Identification

Similar to the interpretation in Felfe and Lalive (2014), in the context of this article reflects the preferences of parents for early school attendance or the need for schools. The likelihood of children attending school is expected to decrease as increases.

The MTE measures how early school attendance affects child development for children whose unobservable determinants of attending school is the same as their propensity score.

It is a marginal effect in the sense that the parents of those children are indifferent between sending them to school at an early age or not. The MTE for children whose unobservable component is is expressed as:

( − , , = ( )) = ∙ − + ∙( − ) + ( − , , = ( )) (2.6)

2.3.2 Identification

Several papers that have studied the effects of school attendance on child development have used different variants of the supply of local education as an exclusion restriction, for example Felfe & Lalive (2014) considered the average attendance at care centers in school districts in Germany (private centers with public subsidies 79% of the total cost of center), Urzúa & Veramendi (2011) considered the capacity of public centers in the municipalities of Chile, and also for the case of Chile, Noboa-Hidalgo & Urzúa (2012) introduced the changes in the number of public care centers at the municipal level.

4 Heckman and Vytlacil (2007) show that for the OLS estimate, in addition to the standard selection bias derived from the correlation between the treatment and the unobservable component of control and treated individuals in the estimate of the performances, , there is a second source of bias associated with the presence of the treatment in the error term of the reduced form. This implies, in this case, that the decision of parents to send their children to school is determined by unobservable gains that are derived from this decision.

With similar criteria to the previous cases, in this paper I consider the supply of preschools as an exclusion restriction. This study separately incorporates the supply of public and private schools as an exclusion restriction, identifying the existing links between the number of places of both types and preschool attendance. A potential weakness of this instrument could be the criteria used by policy makers to select the location of these schools. If these criteria are linked to the relative income of the average population of each neighborhood, then supply will most likely be higher in the areas where the poorest children reside. If this were the case then the instrument could be correlated with the level of child development and would not be useful. In this section I aim to show that this association is weak in the case of Montevideo in Uruguay. On the other hand it is expected that there is a certain lag in the construction of schools in response to the demographic changes that occur in each of the neighborhoods, and this potential lag in the coverage of the schools allows us to further relativize the endogeneity of the supply of schools.

In order to identify the above restriction the fact that the ENDIS reports the child’s neighborhood of residence and the neighborhood of the school which the children attend is considered. In order to obtain the supply of education for this age group in the different neighborhoods I used the records of the Ministry of Education and Culture, which contains information regarding the number of preschools, both public and private (approved), as well as their geographical location. In order to calculate the number of places available, I used the parameters established by the national regulations. For children aged from 12 to 24 months it is considered that the maximum number of children that can attend per group is 12, regardless of whether the center is public or private. For classes for children aged from 24 to 47 months, two types of public centers are considered separately: Child and Family Care Centers (CAIF, by Spanish name) and kindergartens. According to the regulations a limit of 15 children per group has been established for the first type (centers covering children aged up to 36 months), while a limit of 30 children has been established for the second type (these centers generally cover children aged up to 36 months). In private centers a limit of 20 children per group has been established, as the majority of these institutions indicate on their websites.

Fig. 2.1 shows the number of children in the 24 to 47 month age group residing in each neighborhood as well as the number of public places in the enabled institutions. The frequency of poor children for the same age group is also included. The information is presented in four panels, the first corresponds to neighborhoods where the relationship between public places and children is less than 10%, that is, where supply is very low; the second and third panels indicate the cases where the relationship is intermediate, between 10% and 20% and between 20% and 30%; while the last panel shows a slightly higher relationship, more than 30% of the potential demand is covered.

Fig. 2.1 – The total number of children and poor children, and public places available in schools (24 to 47 months) by area of residence

According to the socio-economic profiles of the neighborhoods, there are very different living situations in these four groups, in each group there are neighborhoods where the incidence of poverty is high with others where high or very high incomes are observed.⁵ This heterogeneity allows us to assume that the degree of correlation between the supply of public schools and the performance of the children is low and, therefore, the exclusion restriction is expected to function adequately.

Table 2.1 summarizes the existing link between educational supply (number of places) and the socioeconomic profile of the neighborhood, distinguishing between public and private schools. In all estimates the dependent variable is the number of places, and the independent variables are the potential demand in the neighborhood and the proportion of children residing in each of the areas belonging to each quintile of the overall income distribution. Additional controls are introduced in columns (2) and (4). For the public

5 In the case where there is less potential demand satisfied there are neighborhoods in which the average income of the residents is low or very low (Cerro, Tres Ombúes, Malvín Norte) and others which have a high average income (Punta Gorda and Carrasco). In the intermediate case there are also neighborhoods of different economic strata, with neighborhoods where the incidence of poverty is high (Casabó or Flor de Maroñas in panel (b) and La Paloma and Ituzaingó in panel (c)), middle-income neighborhoods (Aguada or Reducto in panel (b) and Centro and La blanqueada in panel (c)), and high-income neighborhoods (Punta Gorda, Buceo or Punta Carretas in panel (b) and Parque Batlle in panel (c)). Finally, in the neighborhoods where the potential demand is best met there is also heterogeneity, with areas where the poverty rate is very high (Casavalle), middle-income neighborhoods (Palermo and Prado) and high-income neighborhoods (Malvín).

supply the proportion of children belonging to each of the quintiles is not significant. In the case of private supply there is a higher private supply in neighborhoods where the proportion of children belonging to the fifth quintile is higher. This effect disappears when the average years of education of the mothers in the neighborhood is introduced as an additional control, a variable which is highly significant for explaining private supply, but not the public supply.

Table 2.1

Coefficients of the proportion of children located in each income quintile in the different neighborhoods. Estimation of the public and private supply in each neighborhood

Public supply Private supply

(1) (2) (3) (4)

Number of children in the neighborhood 0.215*** 0.253*** 0.174** 0.338***

[0.039] [0.042] [0.084] [0.108]

Proportion of children belonging to each quintile (omitted: 1^st quintile)

Quintile (=2) -14.85 -18.45 28.25 25.56

Note: Control variables: proportion of boys in the neighborhood, average years of education of the mothers, average age in months of children in the neighborhood and complementary public supply (private supply in estimate of public supply and vice versa) Standard errors are clustered at the neighborhood level and are shown in parenthesis: *p < 0.10, **

p<0.05, ***p<0.010.

Several studies have indicated that the quality of the school, and not only attendance, is a key determinant of child development. Blau & Currie (2006) considered the teacher-student ratio and the class size as measures of quality.⁶ These measures are regularly used and Felfe & Lalive (2014) applied them coupled with other measures such as the full-time dedicated of staff, their training and age, and found a positive relation between the quality of the school and child development. Furthermore, Bernal in a forthcoming paper (cited in Araujo & Schady, 2015) indicates that an initiative to increase the quality of schools (measured by FCCERS) in Colombia by training the staff in health, nutrition, educational practices and child development had positive impacts on child development. Unfortunately in this paper the types of measures that reflect the quality of the schools were not available.

The quality of the school can also influence the decision of parents about whether to send their children to school or not, or more specifically, what influences their decisions is their perception of that quality relative to the quality of care offered in the household. Felfe

& Lalive (2014) indicate that this quality gap is part of the unobservable costs when

6 These measures are indirect ways to approximate the quality of the schools, however I have not found any papers that use measures that report directly on this quality as an exclusion restriction, for example, the instruments indicated in Araujo and Schady (2015) (ECERS-R, FCCERS-R, CLASS).

parents make the decision of whether to send their children to school or not. The perceptions of adults do not necessarily have to correlate with the actual quality of the service on offer, as it is mediated by a set of information required to evaluate that quality, which in many cases is not public knowledge. Perceptions also vary according to the requirements that are established from what happens in the household. As such, the perceptions of parents about the quality of schools relative to the quality of care offered in the household is a good candidate for use as an exclusion restriction. In the paper I approximate this dimension through a variable that indicates the perception of the matching between the supply and demand of schools in the neighborhood of residence. It is assumed that this perception should incorporate, among other arguments that explain it, the distance between the perceived quality of both the school and the quality of care offered in the household. If parents perceive the quality of the centers to be low, in many cases they opt not to send their children to them.

For the above mentioned reasons a question from the ENDIS is used as an instrument in which the respondent is asked to indicate whether they believe there are options available to send their children to school in the area in which they reside. In addition to the objective availability it is expected that the response of the parents considers whether they believe that the available schools provide a good level of care for their children.

Therefore, given the expectations of the parents, they will respond that there are or are not options and that will partly explain the variety of responses observed for the same neighborhood. In fact, as shown in Fig. 2.2, the responses are relatively stable when the respondent resides in neighborhoods where the supply is low or intermediate, with approximately 50% of the respondents indicated that there were options. In the areas where the supply is high the positive responses decrease slightly, to about 40%, and the dispersion of the responses also increases. Neighborhoods with high and medium income levels coexist in these areas. It is also not observed that the greater relative supply may be related to the size of the neighborhood, in fact the same chart shows how absolute supply increases when relative supply is greater than the number of children residing in the neighborhood. This aspect is relevant as the stability in the responses could be associated with a lack of schools close to the household.

Fig. 2.2 – Relationship between the number of places and children in the neighborhood and the perceptions of those interviewed regarding the supply of schools in the neighborhood

In addition, I made an estimate of the perceptions about how good the matching was in the neighbourhood, including the public and private supply of schools aimed at early childhood, as well as the number of children residing in the neighbourhood as explanatory variables. None of these variables are significant, so this association was discarded (see Table 2.2). Additionally, I included some variables that may affect these perceptions. For example, it is possible that the more educated parents have more information about the available supply, or that the perceptions were influenced by the age of the child or have other children. These variables are also not significant.

Therefore, responses about the options available will be interpreted as an approximation of the perception about the matching or the different requirements that adults demand from the school in order to send their children there.⁷

7 In Table A.2.1 of the Annex I present the coefficients of the perceptions of the matching on the estimates of each of the components of child development. The variable is not significant in any of the cases, which reaffirms that it may be an adequate exclusion restriction.

Table 2.2

Estimates of perception of the goodness of matching in the neighborhood

Public supply 0.001 0.001

[0.0003] [0.0003]

Private supply -0.0001 -0.00001

[0.0003] [0.0004]

Private supply² (/ 1000) 0.0002 0.0002

[0.0005] [0.0006]

Number of children in the neighborhood -0.00001 -0.00004 [0.0001] [0.0001]

Years of education of the mother -0.009

[0.006]

Months -0.002

[0.003]

Mother alone (1=Yes) -0.014

[0.045]

Other child in the household

< 4 years (1=Yes) 0.015

[0.041]

Between 4 and 12 years 0.012

[0.038]

Constant 0.410*** 0.554***

[0.046] [0.104]

Observation 813 801

R2 0.014 0.019

Note: Standard errors are shown in parenthesis: *p < 0.10, ** p<0.05, ***p<0.010.

The estimates are made considering these exclusion restrictions and from which we can identify the expected gains resulting from participation in the school, and which are generated by a change in the supply and quality of the school. That is, they capture how a change in the latter variables (which approximate the policy in effect) affects early child development. The reduced form to estimate is:

( | , , ( ) = ) = ∙ + ∙ + ∙ ∙ − + ∙ ∙( − ) + _, ( ) (2.7)

The conditional independence of in relation to Z implies that , , ( ) =

= 0, where the restriction Z may be excluded from the potential results. The conditional independence of , , in relation to Z also implies that:

( − ) , , ( ) = = ∙ − , , ( ) = ≡ _, (2.8)

where _, ( ) is an unknown function that measures how the effect of the treatment due to unobservable characteristics, − , varies with the preferences for attending schools, . Therefore _, ( ) depends on the propensity score in two ways. First, if increases it

means that a growing proportion of the children attend school in early childhood, such that the result of the reduced form reflects more of the unobserved component of the treatment effect, − , , ( ) = . Second, the increase of implies increased parental preferences for attending schools at an early age, . This in turn changes the unobserved component of the treatment effect, − , , ( ) = , if there is a correlation between the preferences for sending children to school in the early years of life and early child development.

Finally, the partial derivative of the reduced form regarding the propensity score is calculated (Heckman & Vytlacil, 2001a):

− , , = ( ) = ^{, , ( )} = ∙ − + ∙( − ) + ^{, ( )} (2.9)

This derivative is called Local Instrumental Variables (LIV) and is what identifies the MTE. The last component ^{, ( )}= ( − , , = ( )) is estimated using a local nonparametric regression.