This study builds on the classic education production model and examines the respective impact of individual classic inputs on a measurable outcome of higher education in Saudi Arabia. In particular, the study specifies and estimates a model of capital embodiment where the endogenous variable is student GPA, and the exogenous variables are student background, student inputs, school inputs, peer characteristics, peripheral influences, and initial endowment. The model allows for exogenous interactions where slopes and intercepts may vary by levels of inputs. Throughout, the objective of the study is to empirically identify the fundamental inputs to the education production process that are critical for Saudi higher education. Once identified, those critical inputs could be managed with the goal of obtaining equal respective ratios of marginal products to prices. This has non-trivial implications for education policy makers and standard setters in SA during a transformation period where the 2030 vision guides almost all aspects of Saudi socioeconomic life. In this fashion, the study complements the positive education research literature in two major ways: 1) estimating an interactive specification of the classic education production model within a framework of capital embodiment of a Saudi higher education setting; 2) reporting and testing parameter estimates, and identifying critical inputs to the higher education process in Saudi Arabia at conventional significance levels.
In the light of the preceding introduction, the following research questions are formulated:
1) What is the impact of student background on student outcome performance given predetermined levels of peer characteristics, student direct inputs, school direct inputs, external influences, and initial endowment?
2) What is the impact of student direct inputs on student outcome performance given predetermined levels of background, school direct inputs, peer characteristics, external influences, and initial endowment?
3) What is the impact of peer characteristics on student outcome performance given predetermined levels of background, student direct inputs, school direct inputs, external influences, and initial endowment?
4) What is the impact of school direct inputs on student outcome performance given predetermined levels of background, student direct inputs, peer characteristics, external influences, and initial endowment?
4) What is the impact of external influences on student outcome performance given predetermined levels of background, student direct inputs, school direct inputs, peer characteristics, and initial endowment?
5) What is the impact of initial endowment on student outcome performance given predetermined levels of background, student direct inputs, school direct inputs, peer characteristics, and external influences?
In this fashion, the main objective of this study is to empirically identify the resource inputs considered critical for the Saudi higher education data generating process. Those resources inputs are important education policy variables that can be managed by standard setters and policy makers to improve the delivery and administration of Saudi higher education. The minor objective, however, is to determine the possible interactions between the four fundamental resource inputs, how the level of a particular input confounds the way a measurable education outcome would vary with other inputs respectively. Along the same lines, the importance of this study can be explained fully along the lines of the 2030 vision that stresses evidence-driven policy and efficient employment and allocation of inputs and resources. In particular, the level of student expenditure entitlement and its relationship with measurable educational outcomes are paramount for adequate and equitable higher education policy necessary for the prosperity of Saudi education sector. Furthermore, the study is significant for the better accountability of the higher education system and public universities. Without accountability, higher education providers may not have the necessary incentive mechanism to operate according to the best interest of student education outcomes. The study also critically reviews contemporary Saudi higher education system, and sheds light on the potential of private universities.
Moreover, the study relates to the research agenda of the author in a principal fashion. The author of this study descends from education and economics background respectively. In this fashion, this coauthored study complements the education economics literature where typical economic tools (e.g., efficiency and variation coefficients) are employed to explain the higher education production process in Saudi Arabia. The author of this study is also instructed by the 2030 vision and how it can be translated into higher education. This can be materialized via evidence-based policy recommendations that reflect the fundamental economic principle of efficient allocation of resources.
In view of the above, given the objectives and research questions, this study is designed after a typical positive research, which is instructed by the traditional quantitative paradigm according to the following sections: literature review, research design, and data analysis & results. The research structure follows that of a positive study that identifies significant inputs to a typical measure of higher education output where a model is specified and estimated according to the education production function framework.
2. Literature Review
The body of research studying the relationship between education and resources and outcomes follows two distinguishable, but related traditions: 1) Institutional process effectiveness, and 2) education production (Levacic & Vignoles, 2002). Process effectiveness research is chiefly concerned with the extent to which effectiveness scores of various institutional factors may explain education outcomes, and so traditional inputs to the education process are greatly assumed away (Anderietti & Su, 2018). On the other hand, education production research directly studies educational outcomes in terms of classic resource inputs where the main concern is typically resource efficiency rather than process effectiveness (Bishop & Wobmann, 2010; Gilead, 2014; Harris, 2007).
Education production models are greatly instructed by school effectiveness research (Hill & Rowe, 1996; Westrick et al., 2015). The effectiveness research is holistic and attempts to include all relevant factors contributing to student performance (Duckworth et al., 2019). In fact, investigating the impact of many factors beyond the time series of the student performance itself (e.g., the impact of high school type on student college performance) is rather scant in academic literature for most research tends to be scholastically-oriented where the objective is to explain college performance in terms of high school performance (see Collins et al., 2000; Jones & Zimmer, 2001; Marks et al., 2001; Machin & Vignoles, 2018). In this regard, this study complements the education production literature and entertains all possible factors identified in the extant literature when explaining contemporaneous college graduation GPA. The study thus follows the tradition of a literature strand where the objective is to predict terminal college performance. For instance, Westrick et al. (2015) show that standardized test scores (e.g., American College Testing (ACT) score) and high school grade point average are strong predictors of college performance. Staiculescu and Richiteanu (2018) study the phenomenon of university dropout and contend that student background has a large and significant impact on dropout in both education and training. They also document that most dropouts happen in the first year at the university. Robbins et al. (2004) identify via a meta-analysis of a large body of the extant literature that the performance of college students may be driven by a variety of factors including social influences, institutional commitment, contextual involvement, psychological forces (self perception and self assessment), academic aptitude, and financial support. Duckworth et al. (2019) argue that as opposed to standardized test scores, high school grade point average is a better predictor of successful college graduation. They explain that high school grades have significantly incremental predictive ability owing to the self discipline and self regulation features entertained by excellent high school students. Marks et al. (2001) show that students coming out at private universities tend to score significantly higher on admission tests and entrance exams as opposed to those coming out at public schools. They also report that in addition to the type of high school, the school characteristic and contextual descriptors tend to heavily contribute to the academic achievement of college students. Win and Miller (2005) specify a model that explains the performance of college students in terms background and school factors. Employing data pertaining to freshmen at the University of Western Australia, they show that students graduating from public schools tend to outperform those graduating at private schools.
3. Research Design
This study adheres to the education production research tradition and estimates a model where a measurable education outcome, namely student GPA, is specified in terms of classic resource inputs in Saudi higher education setting. The model allows for multiplicative interactions where parameter estimates and rates for change vary by state levels of inputs. Toward this end, the study contributes to the contemporary literature in two key ways: 1) estimating an interactive specification of the classic education production model within a framework of capital embodiment of a Saudi higher education setting, and 2) reporting and testing parameter estimates, and identifying critical inputs to the higher education process in Saudi Arabia at conventional significance levels. The study in this fashion complements the education production function literature since the theory of education production functions revolves around choosing relevant inputs so as to maximize a single educational output by equating input marginal products for every level of output (Jones & Zimmer, 2001).
Given the objectives and research questions is instructed by the traditional quantitative where archival data is collected via a large enough sample size as reflected by the underlying population of Saudi college graduates of 2018. Whereas the endogenous variable is continuous, the explanatory variables are all categorical. The study then estimates the regression, and analyzes and reports results according to the following subsections: 1) study sample, and 2) model specification.
3.1. Study Sample
A random sample of graduating students is collected using a random-number generator software. The population of data is available at the ministry of higher education statistics office. The size of the population of graduating students for the year 2018 is about 350,000. We employ the conventional significance level of 5%, a confidence interval error margin of 4, and assume maximum population variability of 50% in order to solve for a sample size of 599 students using Cochran’s sample size determination approach.
where z is a tabulated value, p is population variability, e is desired margin of error, and N is the population size.
The sample inclusion criterion is the combinatory output of a random number generator process that runs from 1 to 350,000. Once a random number is generated, student data pertaining to that number are recovered at the Saudi higher education statistics database. The process is then repeated iteratively until 599 data points are obtained. All data points are recovered without replacement in the sense that once a data point is identified, it is immediately dropped before the iteration continues to identify the remainder of points.
3.2. Model Specification
The study specifies the following functional form:
According to the generalized least squares specification:
where education outcome is student GPA, background is student type of high school (i.e., public or private), student is student type of average major-specific study time, peer is student type of learning environment (i.e., female or male), school is student type of school-oriented student-teacher ratio, external is student type of parental education, endowment is student type of school-oriented extracurricular activities, and e is a well-behaved error term with convenient piece-wise statistical properties. Toward this end, traditional assumptions of school utility functions that abstract away from possible endogeneity, social values, and students with special needs are maintained.
4. Data Analysis & Results
The following Table1 summarizes the results of estimating this study’s parsimonious specification as per the spreadsheet output in TableA2 in the Appendix, which presents model estimation details along with the explanatory power, parameter estimates, and corresponding p-values:
All regression coefficients (i.e., parameter estimates) in the preceding table are interpreted in the sense that the derivatives of exogenous variables with respect to the endogenous variable of higher student education outcome would show the extent to which a response group would deviate from an underlying reference group as defined by the respective dummy variables.
The endogenous variable of student education outcome is measured in terms of degree grade point average (GPA), which assumes the behavior of a continuous random variable with values ranging from 1 to 4 where 1 is 65%, and 4 is 100%. The eight exogenous variables in the study are measured using dummy variables with two categories 0 and 1. The first exogenous variable ‘background’ defines student’s educational background and prior experience, and is measured in terms of whether the student graduated at a private high school (i.e., the type of high school). The second exogenous variable “student” defines the student’s direct contribution toward the outcome performance, and is measured in terms of whether the normal weekly study time per major is above average (the national survey of student engagement). (Majors: engineering, medicine & biological sciences, physical sciences, social sciences & arts, business, and education).
Table 1. Summary of empirical findings.
The third exogenous variable “school” sums up the set of school educational inputs and resources, and is measured in terms whether the school’s student-teacher ratio is below average. The fourth exogenous variable “peer” entertains the characteristics of student’s peers and the immediate surrounding environment, and is measured in terms of gender. This is relevant for the Saudi setting since public higher education in Saudi Arabia is not coed. The fifth exogenous variable “peripheral” exhausts all the external (non-school) factors and influences that contribute to student’s educational performance, and is measured in terms of whether the parental education level is above average. The sixth exogenous variable “endowment” defines the indirect and support inputs of the school, and is measured via the overall financial health of the school in terms of whether the endowment per student is above average.
Since all exogenous variables are dummies, the model is estimated piecewise linearly under the umbrella of generalized least squares (GLS) where the objective is to produce efficient and unbiased estimates of the magnitude of group variation with respect to the endogenous variable of graduating student GPA.
The intercept of 2.55 is statistically significant at all levels and is interpreted as the average student performance had all explanatory variables been dropped out. This intercept is indeed very close to the 2.58 sample mean of the exogenous variable (shown in TableA1, which presents descriptive statistics in the Appendix). This analytically allows for interpreting the regression coefficients as parameter estimates of group variation with the intercept as a base.
Student background matter significantly for terminal academic performance at all conventional significance levels, and students coming out of public high schools tend to score a GPA of 0.31 points lower than that scored by students coming out of private high schools. The student direct input toward the terminal performance is correlated positively with GPA where students belonging to higher study time tend to score a GPA of 0.07 points higher than that scored by students belonging to the lower study time group. This variable, however, is not statistically significant at conventional levels owing to the fact that the size of the coefficient is not large enough when compared to the standard error of 0.0655. The surrounding environment variable matters significantly for academic performance in Saudi Arabian higher education. Toward this end, female Saudi graduates tend on average to score a GPA of about 0.833 points higher than that scored by their male counterparts. The school input variable measured by average student-teacher ratio matters significantly for graduation GPA in this study with students coming out of lower student-teacher universities scoring on average a GPA of about 0.29 points higher than that scored by students affiliated with higher student-teacher ratio universities. External influences as measured by parental education level correlates significantly positively with student terminal academic achievement with students representing the group of lower parental education scoring on average a GPA of 0.54 points lower than that scored by students representing the group of higher parental education. The variable of school endowment and the contribution of extracurricular activities correlate significantly positively with collegiate academic achievement in Saudi Arabian higher education with students graduating at lower student endowment universities scoring on average a GPA of 0.24 points lower than that scored by students graduating at higher student endowment universities.
For the interactive term that measures peripheral characteristics given background, Students belonging to the group of high parental education type with a private high school background tend to score a GPA of 0.11 higher on average than that scored by other groups. The variable, however, is not statistically significant and is not far away from zero because of a rather large standard error of 0.10 relatives to the size of the parameter estimate.
For the interactive term that measures study time given peer characteristics, male students belonging to the lower study time group tend to score on average a GPA of about 0.38 points lower than that scored by other groups.
The results of this study indicate that the fundamental educational process inputs of student background, peer characteristics (and the surrounding educational setting), direct school inputs, peripheral influences (e.g., parental educational attainment), and indirect school inputs (e.g., extracurricular activities) are empirically critical for Saudi higher education. In line with conventional wisdom and prior documented empirical evidence (see, e.g., Andrietti & Su, 2018), the impact of student direct inputs measured in terms of the normal major-specific study hours significantly depend of the type of peer characteristics (i.e., peer characterstics and the surrounding educational seem to significantly structurally shift the impact of student direct inputs on terminal performance). Furthermore, in line with extant empirical evidence (see, e.g., Ahn et al., 2012; Bishop & Wobmann, 2010) and the widespread belief in Saudi Arabia, external influences measured in terms of parental educational level seem to alter the direction of the impact of student background on ultimate outcome performance. However, this alteration is not significant in magnitude and the impact of student background on terminal performance given the type of parental educational level is not far away from zero. In this fashion and for education policy making and standard setting purposes, the empirically identified critical inputs of background, peer influences, school direct inputs, external influences, and school indirect inputs could be managed with the goal of obtaining equal respective ratios of marginal products to prices. This has non-trivial implications for Saudi Arabia during a transformation period where the 2030 vision instructs all aspects to underlying socioeconomic life. However, a point in order, it’s chiefly important to qualify the outcomes of this study by variable measurements and the piecewise econometric specification. Though this study is in unison with empirical identification of fundamental educational inputs, the set of viable measures are so large that econometric misspecification due to omitted variable bias is always a possibility. In this regard, future research may entertain alternative measures of the same identified constructs or employ a meta-analysis of all relevant factors identified in the extant literature.
In view of the preceding discussion and conclusion, this study has two main limitations, the first limitation is due to possible error in measurement and how the study variable is measured. Though we closely followed the extant empirical literature in this regard, there are vast possible measures for the same abstract variable. Here, future research may replicate the study while using different measures. The source of the second limitation, however, is the linear model specification whereas typical education production function models are intrinsically non-linear since rates for change typically depend on the status quo. In this regard, we chose a simpler specification in order to accommodate meaningful interpretations of parameter estimates particularly when dummy variables are extensively involved.
This study is funded by the deanship of research at the Islamic University of Madinah.
Table A1. Descriptive statistics.
Table A2. Model estimation.