Policies guiding the education sector evolved since independence with over six commissions and committees established to review or develop education policies that will lead to developing self-expression, discipline and self-reliance in an all-round educational experience for learners. The latest commission was tasked to review the 8-4-4-education system and proposed the 2-6-6-3 education framework that was rolled out in 2017/8 with much emphasis on the level of education [9] - [21].

Across the years, the policies developed were geared towards achieving the Educational for All (EFA) and Universal Primary Education (UPE) framework which targets a 100 percent gross enrolment rate. In 2003, the country implemented the Free Primary Education (FPE) in line with the EFA and UPE fast track Millennium Development Goals (MDG) number 2 and Sustainable Development Goals (SDGs) number 4 on “ensuring inclusive and equitable quality education and promote lifelong learning opportunities” as well as facilitate achievement of 100 percent (UPE) for school-going age.

Various studies showed that very little had been done to establish the impact of government expenditure on other school performance indicators especially the quality of education despite increased enrolment with FPE and increasing government allocation to education as presented in Figure 1 education [22] [23] [24] [25].

Government financing towards the education system started in the 1970s through the Harambee education programme for standard one to four. This was followed by the cost-sharing Structural Adjustment Programme (SAPs) period in the 1980s. The SAP financing framework increased household’s contribution to an average of 35 percent of the total education costs in school costs in public schools. This led to low enrolment, high dropouts, grade repetition, low completion, and poor transition rates, hence inefficiencies in resource utilization. The FPE implementation in 2003 sought to address the cost-sharing/SAP effects though with more concerns over the quality of education. During the time, the budget allocation increased from 6.2 percent of the proportion of the Gross Domestic Product (GDP) in 2002/03 to 7.4 percent in 2005/06. It, however, dropped to 5.3 percent in 2014/15 and further to 5.24 in 2017/18. As a result, Gross Enrolment Rate rose to 104 percent in 2003 from 92 percent in 2002 and further rose to 105.3 percent in 2017. As a consequence, pupil-teacher and pupil-class ratios increased from 36:1 and 42:1 to 45:1 and 57:1 between 2002/03 and 2012/03 and further 42:1 and 55:1 in 2017, respectively. Despite the increased expenditure on the education sector by the government, the changes in levels of enrolment were not in tandem with the trends of increased government expenditures, further, these in enrolment further compromised the education quality and schools’ levels of technical efficiency were compromised [16] [17] [18] [19] [22] [23] [26] [27]. The government allocation to the education sector is presented in Figure 1.

From Figure 1, with the introduction of FPE in 2002/3, the Ministry of

Education allocation to primary education increased by 275.22 percent in 2002/3 reducing by 144.37 percent in 2003/4 and low of 19.55 percent in 2004/5 respectively, though the trend had irregular budgetary allocations until 2014/5 [22] [26] [27].

Policies developed by various commissions and committees emphasized highlighted the need for enhanced performance in Kenya’s primary schools related to quality of education [12] - [21]. However, there were various notables limitations related to school performance that had been identified from previous studies that evaluated primary education performance based on overall school enrolment and KCPE results rather than overall quality of education [5] [20] [27] [28].

Measurement of education quality was for a long time pegged on KCPE examinations scores in line with various policies [12] - [21]. An analysis of KCPE scores and the relationship to growth in candidature had marginal changes when compared to changes in budgetary allocation to primary education as compared in Figure 1 and Figure 2.

Further, the effect of enrolment of pupil-class and pupil-class ratio are presented in Figure 3.

The effect of increased enrolment on pupil-teacher and pupil-class ratio presented in Figure 3 created an environment where teachers were constrained to deliver the curriculum on a result basis [27] [29] [30]. Other than KCPE measurement of quality of education, two independent assessments that included; the Monitoring Learning Achievement in Lower Primary (MALP) which carried out assessment in class 2 and South African Consortium for Monitoring Education

Quality (SACMEQ) to assess class 6 pupils were undertaken respectively were also used to evaluate education quality. SACMQE mean scores from three assessments are presented in Table 1.

The class 6 SACMEQ scores shown in Table 1 supported by Klee’s [31] and Musyoka [32] who argued that in a controlled environment where education variables are equally comparable to all students, pupils perform in every bit as well irrespective of school location and related households differences. Further, variation in scores was attributed to the fact that urban public primary schools have a much more advantaged student body and work on the contusive environment which has had more learning opportunities from birth. The truth in this assertion has not been established and thus remain a critical hypothesis for empirical justification this study.

Despite government’s determination to achieve Universal Primary Education through overall financing under FPE, the performance measure of the quality of education by KCPE scores has been biased resulting from targeted teaching and examination malpractices in most schools which did not clearly explain the impact of FPE financing and quality of education. This was despite high enrolment, high pupil-class, and pupil-teacher ratio [27] [29].

The randomly sampled class six scores from the SACMEQ evaluation process under UNESCO [33] were collected from unbiased environment and thus used as the key measure of pupil acquisition and level of education quality; a factor not instituted in KCPE results.

Secondary data collected from the United Nations Education, Scientific and Cultural Organization (UNESCO) [33] —the Southern and Eastern Africa Consortium for Monitoring Educational Quality (SACMEQ) I, II and III for the

Source: SACMEQ, 1997, 2004, 2007.

years 2000, 2004 and 2012. SACMEQ IV data have not been released for use hence once published will be applied in enhanced research. Data on government expenditure was collected from Statistical Abstracts for the year 1996/7 to 2014/15 using a school-based cross-section survey covering the 8 regions were also used in this study. The data sampled included variables explaining pupil characteristics, teacher characteristics and school-based characteristics as well as teacher and household characteristics. The relevant variables specific to the study were extracted from the data set, coded and applied in analysis using STATA statistical package.

The adoption of human capital theory in education takes an altruistic set up where parents care about the present educational consumption and current leisure of their children [51] [52]. The number of children in a household attending school is taken as given thus, to allow for simplicity of exposition it’s normalized to 1 [53].

The model assumes that children spent part of their time in leisure h l which is flexible and therefore treats them as a continuous choice variable thus taking the form:

H = h ( h l ; h s ) where ∂ H ∂ h l < 0 (4)

In a school setting, this is a utility from the production function defined over the current consumption by children enrolled in schools, the current leisure enjoyed by children and levels of human capital achieved. When related to household contribution in its acquisition, the current household consumption c 1 is given by:

c 1 s = y + w h l − q (5)

where

y is the expenditures on education.

h l are the hours of leisure.

w is the cost of hours of leisure assumed as wage.

q is the direct cost of education.

Relating Equations (3) and (4), the quality of education achieved is equated to the sums of human capital accumulation defined by the knowledge acquired by learners enrolled in a given school and expressed as:

c 2 s = K + H (6)

where

K is the exogenous endowment of human capital.

H is defined in Equation (3).

Therefore, school environment facilitates human skill acquisition such as the provision of playing field also attach value to leisure enjoyed by learners enrolled in a given school expressed as:

L = 1 − h s − h l (7)

where L and time are normalized to 1.

The parents’ choice for learner enrolment of h l (in a situation where children are in school) is given as:

max [ μ s * ( h l ) , μ l * ( h l ) ] (8)

where

u s * = max h l u ( y + w h l − q , K + H ( h l ; h s ) , 1 − h s − h l ; M ) (9)

The expression in equation 8 shows that at this point μ is regarded as the amount of human capital acquired expressed in terms of test scores. Therefore the scores acquired are expressed as:

S c o r e s l * = max s c o r e s h l ( y + w h l − K , 1 − h l ; M ) (10)

where M represent characteristics related to the quality of education acquired. Teacher education and experience and school characteristics among others.

Following Taylor et al. [54] and Kings et al. [55] , student achievement is a function of endogenous school inputs (family background, school characteristics, physical characteristics, and school enrolment) and a function of exogenous educational environment.

From Equation (9), and adopting Taylor et al. [54] , Kings et al. [55] and Hanushek [51] , this study relates the models to Todd and Wolpin (2003) and Rugiero [53] model where the human capital function is determined by score acquired expressed as:

S c o r e s l * = max s c o r e s h l ( y + w h l − K , 1 − h l ; M ) (11)

The framework presented in Equation (10) adopts various variables such as pupil characteristics, school characteristics and government expenditure as independent variables determining score levels to have:

S c o r e i j t = c + ∑ k = 1 N x α k x k + β 1 z j t + β 2 Y j t + X j t + ∑ t = 1997 , 2004 , 2007 D t + ε i j t (12)

where

i , j , t are indices for total pupil i, enrolled in school j at time t.

N x is the number of schools that explained as the control variable x.

X t is the school observable school characteristics.

z j t is the Pupil and Teacher related characteristics.

Y j t is the government expenditure.

D t are dummies for 2000, 2004 and 2012.

Equation (11) is improved to include the stock of human capital expressed as aggregated school scores (score = S) in arithmetic and reading for different schools located in different regions. The schools have specific variables that determine the various scores estimating the model as:

S j t k = α + X j t d γ + X j t s μ   + ∈ j t k : t = 1 , 2 , 3 , k = 1 , 2 (13)

where

S j t k = the average score on the class six SACMEQ test on arithmetic and comprehension, k for school j in year t.

X j t d = specific observable variables for school i in year t that include the number of classes, number of toilets, availability of playfield, number of textbooks, school possession index, location of the school and class types.

X j t s = school-specific variables for school j in year t:

γ and μ are vectors of parameters to be estimated, α is the intercept and ∈ is an iid disturbance term.

The framework by Coates, Hamish, and Rothman [56] , Ferguson and Ladd [57] and Ladd, Roselius, and Walsh [58] were used to develop the model relationship between the expected school performance and various characteristics presented as:

S j t k = α + X j t d γ + X j t s μ + Z j t β + ( Z j t * X j t ) δ + ( E j t * X j t ) ϕ   + ∈ j t k . (14)

Equation (14) ensured ad-hoc variable inclusion and understanding thus the relationship between government expenditure and quality of education. The study adopts a log-linear model given that all observations are positive (McGraw, 1995) presented in Equation (14) written as:

ln S j t k = α + d ln X j t γ + s ln X j t μ + ln Z j t β + ln ( Z j t * X j t ) δ                       + ln ( E j t * X j t ) ϕ   + ∈ j t k (15)

where

Z i ( t ) , t = a vector of observable variables including pupil and teacher characteristics that include pupil-teacher ratio, pupil-class ratio, pupil–book ratio, pupil-toilet ratio, teacher experience, and teacher absenteeism, presented as:

X j t = ( X j t d , X j t s ) (16)

Which explains variables defined in Equations (14)-(16).

With the adoption of the model explained in Equation (15), the equation assumed that the parameter vector β is closely related to scores with a positive sign and the vector parameter δ and φ captures interaction effects during analysis.

Estimation of cross-section panel data outlining the effect of government expenditure on quality expenditure is presented in Table A1.

The study used datasets for the years 2000, 2004 and 2012. These data sets were not as recent but were the current data that had been undertaken in the country. The SACMEQ IV, 2018 had not been released during the time of this study; hence provides a critical area of further studies when the data set has been released.

In addition, Model specification tests were carried out, though several limitations that included potential selection bias, potential endogeneity, and potential unobserved heterogeneity were experienced and corrected using Olsen (1980)—Ordinary Least Squares (OLS) and Terza, Basu and Rathmouz [59] Two-Stage Residual-Inclusion (TSRI) method. In addition, data, robustness was tested using pedagogical cohorts or a sample that would be more motivated for over or underestimation of the effort to use the data. Further, panel data estimation took-in-to consideration heterogeneity of individual cross-section units occasioned by allowing for individual specific fixed effects that gave more variability and degrees of freedom.

The study sampled 174,173 and 181 schools for the years 2000, 2004 and 2012 with means and standard deviations presented in Table A2 while the mean government expenditure per region was presented in Table A3. The school performance measure for quality of education was determined by the test scores achieved in arithmetic and reading analysed from the SACMEQ reports presented in Table A4. The various school locations, school distance from social amenities, school characteristics, class types, and teacher numbers are presented in Tables A5-A10 respectively.

The analysis used Haussmann tests to verify the use of Fixed Effects (FE) or Random Effects (RE) that helped undertake the regression analysis on the effect of government expenditure on quality of education given school characteristics presented in Table 3.

The Haussmann test on the xtreg fixed and random effect models (see Table A10 and Table A11), Prob > chi2 = 0.045 and chi2 (16) = (b-B)'[(V_b-V_B) ^ (−1)] (b-B) = 2.14e−20 was achieved. Given that 0.045 < 0.05, then, the unique errors (ui) were uncorrelated with the regressors, and therefore the null hypothesis was rejected, thus, the regression analysis adopted fixed-effect analysis for objectives one and two (Greene, 2010; Williams, 2015).

The regression analysis using the fixed-effect model is presented in Figure 3.

The coefficients for pupil-book ratio, pupil-toilet ratio were related to Hanushek [51] and Greenwald, Hedges and Laine [60] who concluded that estimates on school performance had no significant effect when teacher/student ratio, teacher education, experience, and salary and government expenditure per student on the final test scores were correlated. In this case, the evaluations were conditioned and had a high probability of bias. Further, coefficients for availability of playfield and quality of education in the selected schools agreed with

***p < 0.01, **p < 0.05, *p < 0.1; Standard errors in parentheses. Source: Authors computation based on SACMEQ survey data.

Carnoy, Ngware and Oketch (2015) who noted that schools resources and school characteristics majorly contributed to student learning as evidenced in 2000 before the introduction of FPE [61] [62].

The analysis on the relationship between class type and quality of education was addressed by Rowe (1988) who affirmed that regardless of class type, temporary and permanent classes were statistically significant with quality of education. In addition, school location relationship with quality of education was supported by Alokan [63] and Coniine and Zappala (2002) who noted that no school set of infrastructure can claim superior performance, though various studies reported the opposite (see also Yodeled, 1988 and Ocoee and yare, 2010).

The enrolment shock in 2004 marginally affected relationship between school possession and quality of education given the various school characteristics, a fact that agreed with Tow (2006) who found that effects of school funding affect student academic achievement though the assertion would be supported by other variables such as school and teacher characteristics [64] [65].

To establish the effect of government expenditure on the quality of education in relation to teacher characteristics, coefficients for government expenditure and quality of education controlled for teacher experience were negative and statistically significant for both arithmetic and reading scores in the three-time period respectively in Table 4.

The coefficients for government expenditure and quality of education controlled for teacher experience, pupil-teacher ratio and teacher number is given both arithmetic and reading scores in the three-time period respectively agreed with Viscusi and Gayer [66] and Tullock [67] who noted that teacher numbers could have had significant relationship with student achievement especially in arithmetic. The relationship was limited to the environment with which class-pupil and pupil-teacher ratios were managed.

Further, coefficients for teacher experience and quality of education were closely related given government expenditure and arithmetic and reading scores were related to Glewwe and Kremer [68] and Clotfelter et al. [69] who found that inexperienced teachers were less effective with little knowledge on the level of effectiveness undertaken in different types of preparation [70] [71].

School performance is depended on various variables that are related to changes in government expenditure. The degree of relationship between various variables determining quality of education with variated government expenditure has been carried out from pupils’ achievement and aggregated school achievement. These results had been subjected to a significance test at each level of correlation [72].

There exist high statistical significance and correlation levels between variables in the study and school performance especially in arithmetic and reading across the three-time periods. There was a positive relationship between book-pupil ratio, class-pupil ratio, school location within small town and large

***p < 0.01, **p < 0.05, *p < 0.1; Standard errors in parentheses. Source: authors computation based on SACMEQ survey data.

town and city, school possession and government expenditure. The relationship indicated that they were key factors for consideration in school performance levels. School distance from social amenities related to all other variables showed that they were negatively related to the quality of education. These findings were consistent with Greenwald, et al. [60] and Michaelowa and Wittmann [73] studies on effects of school resources on student achievement in Francophone sub-Saharan Africa.

Notably, teacher characteristics have a highly statistically significant relationship with quality of education at school level achievement, thus critical in school performance. Teacher experience is also crucial in determining school performance. These outcomes were also outlined in Greenwald et al. [60] and Lee, Zuve & Ross [74] while investigating school effectiveness in 14 sub-Saharan African counties and realized that with increased class size, teacher’s satisfaction is low which also affects the pupils’ performance.

The fact that government expenditure has been seen to influence quality also affects other necessary variables that may impact the quality of education. In a school setting, the government role in development of policies on education that targets to spur quality of education, school characteristics such as number of classes, number of teachers and number of toilets are outlined [12] - [21] , adopted and implemented by the various stakeholders who have identified the causal relationship between available resources and quality of education given other variables controlled for [6] [22] [23] [60] [75] [76] [77].

Although the government has for a long time measured UPE policy from access levels expressed by school enrolment, it’s clear that school performance defines more especially quality of education which can be affected by variables such as class-pupil ratio, pupil-teacher ratio, pupil-book ratio, and pupil-toilet ratios. Studies by Klees [31] , Bold, et al. [22] ; Mazar et al. [23] and Cohen & Dupas [24] noted that the existing ratios in Kenya were above the internationally recognized standards which will affect performance negatively. In regard to these, the government should develop guidelines on the nationally stipulated class-pupil ratio, pupil-teacher ratio, pupil-book ratio and pupil-toilet ratios that are adaptable in all schools as the new curriculum 2-6-3-3-3 are implemented as it will ensure the ratio that leads to enhanced school performance achieved.