50 CHAPTER 3
Empirical Framework and Data School Fees
To assess the effects of historical and spatial factors on school quality, we estimate the following equation in which the log of school fee represents school quality:
ln pjkt = α + x′kt–sβ1 + z′jkβ2 + εjkt, (3.1)
where ln pjkt is the log of the school fee at school j in location (subplace) k at year t; xkt–s is location factors such as local population composition and eco- nomic conditions at s years prior to t; zjk is historical factors at school j, such as the former department; and εjkt is an error term. Officially, a subplace is defined as the smallest geographic unit available from the census, by which
we can identify the location as well as its characteristics. The novel feature of this approach is that location factors are discovered from merging school data and geographic database by GIS.10
The data come from two different sources. Local characteristics are taken from the Census 2001 Community Profile Database (Statistics South Africa). This database provides distributions of socioeconomic characteristics in the 2001 census at the subplace level for the whole country. It covers, for example, education, labor force, migration, settlement types, and popula- tion group compositions.
GIS data available in school censuses can help identify in which subplace a school is located.11 The school identification codes, EMIS, enable us to merge the Census 2001 subplace data and school censuses. School fees in 2001 are captured in the Annual School Survey 2002 (National Department of Educa- tion). The information on former education departments is available in the SRN 2000 (National Department of Education).
School Quality
To answer the question of how the government can improve school quality and support the poor with spatially targeted interventions, we estimate the following school production functions:
∆yjk = γ0 + γ1 ln pjkt + γ2 ln gjkt + z′jkζ + ∆ξj (3.2) 10 In the estimation, spatial dependence is not explicitly identified in the error term, beyond
allowing clustered correlations within each subplace (robust standard errors). 11 Using the same datasets, Yamauchi and Nishiyama (2005) analyze the effect of local income distribution within a subplace on the determination of school fees in public schools therein.
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