metadata: authors: 0: author: Amaro Da Costa Luz Carneiro,Pedro Manuel
1: author: Lokshin,Michael M.
2: author: Ridao-Cano,Cristobal
3: author: Umapathi,Nithin
count: Indonesia
docna: 0: docna: Average and marginal returns to upper
            secondary schooling in Indonesia
docty: Policy Research Working Paper
subtopic: Health Care Services Industry,Labor Markets,Secondary Education,Economics of Education,Educational Sciences,Rural Labor Markets
teratopic: Health, Nutrition and Population,Education
abstracts: cdata!: This paper estimates average and
            marginal returns to schooling in Indonesia using a
            non-parametric selection model estimated by local
            instrumental variables, and data from the Indonesia Family
            Life Survey. The analysis finds that the return to upper
            secondary schooling varies widely across individual: it can
            be as high as 50 percent per year of schooling for those
            very likely to enroll in upper secondary schooling, or as
            low as -10 percent for those very unlikely to do so. Returns
            to the marginal student (14 percent) are well below those
            for the average student attending upper secondary schooling
            (27 percent).
geo_reg_key: 517191,517198
repnme: repnme: Average and marginal returns to upper
            secondary schooling in Indonesia
display_title: Average and marginal returns to
            upper secondary schooling in Indonesia
listing_relative_url: /research/2011/11/15460986/average-marginal-returns-upper-secondary-schooling-indonesia
topicv3: Labor Markets m1326488 855,Education m1327048 470,Secondary Education m1327058 481,Returns to Education m1327513 2174,Health m1504661 3480
publishtoextweb_dt: 2011-11-01T00:00:00Z
historic_topic: Health, Nutrition and Population,Education
no_of_pages: 40
author_keys: 0: author_key: 452588
1: author_key: 144523
2: author_key: 658866
3: author_key: 659805
model_extractions: WPS5878 Policy Research Working Paper 5878 Average and Marginal Returns to Upper Secondary Schooling in Indonesia _Pedro Carneiro Michael Lokshin Cristobal Ridao-Cano Nithin Umapathi_ The World Bank Development Research Group & East Asia Pacific Region Social Protection Unit November 2011
Policy Research Working Paper 5878

# **Abstract**

This paper estimates average and marginal returns to schooling in Indonesia using a non-parametric selection model estimated by local instrumental variables, and data from the Indonesia Family Life Survey. The analysis finds that the return to upper secondary schooling varies widely across individual: it can be as high as 50 percent per year of schooling for those very likely to enroll in upper secondary schooling, or as low as −10 percent for those very unlikely to do so. Returns to the marginal student (14 percent) are well below those for the average student attending upper secondary schooling (27 percent).

This paper is a product of the Development Research Group; and East Asia and Pacific Region, Social Protection Unit. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank. org. The author may be contacted at numapathi@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Average and Marginal Returns to Upper Secondary Schooling in Indonesia

Pedro Carneiro<sup>†</sup> Michael Lokshin Cristobal Ridao-Cano Nithin Umapathi JEL Code: J31 Key words: Returns to Schooling, Marginal Return, Average Return, Marginal Treatment Effect __________________ † Pedro Carneiro is affiliated with University College London, IFS, Cemmap and Georgetown University, Nithin Umapathi is Economist with Social Protection sector in East Asia and Pacific, Michael Lokshin is Advisor, DECRG, and Cristobal Ridao-Cano is a Senior Economist with Education sector in ECA. Carneiro and Umapathi gratefully acknowledge the financial support from the Economic and Social Research Council for the ESRC Centre for Microdata Methods and Practice (grant reference RES-589-280001) and the hospitality of the Development Economic Research Group of the World Bank. Carneiro gratefully acknowledges the support of ESRC-DFID (grant reference RES-167-25-0124), the European Research Council through ERC-2009-StG-240910-ROMETA and Orazio Attanasio‟s ERC-2009 Advanced Grant 249612 “Exiting Long Run Poverty: The Determinants of Asset Accumulation in Developing Countries”. These are the views of the authors and do not reflect those of the World Bank, its Executive Directors, or the countries they represent. Correspondence by email to numapathi@worldbank.org
# **1. Introduction**

The expansion of access to secondary schooling is at the center of development policy in most of the developing world. Analyzing the effects of such expansion requires knowledge of the impact of education on earnings. In contrast with the standard model, much of the recent literature on the returns to schooling emphasizes that returns vary across individuals, and are correlated with the amount of schooling an individual takes (e.g., Card, 2001, Carneiro, Heckman and Vytlacil, 2011). In terms of the traditional Mincer equation, _Y_  _a_  _bS_  _u_ (where _Y_ is log wage and _S_ is years of schooling), _b_ is a random coefficient potentially correlated with _S_ . This has dramatic consequences for the way we conduct policy analysis.

In this model there is no single average return that summarizes the distribution of returns to schooling in the population. For example, the individual at the margin between two levels of schooling may have very different returns from all the infra-marginal individuals. Standard instrumental variables estimates of the returns to schooling estimate the Local Average Treatment Effect (or LATE; Imbens and Angrist, 1994), which does not in general correspond to the return to the marginal person, who is most likely to be affected by the expansion of secondary schooling than anyone else in the economy. Furthermore, different policies may affect different groups of individuals.

This paper studies the returns to upper secondary schooling in Indonesia in a setting where _b_ varies across individuals and it is correlated with _S_ (which in this paper is a dummy variable indicating whether an individual enrolls in upper secondary school or not). We find that the return to upper secondary schooling for the _marginal_ person who is indifferent between going to secondary schooling or not is much lower than that of the _average_ person enrolled in upper secondary schooling (14.2% vs. 26.9% per year of schooling).<sup>1</sup> Finally, we simulate what would happen if distance to upper secondary schooling was reduced by 10% for everyone in the sample, and we estimate that the return to upper secondary schooling for those induced to attend schooling by such an incentive is 14.2%.

> 1 The estimated average and marginal returns to upper secondary schooling in Indonesia are 96% and 111% respectively. Average years of schooling for those who have and who have not enrolled in upper secondary schooling in Indonesia are 13.133 and 5.341, so the difference between the two is 7.79. We use this number to annualize the returns to schooling from total return.

2
When evaluating marginal expansions in access to school, the relevant quantities are the returns and costs for the marginal student, not the returns and costs for the average student. In spite of the importance of this topic, there are hardly any estimates of average and marginal returns to schooling in developing countries. Two exceptions using Chinese data are Heckman and Li (2004) and Wang, Fleisher, Li and Li (2011).

Estimating the extent to which returns vary across individuals is also important if we want to understand schooling choices, and their relationship with labor market performance. Studying who is more likely to attend school, and documenting how returns differ between those who attain high and low levels of education, and across individuals more generally, is essential for learning about the main incentives and constraints to school attendance.

We estimate a semi-parametric selection model of upper secondary school attendance and wages using the method of local instrumental variables (Heckman and Vytlacil, 2005). Our data comes from the Indonesia Family Life Survey. Carneiro, Heckman and Vytlacil (2011) use a similar model to estimate the returns to college in the US. Although they examine a different country in a different time period, and a different level of schooling, they also find that the returns to college vary widely across individuals in the US, and that the return to college for the marginal student is well below the return to college for the average student (see also Carneiro and Lee, 2009, 2011).<sup>2</sup> These papers document, across very different environments, how important it is to account for heterogeneity in the returns to schooling. They also show how it is possible to take exactly the same data which is used to estimate a measure of the return to education by instrumental variables methods (IV), and extract much more information from it (allowing us to characterize the heterogeneity in returns across individuals). This can be done using fairly standard parametric methods for estimating selection models, or using a more recent non-parametric approach to the same problem.

Vytlacil (2002) shows that the assumptions underlying standard IV estimates of the effect of a particular program (such as attendance of upper secondary school) are the same as the assumptions underlying a fairly standard non-parametric selection model, and

> 2 There exist also papers which estimate returns for average and marginal student but which account only for selection and heterogeneity given by observable variables (ignoring selection on unobservables). One example is Dearden, McGranahan and Sianesi (2004).

3
thus the two are equivalent. Heckman and Vytlacil (2001a, 2005) explain how to estimate the model using the method of Local Instrumental Variables. We present estimates from both parametric and non-parametric models. Both show the importance of heterogeneity. The former are more precise than the latter, but the parametric model is more restrictive.

This paper also proposes a methodological innovation. In the presence of multiple control variables, constructing various average parameters of interest (average returns for different groups of individuals) using the framework of Heckman and Vytlacil (2005) requires the estimation of high dimensional conditional densities, which are notoriously difficult to implement. We use instead a simulation method that avoids this high dimensional non-parametric estimation problem (in contrast, Carneiro, Heckman and Vytlacil, 2010, 2011, need to impose restrictive assumptions to reduce the dimensionality of the problem).

Since schooling is endogenously chosen by individuals, we require (at least) one instrumental variable for schooling. We propose to use as the instrument the distance from the community of residence to the nearest secondary school (Card, 1995). Distance takes the value zero if there is a school in the community of residence. This variable is a strong determinant of enrolment in upper secondary school. But one could be concerned that the forces driving the location of schools and parents are correlated with wages, implying that distance is an invalid instrument. We discuss this problem in detail.

We control for several family and village characteristics, namely father‟s and mother‟s education, an indicator of whether the community of residence was a village, religion, whether the location of residence is rural, province dummies, and distance from the village of residence to the nearest health post. Our assumption is that if we take two individuals with equally educated parents, with the same religion, living in a village which is located in an area that is equally rural, in the same province, and at the same distance of a health post, then distance to the nearest secondary school is uncorrelated with direct determinants of wages other than schooling. We present evidence that this assumption is likely to hold. In particular, we show that, once these variables are controlled for, there is no correlation between the distance to the nearest secondary school and whether the individual ever failed a grade in elementary school, how many times he repeated a grade in elementary school, and whether he had to work while 4
attending elementary school. In addition, we show (using a different sample) that our distance variable is uncorrelated with test scores (Math, Bahasa, Science, and Social Studies) in elementary school. These are very important dimensions of the pre-secondary school experience that are measures of early ability and early home environments, and which we would expect to be correlated with distance to the nearest secondary school if this variable was endogenously determined.

Our instrumental variable estimates of the returns to schooling are higher than the returns to schooling for Indonesia found in Duflo (2000) with the qualification that the dataset, the instrumental variable, and the time period are not the same. Petterson (2010) finds similar rates of return using the same year, same data but a different sample and a different instrument variable.

This paper proceeds as follows. Section 2 discusses the data. Section 3 reviews the econometric framework. Section 4 presents our empirical results. Section 5 concludes.

# **2. Data**

We use data from the third wave of the Indonesia Family Life Survey (IFLS) fielded from June through November, 2000<sup>3</sup> . The IFLS is a household and community level panel survey that has been carried out in 1993, 1997 and 2000. The 2000 sample was drawn from 321 randomly selected villages, spread among 13 Indonesian provinces containing 83% of the country‟s population containing over 43,000 individuals. The sample we used consists of males aged 25-60 who are employed in the labor market and who have reported non-missing wage and schooling information. We consider only salaried workers, both in the government and in the private sector. We exclude females from the analysis because of low labor force participation, and we exclude self-employed workers because it is difficult to measure their earnings. The dependent variable in our analysis is the log of the hourly wage. Hourly wages are constructed from self-reported monthly wages and hours worked per week. The final sample contains 2608 working age males.

> 3 For a description of the survey see Strauss, J., K. Beegle, B. Sikoki, A. Dwiyanto, Y. Herawati and F. Witoelar. "The Third Wave of the Indonesia Family Life Survey (IFLS): Overview and Field Report", March 2004. WR-144/1-NIA/NICHD. In the appendix we list the main variables we use.

5
In our empirical model we collapse schooling into two categories: i) completed lower secondary or below, and ii) attendance of upper secondary or higher. While this division groups together several levels of schooling, it greatly simplifies the model and is standard in many studies of the returns to schooling (e.g., Willis and Rosen, 1979). The transition to upper secondary schooling is of substantial interest in the Indonesian context given its current effort to expand secondary education. We present both the return to upper secondary schooling, as well as an annualized version of this parameter which we obtain by dividing the estimated return by the difference in average years of schooling completed by those with lower secondary or less and those with upper secondary or more. Upper secondary schooling corresponds to 10 or more years of completed education.<sup>4</sup> In order to compare our estimates with the rest of the literature (in particular, Duflo, 2000) in the appendix we also present OLS and IV estimates of returns using a continuous education variable, corresponding to years of completed schooling.

We run ordinary least squares (OLS) and IV regressions of log wages on years of schooling. The control variables we use are dummies for age, indicators of the level of schooling completed by each of the parents (no education, elementary education, secondary education; we also have an indicator for unreported parental education), an indicator for whether the individual was living in a village at age 12, dummies for the province of residence, an indicator of rural residence, and distance (in Km) from the community of residence to the nearest community health post.

Our instrumental variable for schooling is the distance from the office of the community head to the nearest secondary school. The distance is self-reported by the community head in the Service Availability Roster of the IFLS.<sup>5</sup> Table 2 presents descriptive statistics on the main variables used in our analysis. It shows that individuals with upper secondary or higher levels of education have, on average, 108% higher wages than those with lower education. They also have 7.778 more years of schooling. The respondents with an upper secondary education are younger than

> 4 It is possible to estimate a non-parametric selection model with multiple levels of schooling but the data requirements to do it are very strong. In particular, one needs one instrumental variable for each transition. It is not feasible to pursue this with our dataset.

> 5 We would have liked to use instead the distance between the community of residence in childhood and the nearest school in childhood. Our hope is that current residence and current school availability are good approximations (as in Card, 1995). We show below that this measure of distance to school is a good predictor of upper secondary school attendance.

6
those without. They are also more likely to have better-educated parents, to have lived in towns or cities at age 12, and to live closer to upper secondary schools, when compared to those with less than an upper secondary education.

# **3. Theoretical Framework**

# **3.1 A Semi-Parametric Selection Model**

We consider a standard discrete choice model of schooling, as used in Willis and Rosen (1979) or Carneiro, Heckman and Vytlacil (2011). Consider a model with two schooling levels:

> <sup>_Y_</sup> 1<sup>are log wages of individuals with upper secondary education and above,</sup> _Y_ 0 are log wages of individuals without upper secondary education, _X_ is a vector of observable

> characteristics that might affect wages, and _U_ 1 and _U_ 0 are the error terms. _Z_ is a vector of characteristics affecting the schooling decision.

Equation (2) is a reduced form model of schooling. Agents decide whether to enroll or not in upper secondary schooling based on the expected net present value of earnings with and without upper secondary schooling, and costs, which can be financial or psychic. There can also be liquidity constraints. There is heterogeneity and we expect agents with the highest returns to upper secondary schooling ( _Y_ 1  _Y_ 0 ) to be more likely to enroll in higher levels of schooling. Costs and returns to schooling can be arbitrarily correlated. For a more detailed explanation see Willis and Rosen (1979) or Carneiro, Heckman and Vytlacil (2011).

It is convenient to rewrite the selection equation as: _P_ ( _Z_ )  _FUS_ ( _Z_  )and _V_  _FUS_ ( _U S_ ) and _FUS_ is a cumulative distribution function of _Us_ . _V_ is distributed uniformly by construction. This is an innocuous transformation given that _US_ can have any density.

Finally, observed wages are: 7
Notice that the return to schooling is _Y_ 1  _Y_ 0   1  0  _X_ (  1   0 )  _U_ 1  _U_ 0 (5) The return to schooling varies across individuals with different _X_ ‟s and different _U_ 1, _U_ 0.

We require that _Z_ is independent of ( _U_ 1<sup>,</sup><sup>_U_</sup> 0 ) given _X_ , and that _Z_ is correlated with _S_ (see Heckman and Vytlacil, 2005, for the full set of assumptions). These are the usual IV assumptions. In practice we use a stronger assumption: _X, Z_ is independent of _U_ 1, _U_ 0, _U_ S. This stronger assumption is fairly standard in empirical applications of a selection model of the type described here. We discuss the advantages of using this stronger assumption in the empirical section (see also Carneiro, Heckman and Vytlacil, 2011).

The marginal treatment effect (MTE) is the central parameter of our analysis. In the notation of our paper it can be expressed as: The MTE measures the returns to schooling for individuals with different levels of observables ( _X_ ) and unobservables ( _V_ ), and therefore it provides a simple characterization of heterogeneity in returns. Heckman and Vytlacil (2005) show how to construct parameters of interest as weighted averages of the MTE. For example: where _ATE(x)_ is the average treatment effect, _ATT(x)_ is average treatment on the treated, _ATU(x)_ is average treatment on the untreated (conditional on _X=x_ ), and is the density of _V_ conditional on _X_ .

A less standard parameter but equally (if not more) important is the policy relevant treatment effect (PRTE), introduced in the literature by Heckman and Vytlacil (2001b). It measures the average return to schooling for those induced to change their enrolment status in response to a specific policy. Obviously, it depends very much on the policy being considered. Consider a determinant of enrolment Z, which does not enter directly 8
in the wage equation. The policy shifts Z from Z=z to Z=z‟. The weights for the corresponding PRTE are:

# **3.2 Estimating the** **_MTE_**

Assuming that the unobservables in the wage (1) and selection (2) equations are jointly normally distributed the MTE can be estimated a standard switching regression model (see Heckman, Tobias and Vytlacil, 2001). Assume: where  represents the variance and covariance matrix. Under this assumption: _MTE_ ( _x_ , _v_ )  _E_ ( _Y_ 1  _Y_ 0 | _X_  _x_ , _V_  _v_ )  (  1   0 )  _x_ (  1   0 )  (  _US_ 1,   _US_ ,0 )   1( _P_ ( _Z_ ))  _US_  _US_

where  _U_ 2 _S_ denotes variance of _U s_ ,  _i_ 2 variance of _U i_ with i = 0,1,  _U_ 2 _S_ , _i_ covariance between _U s_ and _U i_ ,  _i_ 2 , _j_ the covariance between _U i_ and _U j_ and Φ is the c.d.f. of the standard normal. Therefore MTE can be constructed by estimating parameters  1,  0 ,  1,  0 ,  1,  2 .

This model relies on strong assumptions about the distribution of the error terms in equations (1-2). To relax these restrictions, we use the method of local instrumental variables that imposes no distributional assumptions on the unobservables of the model (Heckman and Vytlacil, 2000). In particular, Heckman and Vytlacil (2000) show that: where, ( _K(P)_ is a function of _P_ , which can be estimated non-parametrically). Therefore, taking the derivative of (10) with respect to _P_ : 9
_V_ can take values from 0 to 1. However, in practice it is only possible to estimate the MTE over the observed support of _P_ . In our data the support of _P_ is almost the full unit interval, so we are able to estimate the MTE close to its full support.

If we had assumed that _Z_ is independent of ( _U_ 1<sup>,</sup><sup>_U_</sup> 0 ) given _X_ , instead of full independence between ( _Z,X_ ) and ( _U_ 1<sup>,</sup><sup>_U_</sup> 0 ), it would be much more difficult to estimate the MTE with full support. In that case, for each value of _X_ it is only possible to estimate the MTE over the support of _P_ conditional on _X_ , which in general can be much smaller than the unconditional support of _P_ (for a detailed discussion see Carneiro, Heckman and Vytlacil, 2011). The assumption of full independence of ( _Z,X_ ) and ( _U_ 1<sup>,</sup><sup>_U_</sup> 0 ) is fairly standard and it allows us to use the full support of _P_ .

Equations (10) and (11) can be estimated using standard methods. In particular, we use the partially linear regression estimator of Robinson (1988) to estimate (  1<sup>,</sup> 0 ). Then we compute _R_  _Y_   0  _X_  0  _PX_  1   0  . (  1<sup>,</sup> 0 ) cannot be identified separately from _K(P)_ . _K(P)_ and _K’(P)_ is estimated using a locally quadratic regression (Fan and Gijbels, 1996) of _R_ on _P_ . A simple test of heterogeneity in the impact by unobserved characteristics is a test of whether _K’(P)_ is flat, or if _E(Y |X, P)_ is nonlinear in _P_ . If the derivative is flat then heterogeneity is not important. **3.3 Average Marginal Returns to Education** Economic decisions involve comparisons of marginal benefits and marginal costs. Therefore it is especially interesting to estimate the returns to upper secondary schooling for those individuals at the margin between enrolling or not. These would be those individuals more likely to change their schooling as a response to a change in education policy.

The definition of who is marginal depends on the policy being considered. This is made clear in Carneiro, Heckman and Vytlacil (2010, 2011), who consider three particularly interesting definitions of individuals at the margin: 10
These correspond to three different marginal policy changes.<sup>6</sup> In this paper we estimate the average marginal returns to upper secondary schooling in Indonesia according to the definition of marginal in ii) above, although we could have chosen a different one. The MTE provides a general characterization of heterogeneity in returns and from it we can construct various other parameters.

Carneiro, Heckman and Vytlacil (2010) show how it is possible to write the average marginal treatment effect (or AMTE, the return for the marginal person) as a weighted average of the MTE:

# **3.4 Estimating vs. Simulating the Weights: A New Procedure**

So far this section has shown how to recover the MTE from the data, and how to construct economically interesting parameters as weighted averages of the MTE. Heckman and Vytlacil (2005) and Carneiro, Heckman and Vytlacil (2010) provide formulas for the necessary weights in equations 7 and 12, conditional on _X_ . Once these are applied it is simple to average over the relevant distribution of _X_ , when that is what is required. In particular, these papers show that:

> 6 The three policy changes considered are (i) a policy that increases the probability of attending college by an amount _α_ , so that ; (ii) a policy that changes each person‟s probability of attending college by the proportion (1+ _α_ ), so that ; and (iii) a policy intervention that has an effect similar to a shift in one of the components of _Z_ , say _Z_<sup>_k_</sup> , so that and for .

11
> where _f P_ | _X_  _p_ | _X_  and _FP_ | _X_  _p_ | _X_  are respectively the p.d.f and the c.d.f. of _P_ conditional on _X_ , _fUS_ | _X_  _uS_ | _X_  and _FUS_ | _X_  _uS_ | _X_  are respectively the p.d.f and the c.d.f.

> of _U S_ conditional on _X_ , and _FP_ '| _X_  _p_ | _X_  is the c.d.f. of _P_ conditional on _X_ when _Z_ takes value _z’_ .

In practice it is difficult to implement these formulas since they involve estimation of conditional density and distribution functions, and _X_ is a high dimensional object in many applications (there are 28 variables in _X_ in our empirical work). Therefore, Carneiro, Heckman and Vytlacil (2010, 2011) have aggregated _X_ into an index, namely _I_  _X_  1  0  , and proceeded by estimating conditional densities and distributions of _P_ with respect to _I_ .

There is little theoretical basis for this aggregation which makes it quite unattractive. In this paper we use an alternative procedure, which avoids making this aggregation, and sidesteps the problem of estimating a multidimensional conditional density function.

Notice that the selection equation relates _S_ , _X_ , _Z_ , and or _V_ . Using the estimates of the parameters of the selection equation, it is straightforward to simulate the following objects: Once we have these, we just need apply them to equations (7) and (12). This simulation procedure is simple, and its steps are described in detail in the appendix.

# **4. Empirical Results**

# **4.1 Is Distance to School a Valid Instrument?**

To account for the potential endogeneity of the schooling decision we instrumented schooling with the distance to the nearest secondary school, measured in kilometers.<sup>7</sup> In order for this to be a valid procedure distance to school needs to satisfy two assumptions: i) distance to school should affect the probability of school enrolment and ii) it should have no direct effect on adult wages.

> 7 Distance to the nearest school has been used as an instrument for schooling by Card (1995), Kane and Rouse (1995), Kling (2001), Currie and Moretti (2003), Cameron and Taber (2004) and Carneiro, Heckman and Vytlacil (2011).

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Condition ii) is controversial if families and schools do not randomly locate across locations in Indonesia. For example, Carneiro and Heckman (2002) and Cameron and Taber (2004) show that individuals living closer to universities in the US have higher levels of cognitive ability and come from better family backgrounds. In fact, it is also true Indonesia that those who have better educated parents are located closer to secondary schools. However, it is possible that school location is exogenous after we account for a very detailed set of individual and regional characteristics, namely: age (or cohort), parental education, religion, an indicator for whether the individual was living in a city or in village at age 12, an indicator for whether the individual lived in a rural area at age 12, dummies for the province of residence, and distance to the nearest health post.

One way to investigate the plausibility of this assumption is to check whether distance to the nearest secondary school is correlated with pre-secondary educational outcomes of each individual. If there was non-random sorting of families and schools across locations in such a way that distance to secondary school was correlated with adult wages, it would surely appear in these variables.

Table 3 examines whether distance to upper secondary school is correlated with whether an individual ever repeated a grade in elementary school, the number of repetitions in elementary school (both of which are measure of early school success), and whether the individual worked while in primary school. If our instrument is valid it should not be correlated with such early measures. Our results show no apparent correlation between distance to school and these variables.

In addition, Table 4 examines comprehensive exam scores in math, science, social studies and Bahasa. The sample used in this table is not exactly the sample used in our regressions, because it is only possible to gather elementary school test scores for a very small proportion of individuals in our original sample. Therefore, in the regression showed in this table, we placed no age or gender restrictions in the sample. Again, we find no correlation between the distance to school and test scores.<sup>8</sup> This evidence is suggestive that our empirical strategy is valid.

> 8 Considering a more restricted sample results in a small number of observations. Our main conclusions are unchanged, but results are fairly imprecise.

13
The first column of Table 5 shows that distance to the nearest secondary school is a strong predictor of enrolment in secondary school. We run a logit regression where the dependent variable is an indicator taking value 1 if an individual ever attended upper secondary school and the regressors include distance to the nearest secondary school and all the control variables mentioned above. The table displays marginal effects of each variable on the probability of enrolling in upper secondary education. We include distance to health post as a proxy for location characteristics and, unlike distance to school, distance to health post does not predict school enrollment. Children of highly educated parents are more likely to attend upper secondary school than children of parents with low levels of education. Catholics and Protestants are much more likely to attend secondary school than Muslims (the omitted category). Children living in small villages and in rural areas were less likely to attend upper secondary school than those living in large cities and urban areas.

In the second column of table 5 we present estimates of a more flexible model where the impact of distance on secondary school attendance varies with _X_ . In particular, we interact distance to school with age (which, for a fixed year, also captures cohort), religion, parental education, and rural residence. It is useful to estimate this richer model for two related reasons. First, it is much more flexible than the model in column 1. Second, because by allowing the impact of the instrument to vary will the variables in _X_ we allow the effect of the instrument to vary more. As a result, the standard errors in the IV estimates and in the selection model are smaller than if we just use the model in column 1. Therefore, the basic estimates in this paper will come from this model, while estimates of the simpler model are presented in the appendix (we discuss them below).

Notice also that table 5 displays p-values for tests of the null hypothesis that distance to school does not affect upper secondary school attendance. In column 1, we look to the single coefficient on distance, while in column 2 we perform a joint test on all coefficients involving distance. In both columns we reject that distance to school does not determine upper secondary school attendance.

There is another important reason why condition ii) may be violated. If regions where schools are abundant are also regions where other infrastructure is also abundant, then we may be confounding the impact of school availability on wages with the impact of other 14
infrastructure on wages (see the argument in Jalan and Ravallion, 2002). This will be true unless labor is perfectly mobile, which is unlikely to be the case in Indonesia.

However, we include detailed regional controls in our models which should absorb much of this variation. Therefore, our argument is that our assumption is valid conditional on all the controls we have in the model. In addition, we show that removing these detailed regional controls hardly affects our results, which indicates that this problem is unlikely to be that important in our setting. Perhaps, as Duflo (2004) argues, the response of other infrastructure (be it private or public) to school construction and to a better skilled workforce is very slow.

# **4.2 Standard Estimates of the Returns to Schooling**

In order to more easily make a comparison between our data and estimates and those in the literature we start by presenting standard OLS and IV estimates of the returns to schooling. Throughout the paper schooling takes two values: 0 for less than upper secondary, and 1 for upper secondary or above. We use the log hourly wage in 2000 as our dependent variable. The full set of controls consists of: age (or cohort), parental education, religion, an indicator for whether the individual was living in a city or in a village at age 12, an indicator for whether the individual lived in a rural area at age 12, dummies for the province of residence, and distance to the nearest health post.

We present ordinary least squares (OLS) and IV results. This is shown in Table 6. The annualized OLS estimate of the return to upper secondary schooling is 9%, while the IV estimate is 12.9%. Recall from table 2 that individuals with upper secondary schooling or above have on average 13.133 years of schooling, while those with less than upper secondary have on average 5.341 years of schooling. The difference between the two groups is 7.792 years of schooling. Using this figure to annualize the returns to upper secondary education we have an OLS estimate of 9% (=70.5%/7.792) and an IV estimate of 12.9% (=100%/7.792).<sup>9</sup>

> 9 Appendix table A1 presents OLS and IV estimates where we use years of schooling as the main explanatory variable (as opposed to upper secondary schooling). The first column in this table shows coefficients of an OLS regression of log wages on years of schooling and several controls. The estimated return to a year of schooling is 9.6%. The second column shows the first stage of the two stage least squares estimator, i.e., a regression of years of schooling on the instrument and the control variables. It shows that distance to school is negatively related to schooling attainment. Finally, column 3 shows the IV estimate of the return to schooling, which is 15.7%.

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These estimates are higher than (but of comparable magnitude to) those in Duflo (2001), although we use more recent data. Petterson (2010) finds a return of 14% using the same data from the same year but a different sub-sample and instrument.

As in most of the literature, our IV estimates of the return to education are larger than OLS estimates. Card (2001) suggests that such a finding indicates that returns to schooling are heterogeneous and the marginal individual induced to enroll in school by the change in the instrument has a higher return than the average individual. Carneiro, Heckman and Vytlacil (2011) show that in the case of college attendance in the US, IV estimates can be above OLS estimates even if the marginal individual has a lower return than the average. Another reason why IV can exceed OLS is measurement error in schooling. Although schooling is relatively well measured in the US (Card, 1999) and other developed countries, that is not necessarily the case in Indonesia.

In appendix table A2 we also present IV estimates of returns for models where we do not interact the instrument with the variables in _X_ . The point estimate is smaller than the one in Table A1, and the standard error is larger. Nevertheless, the main pattern remains: the IV estimate is much higher than the OLS estimate. In a model with heterogeneous returns, it is not surprising that the instrumental variable is sensitive to the choice of instrument. For the remaining of the paper, we present a parallel set of results in the appendix in which we do not interact the instrument with _X_ in the selection equation.<sup>10</sup> Finally, in appendix table A3 we present results were we omit all regional dummies from the model. Our IV estimate is very similar to the ones in tables A1 and A2. This indicates that regional variation in infrastructure, which is correlated with the availability of schooling, is unlikely to be driving our results.

OLS and IV estimates hide considerable heterogeneity in returns and, as emphasized in Heckman and Vytlacil (2005), Heckman, Urzua and Vytlacil (2006), and Carneiro, Heckman and Vytlacil (2011), it is not clear what economic question is answered by the IV estimate. In order to further investigate this issue we use the framework of section 3.

> 10 We do this for two reasons. First, to show that the main patterns in our results are not driven by choosing the specific way the instrument enters the model. Second, because the first stage F-statistic is higher in the case where we use a single IV (F=11.34) than when we use multiple IVs (F=3.62) consisting of distance interacted with different components of _X_ . We will see throughout the paper that using the expanded set of instruments allows us to get similar results and lower standard errors than we use a single (but apparently stronger) instrument.

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We estimate parametric (assuming joint normality of ( _U_ 1, _U_ 0, _U_ S)) and semi-parametric versions of the model (which does not put assumptions on the joint distribution of ( _U_ 1, _U_ 0, _U_ S)).

# **4.3 Average and Marginal Treatment Effect Estimates**

We start with the semi-parametric model. We construct _P_ as a predicted probability of ever attending upper secondary school from a logit regression of upper secondary school attendance on the _X_ and _Z_ variables of section 3. Table 5, discussed above, reports the coefficients of the logit model. All average derivatives presented in the table have the expected sign.

It is only possible to identify the MTE over the support of _P_ . Therefore, we need to examine the density of _P_ for individuals who attend upper secondary school or above and those who do not. This is done in both panels of Figure 1, which shows the distributions of the predicted propensity score ( _P_ ) for these two groups. The supports for these distributions overlap almost everywhere, although the support at the tails is thin for low values of _P_ among those with upper secondary school or above. We construct the MTE as described in Section 2. In order to estimate _K(P)_ we run a local quadratic regression of _R_ on _P_ , using a Gaussian kernel and a bandwidth of 0.2. The implied _MTE_ ( _x,v_ ) is computed by calculating the slope on the linear term of the local quadratic regression.<sup>11</sup> Figure 2 displays the estimated MTE (which we evaluate at the mean values of the components of _X_ ). The MTE is monotonically decreasing for all values of _V_ . Returns are very high for individuals with low values of _V_ (individuals who are more likely to enroll in upper secondary school or facing high costs). The figure demonstrates substantial heterogeneity in the return to schooling, which ranges from 34% for individuals with V around 0.1 to 13% for those with V close to 0.5, and becomes negative for those with values of V close to 1. The fact that returns are the lowest for individuals who are least likely to go to school is consistent with a simple economic model where agents sort themselves based on their comparative advantage.

Unfortunately the standard errors on our estimated MTE are quite wide (standard errors are estimated using the bootstrap). However, it is still possible to reject that the

> 11 The coefficients on _X_ in the outcome equations are presented in table A4 in the appendix.

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MTE is flat. Table 7 tests whether adjacent segments of the MTE are equal. Take, for example, the first line of the table. In the first column we show the average value the MTE takes when _X_ is fixed at its mean and _V_ takes values between 0.1 and 0.2, while the second column corresponds to values of _V_ between 0 and 0.1. The third column shows the t-statistic for a test of whether the numbers in the first two columns are equal. We reject equality in almost all lines of the table at the 5% significance level. Therefore, we are able to reject that the MTE is flat, even with the large standard error bands shown in figure 2.

Standard errors improve when we estimate the MTE assuming joint normality of ( _U_ 1, _U_ 0, _U_ S) as shown in Figure 3. The shape of the MTE is declining as in Figure 2, although the normality assumption does not allow the MTE to have a flat section as in Figure 2 so the MTE is declining everywhere, again taking negative values for very high values of _V_ .

Table 8 presents average returns to upper secondary schooling for different groups of individuals. The return to upper secondary school for a random person is 12.3%. The return for the individuals who were enrolled in upper secondary schooling is considerably higher, at 26.9%. If individuals who did not go to upper secondary school would have gone there, they could expect the returns of 1.7%. In the parametric case the average parameters are estimated with the assumption of full support. Estimates of the return to the marginal student (AMTE) are robust to the lack of full support. The return to the marginal student is 14.2%, well below the return to the average student in upper secondary school (26.9%).

Finally, the last line of Table 8 reports the average return for those induced to attend upper secondary school by a particular policy shift: a 10% reduction in distance to an upper secondary school. This is the parameter needed to understand the impacts of such an education expansion. By coincidence, it is remarkably similar to the MPRTE.

In the appendix we show that results are similar but more imprecise when we do not interact _Z_ and _X_ in the selection equation. This is reassuring, and shows the usefulness for the precision of our estimates of accounting for a more flexible model.<sup>12</sup>

> 12 See tables A2 , A5 and A6, and figures A1, A2 and A3.

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# **5. Conclusion**

Indonesia has an impressive record of educational expansion since the 1970s. The enrollment rates are nearly universal for elementary schooling and are around 75% for secondary education. There is an ongoing effort to extend universal education attainment to the secondary level. And although enrollment in secondary education continues to rise we find striking inequality in returns to education. The individuals who are most likely to be attracted by educational expansions at the upper secondary level (marginal) have lower average returns than those already attending upper secondary schooling. In this paper we document a large degree of heterogeneity in the returns to upper secondary schooling in Indonesia. We estimate the return to upper secondary education to be 12 percentage points higher (per year of schooling) for the average than for the marginal student.

Therefore, efforts aimed at educational expansion will attract students with much lower levels of returns, although the returns are still fairly high for the marginal person, and therefore further expansions are probably justified. But our estimates also show that it is probably not optimal to bring everybody into upper secondary education.

Is it possible to reduce such a high degree of inequality in the returns to schooling? There is a growing body of literature that argues that human capital outcomes later in life are largely determined early in life (e.g., Carneiro and Heckman, 2003). It is therefore important for the design of schooling policy to determine whether the inequality in secondary schooling outcomes can be remedied at earlier stages, for example during elementary education or even earlier. In an impressive drive to increase the quantity of education, there should be a renewed emphasis on quality of education that ensures a more relevant learning environment for the disadvantaged children that reduces the inequity in lifetime outcomes. This can be achieved by raising the return for the marginal student, and therefore the increased equity need not cost in terms of efficiency.

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