.7	-5.4	1.3
	NWFP	12.6	1.6	4.5	4.6	10.2	10.2	-6.8	0.6
	BALOCHISTAN	13.3	0.6	1.8	2.4	9.9	9.7	-4.6	2.0
	AJK	14.0	3.4	6.8	7.9	8.3	8.4	-3.9	-1.0
	NORTH	12.1	3.1	6.8	6.9	9.5	9.2	-2.3	2.2
	FATA	11.0	0.1	1.6	1.7	10.9	10.8	-3.0	0.6
	Note 1: Shaded cells represent significance at 10 % or better

Table 4A Difference in Marginal Effects (DME) x 100 of gender variables males5-9 and females5-9, and p value of the associated test (HH level results)

 4A

	Province	Sample Size	Probit of	Conditional	Combined	Unconditional
			ANYEDEXP	OLS of	Probit +	OLS
				EDU_SHARE	Conditional	(Conventional
					OLS	Engel Curve)
			(a)	(b)	(c) = f(a,b)	(d)
	PAKISTAN	Full	37.35	5.09	2.50	1.77
			(0.00)	(0.46)	(0.00)	(0.00)
		Urban	20.84	-0.84	0.91	0.82
			(0.01)	(0.51)	(0.01)	(0.50)
		Rural	44.57	1.14	2.85	2.41
			(0.00)	(0.15)	(0.00)	(0.00)
				Full Sample
	PUNJAB		12.97	1.14	1.78	1.35
			(0.19)	(0.37)	(0.16)	(0.19)
	SINDH		53.54	-1.32	1.78	1.37
			(0.00)	(0.29)	(0.08)	(0.18)
	NWFP		60.06	-0.36	2.66	1.53
			(0.00)	(0.77)	(0.03)	(0.27)
	BALOCHISTAN		61.33	0.73	2.96	1.40
			(0.00)	(0.72)	(0.01)	(0.09)
	AJK		27.84	3.40	5.51	3.72
			(0.04)	(0.22)	(0.09)	(0.24)
	NORTH		-18.65	2.92	1.16	4.45
			(0.13)	(0.59)	(0.81)	(0.19)
	FATA		67.37	7.29	4.51	3.80
			(0.17)	(0.00)	(0.01)	(0.01)

Table 4B Difference in Marginal Effects (DME) x 100 of gender variables males10-14 and females10-14, and p value of the associated test (HH level results)

 4B

	Province	Sample Size	Probit of	Conditional	Combined	Unconditional
			ANYEDEXP	OLS of	Probit +	OLS
					EDU_SHARE	Conditional	(Conventional
							OLS	Engel Curve)
				(a)	(b)		(c) = f(a,b)	(d)
	PAKISTAN	Full		60.15		3.30	5.80	3.22
				(0.00)		(0.00)	(0.00)	(0.00)
		Urban		4.46		2.71	2.63	1.28
				(0.61)		(0.06)	(0.06)	(0.42)
		Rural		91.40		3.68	6.70	5.57
				(0.00)		(0.00)	(0.00)	(0.00)
	PUNJAB SINDH	F o r	36.42 (0.00) 12.39 (0.00)	Full Sample 1.72 (0.22) 2.82 (0.04)	3.90 (0.00) 4.63 (0.00)	1.53 (0.28) 1.04 (0.56)
	NWFP BALOCHISTAN AJK		94.42 (0.00) P 101.90 (0.00) e 25.80 e r	6.58 (0.00) 1.43 (0.63) 9.28	9.85 (0.00) 5.04 (0.00) 11.02	7.49 (0.00) 3.61 (0.00) 10.10
	NORTH FATA Note: See note in Table 4A.		(0.03) -3.43 (0.83) 193.44 (0.00)	(0.00) 4.21 (0.39) 9.22 (0.00) e R v i e	(0.00) 3.68 (0.49) 8.21 (0.00)	(0.01) 6.01 (0.16) 8.41 (0.01)
							w

Table 4C Difference in Marginal Effects (DME) x 100 of gender variables males15-19 and females15-19, and p value of the associated test (HH level results)

 4C

	Province	Sample Size	Probit of	Conditional	Combined	Unconditional
			ANYEDEXP	OLS of	Probit +	OLS
					EDU_SHARE	Conditional	(Conventional
							OLS	Engel Curve)
			(a)	(b)		(c) = f(a,b)	(d)
	PAKISTAN	Full		24.70		3.39	3.84	3.13
				(0.00)		(0.00)	(0.00)	(0.00)
		Urban		8.85		0.60	1.19	0.20
				(0.23)		(0.72)	(0.45)	(0.90)
		Rural		36.40		5.21	5.04	5.57
				(0.00)		(0.00)	(0.00)	(0.00)
	PUNJAB SINDH	F o r	15.31 (0.11) 48.50 (0.00)	Full Sample 2.80 (0.14) 3.12 (0.04)	3.18 (0.04) 4.32 (0.00)	3.03 (0.07) 1.94 (0.28)
	NWFP BALOCHISTAN AJK		19.31 (0.15) P 15.23 (0.43) e 6.09 e r	5.02 (0.00) 5.60 (0.02) 5.38	4.34 (0.00) 3.82 (0.05) 5.67	4.76 (0.01) 1.68 (0.21) 7.22
	NORTH FATA Note: See note in Table 4A.		(0.44) -45.69 (0.01) 53.87 (0.50)	(0.08) -9.86 (0.18) 10.25 (0.08) R e v i e (0.12) -5.40 (0.54) 5.41 (0.16)	(0.06) 3.14 (0.48) 8.05 (0.17)
							w

Table 5A Marginal effect of the gender dummy variable MALE and p value of the associated t-test, age group 5-9 (Individual-level results)

 5A The figures in parentheses are p-values of the t-test of the DME of the MALE dummy computed using MALE =1 and MALE =0 and the shaded cells represent significance at 5%. The DME in the conditional OLS equation in Column (b) were transformed as the dependent variable of the conditional OLS equation fitted only on positive expenditure households is the natural log of total expenditure on education for the household while the dependent variable in (d) is the absolute value of total educational expenditure. Column (b) reports results after transforming the dependent variable of the conditional into absolute terms. The standard errors for the t-test in column (c) were obtained by bootstrapping in STATA.

	Province	Sample Size	Probit of	Conditional	Combined	Unconditional
			ANYEDEXP	OLS of	Probit +	OLS
				TOTAL_EDU	Conditional
					OLS
			(a)	(b)	(c) = f(a,b)	(d)
	PAKISTAN	Full	0.142	96.84	195.47	174.20
			(0.00)	(0.00)	(0.00)	(0.00)
		Urban	0.067	143.45	216.42	215.20
			(0.00)	(0.00)	(0.00)	(0.00)
		Rural	0.169	83.95	168.19	161.00
			(0.00)	(0.00)	(0.00)	(0.00)
	Full Sample 93.19 (0.00) 20.53 (0.52) -24.67 (0.89) 76.20 (0.17) 389.64 (0.00) -24.67 (0.89) -19.70 (0.91) e 0.059 (0.00) 0.171 (0.00) 0.192 (0.00) 0.170 (0.00) 0.119 (0.00) 0.072 (0.07) 0.346 (0.00) P o r e r R e v Note: F PUNJAB SINDH NWFP BALOCHISTAN AJK NORTH FATA i e 130.31 (0.00) 160.54 (0.00) 102.09 (0.99) 159.75 (0.00) 536.79 (0.00) 102.10 (0.99) -	118.6 (0.00) 96.0 (0.01) 277.0 (0.00) 210.0 (0.00) 436.8 (0.00) 187.4 (0.02) 286.5 (0.00)
					w

Table 5B Marginal effect of the gender dummy variable MALE and p value of the associated t-test, age group 10-14 (Individual-level results).

 5B

	Province	Sample Size	Probit of	Conditional	Combined	Unconditional
			ANYEDEXP	OLS of	Probit +	OLS
					TOTAL_EDU	Conditional
							OLS
				(a)		(b)	(c) = f(a,b)	(d)
	PAKISTAN	Full		0.261		174.84	498.88	380.6
				(0.00)		(0.00)	(0.00)	(0.00)
		Urban		0.653		263.73	343.65	261.7
				(0.00)		(0.00)	(0.00)	(0.00)
		Rural		0.368		136.62	510.91	440.7
				(0.00)		(0.00)	(0.00)	(0.00)
	PUNJAB SINDH	F o r	0.125 (0.00) 0.277 (0.00)	Full Sample 49.88 (0.32) 199.76 (0.00)	249.13 (0.00) 474.34 (0.00)	223.5 (0.00) 241.9 (0.00)
	NWFP BALOCHISTAN AJK		0.399 (0.00) P 0.375 (0.00) e 0.115 e r	428.69 (0.00) 31.04 (0.74) 630.47	780.06 (0.00) 429.94 (0.00) 826.21	708.0 (0.00) 388.1 (0.00) 763.0
	NORTH FATA Note: See note in Table 5A.		(0.00) 0.207 (0.00) 0.606 (0.00)	(0.00) 19.40 (0.96) -e R v i e	(0.00) 505.87 (0.06) -	(0.00) 536.3 (0.00) 727.6 (0.00)
							w

Table 5C Marginal effect of the gender dummy variable MALE and p value of the associated t-test, age group 15-19 (Individual-level results).

 5C

	Province	Sample Size	Probit of	Conditional	Combined	Unconditional
			ANYEDEXP	OLS of	Probit +	OLS
				TOTAL_EDU	Conditional
					OLS
			(a)	(b)	(c) = f(a,b)	(d)
	PAKISTAN	Full	0.192	375.39	613.98	583.3
			(0.00)	(0.00)	(0.00)	(0.00)
		Urban	0.087	319.59	398.91	394.7
			(0.00)	(0.00)	(0.00)	(0.00)
		Rural	0.239	445.45	671.03	699.4
			(0.00)	(0.00)	(0.00)	(0.00)
				Full Sample
	PUNJAB		0.093	400.96	390.11	390.7
			(0.00)	(0.00)	(0.00)	(0.00)
	SINDH		0.168	498.90	518.64	478.0
			(0.00)	(0.00)	(0.00)	(0.00)
	NWFP		0.316	656.29	931.55	960.8
			(0.00)	(0.00)	(0.00)	(0.00)
	BALOCHISTAN		0.244	476.30	539.81	547.1
			(0.00)	(0.01)	(0.00)	(0.00)
	AJK		0.219	202.20	828.24	883.7
			(0.00)	(0.54)	(0.00)	(0.00)
	NORTH		0.380	-186.22	567.81	536.3
			(0.00)	(0.03)	(0.55)	(0.00)
	FATA		-	-	-	531.8
						(0.02)

Note: See note in Table

Table 6 Household Fixed Effects: Coefficient of the gender dummy variable MALE and associated t-test by age group (Individual level data).

 6

e w Appendix Table 1 OLS on Budget share, Probit and Conditional OLS, Pakistan

					FULL							URBAN							RURAL
		EDU_SHARE	ANYEDEXP	LN_EDUSHARE	EDU_SHARE		ANYEDEXP	LN_EDUSHARE	EDU_SHARE	ANYEDEXP	LN_EDUSHARE
			(a)		(b)		(c)		(a)			(b)			(c)			(a)	(b)	(c)
		Coeff	t-val	ME	t-val	Coeff	t-val	Coeff	t-val	ME	t-val	Coeff	t-val	Coeff	t-val	ME	t-val	Coeff	t-val
	CONSTANT		-6.73	-1.39	-	-	-6.66		-8.47	-43.28	-5.06		-		-	-10.60	-8.22	-0.56	-0.07	-	-	-6.97	-5.03
	LNPCE		-0.48	-0.39	0.51	7.31	0.53		2.93	7.25	3.66		0.60		6.16	-0.06	-5.01	-1.55	-0.77	0.65	4.29	-0.65	-1.90
	LNPCE2		0.15	2.00	-0.02	-5.07	-0.02		-1.47	-0.26	-2.19		-0.03		-4.90	0.13	-3.97	0.19	1.47	-0.03	-3.26	-0.03	-1.32
	LNHHSIZE		2.15	18.72	0.40	32.40	0.20		6.10	2.71	12.28		0.30		17.91	0.99	2.81	2.05	16.57	0.44 24.41	0.26	5.88
	M0TO4		-1.26	-1.28	-0.06	-0.65	-0.72		-2.99	-2.73	-1.31		-0.02		-0.15	0.82	-2.55	-0.84	-0.82	-0.10	-0.86	-0.57	-1.88
	M5TO9 M10TO14 Pakistan M15TO19	Full sample 7.95 12.42 8.57	7.56 11.88 7.78	0.135 (17.43) 1.14 1.24 0.46	0.145 (9.01) 12.06 13.18 4.84	0.69 1.63 1.18	200.06 (12.68)	2.96 6.72 4.91	0.237 (26.27) 10.96 14.24 8.60	5.19 6.51 3.90	0.172 (7.49) 0.97 0.80 0.36		462.15 (16.68) 7.52 6.61 2.88	1.46 0.72 -0.06	0.164 (17.31) 2.25 4.11 1.97	6.43 11.11 8.88	0.182 (3.95) 5.67 10.27 7.57	1.15 551.57 9.41 (11.64) 1.43 11.74 0.51 4.26	0.60 1.75 1.64	2.05 5.62 5.23
	M20TO24 M25TO60 M60MORE	Urban	1.10 -1.04 -0.75	0.88 -0.93 -0.51	0.068 (5.10) -0.18 -0.27 -0.22	0.138 (6.07) -1.87 -2.72 -1.76	0.04 -0.49 0.08	253.42 (5.93)	0.14 -1.87 0.26	0.083 (5.87) 1.30 -2.21 -1.87	0.56 -1.02 -0.63	0.128 (4.07) 0.05 -0.14 -0.15		342.45 (5.80) 0.41 -1.12 -0.94	-0.63 -0.21 -0.71	0.072 (4.63) -0.15 -1.66 -0.44	1.61 -0.15 -0.33	0.193 (3.37) 1.19 -0.12 -0.21	-0.38 -3.05 344.69 -0.34 -2.59 (4.07) -0.27 -1.62	0.18 -0.35 0.23	0.50 -0.96 0.53
	F0TO4 F5TO9 F10TO14	Rural	-1.04 6.18 9.20	-1.06 5.87 8.48	0.164 (17.30) -0.09 0.76 0.64	0.147 (6.53) -0.94 8.08 6.73	-0.68 0.60 1.06	177.47 (13.42)	-2.77 2.54 4.61	0.328 (28.95) -1.85 10.13 12.96	-0.88 4.69 5.96	0.207 (6.20) -0.04 0.76 0.76		532.85 (19.84) -0.32 5.82 6.11	0.93 1.11 0.64	0.229 (19.67) -1.94 2.56 3.13	-0.61 4.02 6.51	0.137 (1.77) -0.62 3.64 5.68	-0.12 697.89 -0.98 0.71 5.71 (12.95) 0.52 4.17	-0.64 0.37 0.98	-2.02 1.23 3.36
	F15TO19 F20TO24		5.44 2.56	4.98 2.44	0.21 -0.31	2.23 -3.24	0.59 0.33		2.47 1.32	8.40 2.04	3.77 Full Sample 0.94	0.27 -0.19		2.21 -1.61	0.41 0.07	1.77 1.14	3.31 2.49	2.92 2.37	0.15 -0.34	1.21 -2.72	0.55 0.21	1.77 0.61
	Punjab F25TO60 HEAD_FEMALE HEAD_MARITAL		2.07 1.28 0.06	2.17 4.34 0.37	0.063 (4.39) 0.38 0.08 0.03	0.104 (3.61) 4.29 3.46 1.90	0.33 0.20 -0.05	122.87 (4.69)	1.29 4.30 -1.45	0.108 (7.06) 2.29 0.94 0.02	1.11 1.62 0.05	0.106 (3.31) 0.27 0.04 0.01		241.19 (5.02) 2.34 1.37 0.66	0.11 0.01 -0.44	0.083 (5.16) 0.19 1.46 -0.12	1.72 1.60 0.08	0.073 (1.07) 1.81 4.65 0.41	0.41 305.01 3.48 0.10 3.37 (3.45) 0.04 2.01	0.47 0.26 -0.07	1.41 4.07 -1.28
	Sindh HEAD_EDU_MISS HEAD_PRIMARY HEAD_MIDDLE		-3.43 -2.70 -1.67	-11.55 -9.05 -5.16	0.159 (10.14) -0.26 -0.12 -0.07	0.100 (3.83) -12.40 -4.94 -2.78	-0.50 -0.36 -0.17	159.80 (5.59) -12.03 -9.07 -3.99	0.233 (12.21) -3.52 -2.74 -1.46	-8.09 -6.42 -3.07	0.179 (4.44) -0.23 -0.08 -0.06		368.96 (6.82) -9.64 -3.37 -2.27	-0.34 -0.14 -0.15	0.135 (4.40) -8.43 -6.89 -2.89	-2.99 -2.18 -1.44	0.156 (1.78) -7.49 -5.41 -3.47	-0.26 -8.08 515.23 -0.11 -3.21 (6.16) -0.06 -1.44	-0.51 -0.33 -0.15	-7.51 -5.14 -2.19
	NWFP HEAD_MATRIC HEAD_OCCU_MISS HEAD_WHITE_COL		-1.32 0.32 1.03	-4.42 2.09 3.97	0.179 (9.40) -0.05 0.04 0.11	0.195 (4.20) -2.18 3.23 6.17	-0.15 0.06 0.07	200.81 (6.61)	-3.85 1.86 1.84	0.368 (5.61) -1.45 0.50 1.68	-3.50 1.61 4.45	0.325 (5.59) -0.02 0.02 0.06		771.12 (11.07) -1.13 1.23 3.14	0.10 0.17 0.13	0.272 (12.12) -3.26 1.76 3.29	-0.78 0.37 0.47	0.267 (2.25) -1.89 2.25 1.37	-0.06 -1.66 863.91 0.05 2.61 (7.52) 0.15 5.63	-0.08 0.07 0.00	-1..34 1.75 0.07
	Balochistan HEAD_SERVICE URBAN SINDH		0.39 0.82 -1.67	3.24 5.44 -10.25	0.124 (6.50) 0.07 0.04 -0.15	0.151 (4.08) 6.41 4.25 -12.48	0.05 0.22 -0.26	167.84 (4.15)	1.96 6.95 -7.50	0.350 (7.15) 0.72 --1.52	3.35 --5.09	0.097 (1.32) 0.04 --0.08		472.34 (9.82) 2.63 --4.90	-0.17 --0.17	0.262 (7.71) 3.13 --3.99	0.23 --1.87	0.368 (1.11) 1.79 --11.09	0.09 342.98 -6.57 --(4.30) -0.19 -7.95	0.00 --0.38	0.12 --7.23
	AJK NWFP BALOCHISTAN NORTH		-0.79 -2.86 1.33	-4.23 -15.57 2.81	0.127 (3.04) 0.03 -0.21 0.13	0.078 (4.51) 2.22 -13.63 4.86	-0.23 -0.65 0.19	349.46 (3.66)	-6.10 -9.14 2.16	0.12 (3.37) -0.53 -3.01 -0.34	-1.43 -7.82 -0.38	0.219 (2.03) 0.03 -0.07 0.02		619.25 (3.25) 1.73 -2.70 0.55	-0.20 -0.49 -0.09	0.178 (3.11) -3.39 -6.89 -0.70	-0.83 -2.77 2.22	0.334 (2.42) -3.92 -14.57 4.30	0.02 888.27 0.80 -0.27 -8.52 (2.75) 0.18 4.25	-0.26 -0.76 0.31	-5.20 -7.02 3.06
	NORTH FATA AJK Adjusted R 2 N DEP VAR. MEAN P-VALUES: AGE 5-9 AGE 10-14 AGE 15-19		-2.44 1.25 0.29 14548 0.0464 0.0001 0.0000 0.0000	-7.73 3.26	0.112 (2.51) -0.24 0.12 0.33 14555 0.6625 0.0000 0.0000 0.0001	0.282 (2.82) -6.51 5.01	299.07 (3.81) 0.24 -0.59 0.23 9594 -3.1230 0.4635 0.0000 0.0000	-4.14 4.53	0.272 (4.51) 1.27 -0.27 5264 0.0673 0.5058 0.4200 0.8971	-2.18	0.260 (1.71) 0.08 -0.34 5268 0.7623 0.0086 0.6134 0.2332	665.92 (5.57) -3.52	0.221 (3.25) -2.96 -2.8246 -0.17 0.24 3995 0.5146 0.0600 0.7200	0.358 (2.28) -8.27 2.70 0.26 -2.47 1.33 9284 0.0345 0.0000 0.0000 0.0000	-0.26 -6.33 559.20 (2.78) 0.13 4.73 0.31 9287 0.6054 0.0000 0.0000 0.0001	-0.63 0.25 -3.3357 -4.57 3.59 0.19 5599 0.1500 0.0000 0.0000

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i

  of other household characteristics such as household head's education, gender and occupation and dummy variables to capture province and region etc. These variables are defined in the note to Appendix Table1; µ i

	z i	is a vector
		F o r
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is the natural log of total per capita expenditure; n ki / n i is the fraction of the household members in the kth age-gender class where k = 1…K refers to the Kth age-gender class within household i;

  one child aged 5-24, which reduces the sample to 14,680 households. Among currently enrolled 5-24 year olds, almost 98 percent reported positive educational expenditures, i.e. enrolment is virtually synonymous with incurring positive education spending. The individual-level analysis is based at the level of the individual child, i.e. on 57,604 children of school-going age 7 .

	with at least
	F o r
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Pakistan Integrated Household Survey (henceforth PIHS) 2001-2002. The PIHS contains rich information on more than 16,000

households from all regions of Pakistan

[START_REF] Gop | Pakistan Integrated Household Survey, Enumerator's Manual of Instructions[END_REF]

. The analysis is limited to households

Table 2

 2 presents current enrolment rates and Table3reports the average unconditional educational expenditure of all children (enrolled and non-enrolled) and the average conditional education expenditure i.e. expenditure on currently enrolled children. These are disaggregated by age-group and gender in each of the provinces and territories of Pakistan.

	Table 2 reveals wide disparities in enrolment between males and females across
	provinces in Pakistan. Table 3 shows very significant differences in average male and female
	unconditional educational expenditures across the provinces. The Federally Administered
	Tribal Areas (FATA), Balochistan and North West Frontier Province (NWFP) emerge as the

provinces with the largest gender differences. Finally, focussing on conditional expenditure makes clear that once enrolled in school, girls generally do not receive significantly lower educational expenditures than boys. For Pakistan as a whole, in the 10-14 age-group conditional educational expenditure is significantly higher on girls (Rs. 2063) than on boys

(Rs. 1941)

. The raw data in Tables

  However, to conserve space we do not present the full underlying equations separately for each province in the Appendix Table regressions, but merely report the main results of interest in Tables 4, 5 and 6 from those underlying equations. In the individual-level equations, the standard errors are robust for clustering at the household level. , reports the conditional OLS equation of the log of budget share of education. As the mean of the dependent variable in column (a) at the bottom of Appendix Table1shows, on average, households in Pakistan devote 4.6 per cent of the total household budget to

	households 9 . 4.1. Household-level outcomes
	4.1.1 Conventional Engel Curve evidence
	Appendix Table 1 reports the results for Pakistan as a whole, both for urban and rural
	areas. Column (a) reports the conventional Engel curve equation, column (b) reports a probit
	of ANYEDEXP (whether household's budget share of education was positive) and the third
	column, (c)	r o F
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6 are also presented by province -Punjab, Sindh, NWFP, Balochistan, AJK, Northern regions (North) and FATA -to allow for area-based differences in expenditure allocations within

  Relative to households with heads in elementary and agricultural occupations (in the base category), those with heads in white collar and service and trade related jobs are inclined to spend a greater proportion of total household expenditure on education.We now turn to the question of most interest here: what do the conventional Engel curve estimates tell us about gender difference in the allocation of educational expenditure in Pakistan? To address this question, p values of the F tests -for the null hypothesis that the coefficients of the age-gender dummies for males and females are equal -are presented in the last four rows of column (a) of Appendix Table1. For example, the p value of the F test that the coefficient on M5TO9 equals the coefficient on F5TO9 for Pakistan (full sample) is 0.0001, suggesting that education budget share increases by significantly more when an extra boy aged 5-9 is added to the household than when an extra girl of that age is added. This suggests very significant bias against females in education expenditure in the 5-9 age range.

	shares.
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There is very significant pro-male bias in the 10-14 and 15-19 age groups as well. Much of this bias manifests itself in rural areas. In equations estimated by province (but not shown for space reasons) bias in the 5-9 age group manifests itself in rural areas of Punjab, Sindh, NWFP and FATA and in urban Balochistan. The reason why there is apparently not much differential treatment among the youngest age group (ages 5-9) in the other areas of Pakistan could be because of incorrect functional form or aggregation issues and we turn to Hurdle Models next to investigate this concern.

4.1.2 'Averaging' explanation for the failure of the Engel curve method

Appendix Table

1

, columns (b) and (c) report Hurdle Model estimates, using household level data. Column (b) presents estimates from the first 'hurdle' -the probability that the household spends anything on education (ANYEDEXP), i.e. that it has a positive education budget share. Column (c) presents estimates of the second stage -the natural log of education budget share (LNEDU_SHARE) conditional on positive education budget share.

  F15TO19), etc., in individual level analysis we use the simple dummy MALE (equals 1 if child is male, 0 otherwise), to capture the gender of the child. All other independent variables are the ones used in the household level analysis. Of course, the marginal effects of MALE in the individual-level equations will differ from the 'difference in marginal effect' of the male and female demographic variables in the household-level equations due to different scaling. However, that does not matter as we are interested primarily in whether the difference in marginal effects (DMEs) of the gender variables in household level equations are statistical significant in those regions/areas where the marginal effect of MALE is significant in the individual level equations.

	14 demographic variables 'proportion of males aged 5 to 9' (M5TO9), 'proportion of females
	aged 15 to 19' (
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  Estimates are obtained by age group and province. As before, we discuss the Pakistan results in detail. Of course, controlling for household implies that coefficients only the child variables (age and gender, MALE) are retained.

	14, 15-19).
	F o r
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These equations are fitted on the sample of only those households that have at least one child of each gender in the relevant age range (ages 5-9, 10-

  also find evidence of gender discrimination in the Pakistan labour market, though they suffer from methodological limitations such as lack of control for sample selectivity in female work participation and for the endogeneity of education.

	F o r F o r F o r F o r
	P P P P
	e e e e
	e r e r e r e r
	R e v R e v R e v R e v
	i e i e i e i e
	w w w w

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

If parents have a preference for having at least one (or some desired number of) boys in the household, they will continue child-bearing till that desired number is reached. This sort of behaviour will lead to girls in the

The effect of censored observations (zero consumption expenditure on an item) is a well-discussed issue in the Engle curve literature. For instance, see[START_REF] Beneito | A Complete System of Engel Curves in the Spanish Economy[END_REF] and[START_REF] Yen | Zero observations and gender differences in cigarette consumption[END_REF].

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript