Equal Access to University Education in Chile? An Application Using Spatial Heckman Probit Models
Round 1
Reviewer 1 Report
I appreciate the extensive data files, which contain data for more than 250,000 students. The results of this article are very interesting and beneficial.
However, I have reservations about working with literature.
- You should add at least 10 references from years 2018 - 2021.
- You should add section literature review (at least 2 pages),
- At the end of the work it is necessary to add a section of the discussion, where the achieved results will be compared with the results achieved by other authors.
Abstract should be extended, add there some numerical results
page 2 line 86: change to ... organized by the Departamento de Evaluación, Medición y Registro Educacional (DEMRE) of ...
page 3 line 142: remove extra ")" respectively).
Figure 1: can you replace lines with arrows ? Now it's really confusing
Page 10: formula (16) and (17).
- Why in formula (16) is distance linear + quadratic and in formula (17) only linear ?
- why in formuls (16) is used lit_score and math_score and in formula sibl_Univ and social_cap
- sibl_univ should not be supscript
Author Response
We thank you for your comments. We found them very useful and have revised our paper accordingly. Our response appears below.
# 1. You should add at least 10 references from years 2018 - 2021.
We have added 11 new references from years 2018–2021. All are cited in the new subsection on determinants of access to higher education, in the literature review section.
# 2. You should add section literature review (at least 2 pages).
We have reformulated section 2 of the paper (literature review), adding a subsection devoted to reviewing previous studies of the determinants of access to higher education.
#3. At the end of the work it is necessary to add a section of the discussion, where the achieved results will be compared with the results achieved by other authors.
We have added a new section (section 6) that discusses the results. First, we have moved the last four paragraphs of section 5 (in the previous version) and second, we have incorporated other authors’ outcomes to the discussion, as the referee suggest.
# Abstract should be extended, add there some numerical results
We have extended the abstract to incorporate some numerical results.
# page 2 line 86: change to ... organized by the Departamento deEvaluación, Medición y Registro Educacional (DEMRE) of ...
Done.
# page 3 line 142: remove extra ")" respectively).
Done.
# Figure 1: can you replace lines with arrows? Now it's reallyconfusing
Done.
# Why in formula (16) is distance linear + quadratic and informula (17) only linear?
Equation (16) models a candidate’s probability of applying to a university as conditioned by having passed the preselection examination (PSU), whereas Equation (17) models a candidate’s probability of passing the PSU. Distance from Santiago maintains a non-linear (quadratic) relationship with the former (as shown in Figure 4), but it is linear in the selection (second) equation.
# Why in formula (16) is used lit_score and math_score and in formula (17) sibl_Univ and social_cap
Again, Equations (16) and (17) model different phenomena. A candidate’s probability of applying to a university depends on the PSU scores in Literature (“lit_score”) and Maths (“math_score”), whereas the probability of passing the examinations in Literature and Maths depends on other different variables, such as having siblings studying at a university (“sibl_Univ”) and having social capital (“social_cap”).
# sibl_univ should not be supscript
This typo has been corrected.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This is an interesting topic. But the paper could be strengthened by making the construct of social capital more clear. According to Bourdieu, social capital is acquired. Generally, there are two types of social capital, bonds and bridges. Examples of the former include family members (i.e., strong ties), close friends (i.e., weak ties), or people who belong to the organizations or institutions (e.g., schools). The latter includes connections to individuals who with whom they share a common sense of identity, such as distant friends and colleagues. The authors operationalize social capital as parents' education and type of student’s secondary school. It is not clear how parents’ education, can be measured by household income (lines 70 & 71). Additionally, the authors created a latent variable of four variables: parents’ father’s and mother’s education, family income, and students’ school type. They do not report any statistics (e.g., factor loadings, ) regarding the variance explained by the variables on the factor or latent variable.
It is not clear why the authors did not use structural equation modeling (SEM) as a research design. Given Figures 1 and 2, a SEM would would be more appropriate. (The authors could have used gsem in Stata to produce a Heckman selection model as a SEM.) Spatial weights could have been created to produce spatially weighted variables to include in the SEM to help capture spillover effects.
It is not clear how the authors referred to local spatial autocorrelation is specified without computing any local spatial autocorrelation statistics (e.g., Geary's ci, Getis and Ord's G1i).
The following statement, "It is thus important for the state to foster policies
that motivate students living in working-class neighborhoods to see the university as a valid option for their personal advancement." (lines 467-469) is not supported by the results. The authors do not provide results that explicitly identify " working-class neighborhoods".
The authors should explicitly note that there study is limited in that it does not take into account unobserved student heterogeniety.
The last part of the manuscript mentions directions for future research, which I think should include examining the effect of unobserved student heterogeneity on the outcome.
Some editing is needed. For example, in the following statement, "Students who graduated are represented as a dummy variable, “rural” if the students graduated from a rural college or “urban” if they graduated from an “urban college.” (lines 151-152). I think the authors meant "graduated from a . . . high school".
Author Response
We thank you for your comments. We found them very useful and have revised our paper accordingly. Our response appears below.
# 1. The paper could be strengthened by making the construct of social capital more clear.
The reviewer is right. We have rewritten some paragraphs in the Introduction and Subsection 3.1.3 and added an Appendix with the statistics used in the factor analysis. We note that this latent variable is used “merely” as one of the excluded variables (instrumental variables) in the selection equation of the two Heckman probit models; our model does not focus on the construct developed from the latent variables. To strengthen the instrumental nature of this composite variable, we have stated it explicitly in the Introduction and renamed it “Model instrumental variable” in Table 1.
# 2. The authors operationalize social capital as parents' education and type of student’s secondary school. It is not clear how parents’ education, can be measured by household income (lines 70 &71).
In examining the literature—specifically Coleman (1988) and Furstenberg and Hughes (1995)—we realized that this latent variable could be considered as a proxy of “social capital,” since these authors propose computing the variable social capital as simply a combination of three variables: tangible economic aspect (income), intellectual aspect (educational level), and social networks (types of school).
This passage is the reason that our statement in lines 70-71 of the first draft of this paper (“…choosing between two well-known proxy variables for students’ social capital: 1) parents’ education, measured by household income”) was wrong, as the reviewer correctly observed. We have revised the text as follows:
“We also employed confirmatory factor analysis to create a latent variable for use in our model that would avoid collinearity and resolve the problem of choosing among four variables: 1) father’s education, 2) mother’s education, 3) household income, and 4) type of student’s secondary school.”
# 3. Additionally, the authors created a latent variable of four variables: parents’ father’s and mother’s education, family income, and students’ school type. They do not report any statistics (e.g., factor loadings) regarding the variance explained by the variables on the factor or latent variable.
Following the reviewer’s request, we have added an Appendix with the statistical tables—specification of the variables, Cronbach’s alpha, and CFA results.
# 4. It is not clear why the authors did not use structural equation modeling (SEM) as a research design. Given Figures 1 and 2, a SEM would be more appropriate. (The authors could have used gsem in Stata to produce a Heckman selection model as a SEM).
As far as we know, it is not possible to estimate a Heckman probit (Heckit) model with SEM. The STATA “gsem” procedure permits binary modelling outcomes (logit/probit models) and Heckman models with continuous outcomes, but not Heckman models with binary outcomes (Heckit models).
# 5. It is not clear how the authors referred to local spatial autocorrelation is specified without computing any local spatial autocorrelation statistics (e.g., Geary's ci, Getis and Ord's G1i).
The reviewer is right, in the sense that we have confused two different concepts. We are not actually estimating any spatial local autocorrelation models, but only SLX models, which are considered as spatial models of a local range of spatial autocorrelation. This is one form that what Anselin (2003, Table 1) calls spatial local externalities or spillovers, can take. This point was already stated in the text, after Equation (12):
“Local spatial spillovers are appropriate when the proper spatial range of the explanatory variables is the location and its immediate neighbors (but not beyond); that is, the range of neighbors considered in the reference space—for example, only direct neighbors, not neighbors’ neighbors.”
The previous paragraph on Figure 4 also cited the argument by LeSage (2014) that this SLX model may be the best fitting specification when spatial autocorrelation in the error terms of a non-spatial baseline model is weak, as is the case of the error terms in our baseline Heckit models.
We have therefore replaced “spatial local autocorrelation” with “spatial local externalities” or “spatial local spillovers” throughout the paper. In this case, the common spatial autocorrelation tests (local Moran’s I, Geary’s ci, and Gi Getis and Ord’s tests) are not useful for identifying the global vs. local nature of spatial externalities.
# 6. The following statement, "It is thus important for the state to foster policies that motivate students living in working-class neighborhoods to. see the university as a valid option for their personal advancement." (lines 467-469) is not supported by the results. The authors do not provide results that explicitly identify "working-class neighborhoods".
We have rewritten this sentence to explain what we understand by “working-class neighborhood” in Chile, as follows:
“…living in working-class neighborhoods, understood as communities that have low social capital, no siblings studying in college, and many classmates who are employed…”
# 7. The authors should explicitly note that there study is limited in that it does not take into account unobserved student heterogeniety. The last part of the manuscript mentions directions for future research, which I think should include examining the effect of unobserved student heterogeneity on the outcome.
We have added a new sentence in the Conclusions to highlight this important issue:
“This study is limited in that it does not consider unobserved heterogeneity—that is, some nonrandom factors specific to the individuals that are not measurable or observable, such as students’ innate learning ability.”
# 8. Some editing is needed. For example, in the following statement, "Students who graduated are represented as a dummy variable, “rural” if the students graduated from a rural college or “urban” if they graduated from an “urban college.” (lines 151-152). I think the authors meant "graduated from a . . . high school".
We have replaced “college” with “high school” in these lines.
References:
Anselin, L. Spatial Externalities, Spatial Multipliers, and Spatial Econometrics. Int. Reg. Sci. Rev. 2003, 26, 153–166, doi:10.1177/0160017602250972
Furstenberg, F.F.; Hughes, M.E. Social Capital and Successful Development among At-Risk Youth. J. Marriage Fam. 1995, 57, 580–592, doi:10.2307/353914.
LeSage, J.P. What Regional Scientists Need to Know about Spatial Econometrics. Rev. Reg. Stud. 2014, 44, 13–32, doi:10.52324/001c.8081.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
I am fully satisfy with improvemnts made by authors. Its really huge progress since last version.
Reviewer 2 Report
The authors addressed all of my concerns and suggestions. The revised manuscript is a major improvement over the original manuscript. Well done!
