Availability of a richer set of information in panel data allows us to consider a
more realistic characterization of the inefficiencies. Pitt and Lee (1981) were
first to propose the ML estimation of Normal-Half Normal SF model and
Kumbhakar (1990) was the first to propose the ML estimation of a time-varying
SF Model. Greene (2005a) approached this issue through a time-varying SF
Normal-Half Normal model with unit-specific intercepts. As pointed out by
Greene (2005b), neither formulation is a priori completely satisfactory nor
should the choice be driven by the features of the data at hand. According to
Atella et al. (1998), as far as panel data analysis is concerned, the social Stata
xtfrontier command allows the estimation of a Normal-Truncated Normal model
with time-invariant inefficiency (Battese and Coelli 1988) and a time-varying version, named as ―time decay" model, proposed by Battese and Coelli (1992). The literature on panel data estimation of frontier models also addresses the
fundamental question of how and whether inefficiency varies over time, and
how econometric models can be made to accommodate the theoretical
propositions. Panel data estimator programmed in STATA 11 using Xtfrontier
166 5.5. THE SELECTED MODEL
Given the nature of the data, I expect individual district-specific heterogeneity to
exist within the model. Districts are likely to vary systematically in terms of
infrastructure, production efficiencies, and institutional factors and so on. As
mentioned earlier, in order to capture the cross-sectional parameter of
heterogeneity, two types of models are generally proposed in the literature. The
random effect model treats the district-specific variables as time-invariant
random variables, which are independent of the explanatory variables of the
model. The fixed effects model (the within, or least squares dummy variable
estimator), on the other hand, allows individual effects to be correlated with the
regressors. The choice of the model can be based solely upon a priori
assumption. Vignoles et al. (2010), suggest that different approaches are
appropriate in different contexts, and suggest that the fixed effects approach
will be preferable in scenarios where the primary interest is in policy relevant
inference. Perhaps the most frequent suggestion is to rely on the Hausman
test, which is designed to assess whether there is a significant difference
between the estimates of the two models (p. 29).
In this study estimations have been carried out using fixed effects (within)
regression procedure as given in the STATA statistical package. I conducted
the Hausman test in STATA to determine whether fixed effects or random
effects should be used to estimate the model, for primary, middle and
secondary level education. As the x2 test statistic was 147 for primary, 39 for middle and 15 for secondary education level models and the Prob>chi2 were
less than 0.05 (i.e. Significant) (for primary, middle and secondary education)
167
significance level, implying that random effects method would yield inconsistent
estimates. This justified the use of the fixed effects model and seems more
realistic as it cannot be assumed that all unobserved fixed effects are
uncorrelated with the regressors in the data set.
The second issue in the estimation was of heteroscedasticity.
Heteroscedasticity arises as a consequence of differences in the conditional
variance of the dependent variable for given distinct levels of an independent
variable or variables. In aggregate, as well as in micro data, the possibility
exists that these conditional distributions do not share the same variance due
to heterogeneity in the unit of analysis. After fitting the model, two test statistics: BP test and White‘s general test. Breusch-Pagan / Cook-Weisberg test were calculatet the null hypothesis that the error variances are all equal versus the
alternative that the error variances are a multiplicative function of one or more variables. White‘s general test is a special case of the Breusch-Pagan test, where the assumption of normally distributed errors has been relaxed. The
Breusch-Pagan test indicates the presence of heteroscedasticity (estimated
chi-squared value > critical value). A large chi-square would indicate that
heteroscedasticity was present. In our model, the chi-square value was large,
indicating heteroscedasticity was a problem ( Appendix 7-A). Taking logs of
dependent and explanatory variables have reduced the problem. Castilla
(2008) argues that there is a lack of evidence as to whether standard tests for
heteroscedasticity can be applied to panel data models; the White and
Breusch-Pagan tests are widely used to detect heteroscedasticity in cross-
sectional data, though their feasibility and performance of fixed-effects models
168 5.6. ESTIMATING EFFICIENCY
For the purposes of clarity, this efficiency has been analyzed at three levels:
First, internal efficiency of the existing portfolio with baseline year 2005-06 has
been calculated in terms of wastage; Second, management comparison of
public and private sector schools were carried out. Finally in chapter seven,
variations in the relative technical efficiency in providing school education have
been analyzed for which econometric techniques have been used.
In Sindh, student-teacher ratios show considerable inefficiency because low
student - teacher ratios imply that more teachers are used to service relatively
few students. To add to this dimension of inefficiency, Sindh is witnessing
another trend of increasing number of schools across all the districts leading to
a low student to school ratio, further skewing the system toward a compounded
case of wastage. Despite decades of research on public – private management debate, there still exists uncertainty regarding the extent to which public and
private management differ, and which factors play a role in such differences. A
survey was carried out to compare the public and the private management
pattern. Results suggest that a mixed phenomenon in both public and private
sector schools was found regarding management practices. In the literature
review, we find conflicting results in assessment of the production function and
cost efficiency. As a consequence, conflicting advices have been given to
policy makers by economists. Hence, following aims and objective of this
research paper will try to answer some of the issues which have plagued
education in Sindh.
To estimate the technical efficiency of the districts of Sindh in providing primary, middle and secondary education.
169
To analyze the factors those explain variations in the relative technical efficiency or inefficiency in providing school education at the provincial level in Sindh.
To examine the structural issues and institutional weaknesses which hamper improvements in education in Sindh.