Journal articles on the topic 'OLS-evaluation of parameters'

The temporal nighttime light (NTL) data generated by DMSP-OLS sensors was discovered to have large gaps (missing values) over time. The research aims to provide a scientifically valid gap-filling mechanism for having consistent DMPS-OLS time series data (1992-2013) and predicting the historic NTL (1991-1985) for long-term studies. A deep learning neural network, Long Short Term Memory (LSTM) has been proposed in the study for temporal gap filling and historic NTL prediction. The developed LSTM model is being tested in a time distributed wrapper way having window size (3-7) for the temporal gap filling and prediction of the historic NTL. According to the accuracy evaluation, the developed model has a testing accuracy of R2 = 0.96 with a window size of 5. The historic population, Gross Domestic Product (GDP), and Electric Power Consumption per capita (EPC) data are utilized to validate the gap-filled and historic NTL. R2 = 0.91 w.r.t population, R2 = 0.71 w.r.t GDP, and R2 = 0.69 w.r.t EPC, is been found during the assessment of these parameters with the sum of light of the year (1985-2013). The historic & gap-filled NTL data can be used in various studies to monitor temporal development.

A computational method for the automated formation of a typical form of a digital image of the investigated objects on a series of digital frames has been developed. Due to the imperfection of the mounting of digital cameras, as well as their automated mounts, their immobility at shooting during exposure time can be disturbed, which leads to the formation of "blurred" images of objects of various forms. Due to such inaccuracies in the tracking of objects on digital frames, even in one series, the typical form of the image of objects can vary from frame to frame. This fact of the difference in the standard form significantly complicates the execution of various image processing tasks. In order to simplify the evaluation of the image parameters of objects in a series of digital frames, it has been proposed to use a typical image on a digital frame corresponding to the average image of objects as a model of object images. In this case, the appearance of the image of the object, its form, the distribution of brightness in the image will be determined only by the typical image. This paper proposes a computational method for the automated formation and evaluation of the typical form of the image of an object in a digital frame based on the initial data – the actual given digital frame. This computational method is based on the selection of single images of objects and the formation of their rectangular area. Next, the offset is evaluated, and the selected single images of objects are normalized to calculate the typical form of the object image. Using the method makes it possible to highlight objects against the background of noise and reduce the number of false detections. It is recommended to apply the method only in the case when the frames have defects and "blurs" during the shooting, otherwise there will be unreasonable additional computational costs. The developed computational method was successfully tested in practice within the framework of the CoLiTec project and implemented in the intraframe processing unit of the Lemur software.

The paper explores of the price-supply flexibility of the Czech commodity market for food quality wheat in the period 1995–2011. For this analysis, inversion definition of the supply function was applied. The model of the inverse supply function in the Czech wheat market was based on the double log-linear construction. The parameters of the given supply model were estimated using OLS-HAC method. The developed regression model of the supply function was statistically tested. Ordinary and dynamic price flexibility of the wheat supply on the Czech commodity market was determined in relation to the parameters of the developed econometric model. In accordance with the estimations, the ordinary price-supply flexibility achieved +0.3492% and the dynamic price-supply flexibility of the first order was –0.2210%. Within the interpretation of both estimated coefficients of the price-supply flexibility, the multi-factor nature of the commodity supply function must be respected. Moreover, it is important to distinguish the short-term and long-term period within the evaluation of the price-supply flexibility.

Nighttime light (NTL) remote sensing data have been widely used to derive socioeconomic indicators at the national and regional scales to study regional economic development. However, most previous studies only chose a single measurement indicator (such as GDP) and adopted simple regression methods to investigate the economic development of a certain area based on DMSP-OLS or NPP-VIIRS stable NTL data. The status quo shows the problems of using a single evaluation index—it has a low evaluation precision. The LJ1-01 satellite is the first dedicated NTL remote sensing satellite in the world, launched in July 2018. The data provided by LJ1-01 have a higher spatial resolution and fewer blooming phenomena. In this paper, we compared the accuracy of the LJ1-01 data and NPP-VIIRS data in detecting county-level multidimensional economic development. In three provinces in China, namely, Hubei, Hunan and Jiangxi, 20 socioeconomic parameters were selected from the following five perspectives: economic conditions, people’s livelihood, social development, public resources and natural vulnerability. Then, a County-level Economic Index (CEI) was constructed to evaluate the level of multidimensional economic development, with the spatial pattern of the multidimensional economic development also identified across the study area. The present study adopted the random forest (RF) and linear regression (LR) algorithms to establish the regression model individually, and the results were evaluated by cross-validation. The results show that the RF algorithm greatly improves the accuracy of the model compared with the LR algorithm, and thus is suitable for the study of NTL data. In addition, a better determinate coefficient (R2) based on the LJ1-01 data (0.8168) was obtained than that from the NPP-VIIRS data (0.7245) in the RF model, which reflects that the LJ1-01 data offer better potential in the evaluation of socioeconomic parameters and can be used to identify, both accurately and efficiently, multidimensional economic development at the county level.

Introduction: The combination of chronic hemolysis and severe cardiopulmonary damage has a profound impact on prognosis and functional capabilities in patients with sickle cell disease (SCD). Voxelotor, which reduces the HbS polymerization has shown efficacy in increasing plasmatic Hb concentration (Hb). The effects of this Hb rise might be counterbalanced by its higher affinity for O2, potentially reducing its peripheral delivery. There are currently no data exploring the complex interplay between Voxelotor effects on peripheral O2 delivery, O2 binding to Hb, erythropoietin (EPO) levels, and functional resonance through exercise. The HEMOPROVE study (NCT05199766) is an open-label, single-arm, single-dose Phase II study in SCD patients treated with Voxelotor 1500 mg daily for 48 weeks. The primary endpoint of this study is to evaluate the effect of Voxelotor on reducing intravascular hemolysis parameters after 48 weeks of treatment.An interim analysis of the HEMOPROVE trial was performed to evaluate the effect of 6 months of Voxelotor on peripheral O2 extraction during exercise in SCD patients and its determinants. Final 48-week results may provide additional insight. Methods: SS or S-beta0 Thal patients were included if they were more than one month from a vaso-occlusive crisis, 3 months from a transfusion. A stable dose for at least 3 months was required for patients treated with hydroxyurea (HU) or angiotensin-converting enzyme inhibitors HU. Patients included benefited from a multi-organ evaluation at baseline (M0), after 6 (M6) and 12 months of treatment. For the present analysis, only patients who underwent a comprehensive cardiopulmonary stress evaluation at M0 and M6 were analyzed - involving a 6-minute walk test (6MWT) and a standardized incremental exercise protocol up to 4 mmol. L-1 blood lactate level (BL4), with concomitant gas exchange and echocardiography measurements. Peripheral O2 extraction at BL4 was directly measured using arterio-veinous difference D(A-V) O2 (= VO2 [mL/min] / cardiac output (L/min) at BL4). In addition to standard clinical and biological parameters, plasma level of EPO was measured and P50 was obtained from oxygen dissociation curve performed on a Hemox analyzer (TCS Scientific). Wilcoxon test was used to compare M0 and M6 parameters. Using BL4 - D(A-V) O2 relative change from M0 to M6 as an endpoint and performing multivariate linear regression analysis applying ordinary least square estimator (OLS) on (M6-M0) delta (∆) parameters, we sought to find determinants of peripheral O2 extraction evolution under Voxelotor. Results: 14 SCD patients had an incremental exercise at M0 and M6. Mean age was 44±10 years, sex ratio F/M was 0.5 and 57% were treated under HU. Hemoglobin level markedly rose under treatment by a mean increase of 2.0±1.1 g.dL-1 per patient (7.1±0.7 vs. 9.1±1.3, p<0.001). P50 decreased from 30.85 [28.92-32.75] to 22.97 Torr [21.06-24.9] (p<0.001). EPO was performed in 11 patients with a median of 107 [57-242] at M0 and 75 mU/L [47-170] at M6 (ns). Notably, EPO increased in 5/11 patients (46%), while it decreased or remained stable in 6/11 patients (54%). Patients with an increase in EPO showed a more pronounced decrease in P50 (20.88 [18.85-22.46] vs 24.58 torr [21.95-27.38], p = 0.02). Overall, lactate curves through exercise remained identical under treatment, as well as D(A-V) O2 at BL4 (71±12 vs. 67±10 O2 mL / L, p=0.3) while SpO2 considerably increased at 6 months. Multivariate OLS regression showed that the best-fitting model to explain an increase in D(A-V)O2 at BL4 between M0 and M6 of treatment with Voxelotor included a decrease in EPO, an improvement in dyspnea (Borg scale after 6MWT), and a decrease in P50 (adjusted R²=0.94). Conclusion: Oxygen delivery to tissues under Voxelotor is an important issue that is difficult to assess. In fact, the treatment increases Hb but maintains it in the oxygenated R conformation, partially reducing oxygen release. Using reference methods, we were able to gain a better understanding of this complex equilibrium. Our interim analysis after 6 months of treatment shows that tissue oxygen extraction increases in patients with a decrease in EPO and dyspnea. Paradoxically, the lower the P50 in these patients, the more beneficial the effect, probably via the increase in Hb and the rheological improvements we also studied. Further investigations are needed to confirm and refine our results.

The traditional linear regression model of mass appraisal is increasingly unable to satisfy the standard of mass appraisal with large data volumes, complex housing characteristics and high accuracy requirements. Therefore, it is essential to utilize the inherent spatial-temporal characteristics of properties to build a more effective and accurate model. In this research, we take Beijing’s core area, a typical urban center, as the study area of modeling for the first time. Thousands of real transaction data sets with a time span of 2014, 2016 and 2018 are conducted at the community level (community annual average price). Three different models, including multiple regression analysis (MRA) with ordinary least squares (OLS), geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR), are adopted for comparative analysis. The result indicates that the GTWR model, with an adjusted R2 of 0.8192, performs better in the mass appraisal modeling of real estate. The comparison of different models provides a useful benchmark for policy makers regarding the mass appraisal process of urban centers. The finding also highlights the spatial characteristics of price-related parameters in high-density residential areas, providing an efficient evaluation approach for planning, land management, taxation, insurance, finance and other related fields.

Tea (Camellia sinensis) is a major cash crop and leading foreign exchange earner, contributing to poverty alleviation by providing employment and livelihood to many stakeholders in the producing countries. Production has increased faster than consumption causing price stagnation, especially for CTC black teas. Kenya is the third-largest tea producer and Lake Victoria Basin produces over 60% of her tea. Selection of tea cultivars in Kenya has been cantered in one location before the selected clones are introduced to other growth environments. This study evaluated if tea clones maintain their yield and plain black tea quality attributes when grown at different locations within Lake Victoria Basin. The basin produces mainly plain black teas whose quality is due to levels of polyphenolic compounds, especially green leaf flavan-3-ols that are oxidized to theaflavins and thearubigins during black tea processing. The theaflavins and thearubigins contribute to the color and brightness of black teas. The trials were done in two sites Timbilil and Kipkebe using twenty clones. All the plain tea quality parameters including individual theaflavins and yields varied (p less than 0.05) with clones, demonstrating diversity in the cultivars used. The levels of the parameters and yields also changed (p less than 0.05) with the location of production. These results demonstrated that clonal tea quality and yields vary depending on the geographical location of production. There were also significant interactions effects between the clones and location of production in the quality parameters and clones showing the extent of the changes varied from clone to clone. Indeed the relative ranking of the clones varied with location. No clone retained its relative superiority ranking at the two locations. Both the Spearman correlation coefficients (rs) and the Pearson correlation coefficients (r) between the individual parameters were positive but low and insignificant, except for theaflavin-3-gallate. These results demonstrate the need for location-specific evaluation of both new and old clones to establish clonal yield and quality potentials in new locations of cultivation.

Sorbus aucuparia L. (rowan tree) is a widely distributed European plant, valued for its nutritional and medicinal qualities. The medicinal application of rowanberries, relying particularly on their antioxidant and antidiabetic effects, is closely connected with the presence of numerous phenolic compounds. However, the broad geographical occurrence of rowan trees may contribute to fluctuations in fruit composition, influencing their biological properties. This study aimed to identify the constituents most involved in this variability to facilitate effective quality control. The investigation encompassed 20 samples collected from diverse locations across Poland, evaluated in terms of the variation in composition and bioactivity. The UHPLC-PDA-ESI-MSn study identified 45 different constituents, including flavonoids, phenolic acid and flavon-3-ols. The detected compounds were quantitatively assessed by HPLC-PDA, alongside spectrophotometric evaluation of total phenolic content and the content of high-molecular-weight proanthocyanidins (TPA). Additionally, •OH scavenging capacity and α-glucosidase inhibition were included as bioactivity parameters. Chemometric analyses, including hierarchical cluster analysis and principal component analysis, revealed geographically dependent variability, with low to moderate variation observed for most factors (variation coefficients 20.44–44.97%), except for flavonoids (variation coefficients 45–76%). They also enabled the selection of seven constituents and TPA as the key markers of variability and biological activity of rowanberries. These markers could be employed for quality control of the fruits, offering a more efficient and cost-effective approach compared to full phytochemical analysis.

The influence of the wine distillation process on methanol content has been determined by quantitative analysis using gas chromatographic flame ionization (GC-FID) detection. A comparative study between direct injection of diluted wine and injection of distilled wine was performed. The distillation process does not affect methanol quantification in wines in proportions higher than 10%. While quantification performed on distilled samples gives more reliable results, a screening method for wine injection after a 1:5 water dilution could be employed. The proposed technique was found to be a compromise between the time consuming distillation process and direct wine injection. In the studied calibration range, the stability of the volatile compounds in the reference solution is concentration-dependent. The stability is higher in the less concentrated reference solution. To shorten the operation time, a stronger temperature ramp and carrier flow rate was employed. With these conditions, helium consumption and column thermal stress were increased. However, detection limits, calibration limits, and analytical method performances are not affected substantially by changing from normal to forced GC conditions. Statistical data evaluation were made using both ordinary (OLS) and bivariate least squares (BLS) calibration models. Further confirmation was obtained that limit of detection (LOD) values, calculated according to the 3σ approach, are lower than the respective Hubaux-Vos (H-V) calculation method. H-V LOD depends upon background noise, calibration parameters and the number of reference standard solutions employed in producing the calibration curve. These remarks are confirmed by both calibration models used.

<strong>Abstract:</strong> The main purpose of this study is to quantitatively explore the empirical evidence either in support of or against the existence of the Phillips curve in Ghana using a modified version of the New Keynesian Phillips curve (NKPC) model with Nigeria and US as benchmarks. With time-series data from 1971-2020, the study uses the Ordinary Least Squares (OLS) regression framework to analyse the statistical significance of the parameters of the model. Using different measures of market tightness, informed by Chow&rsquo;s structural break test, and drawing on variants of the NKPC, the study interestingly&nbsp; finds that the standard positive association between the output gap and inflation for the US and other advanced economies is not present for Ghana and Nigeria. This new discovery has important relevance for the conduct of economic policy in Ghana, Nigeria and other developing countries and warrants a careful evaluation of the application of the NKPC for developing and emerging economies. <strong>Keywords:</strong> Inflation, Money, Monetary Policy, New Keynesian Model, New Keynesian Phillips curve, Phillips curve, Phillips curve evidence,&nbsp; flattening of the Phillips Curve, Phillips curve evidence in developed and developing countries. <strong>Title:</strong> Investigating the Evidence of the Philips Curve in Ghana, Nigeria and the US:&nbsp; Does the empirical evidence support the Philips Curve in Ghana, Nigeria and the US? <strong>Author:</strong> John Adjei <strong>International Journal of Novel Research in Marketing Management and Economics</strong> <strong>ISSN 2394-7322</strong> <strong>Vol. 10, Issue 1, January 2023 - April 2023</strong> <strong>Page No: 1-16</strong> <strong>Novelty Journals</strong> <strong>Website: www.noveltyjournals.com</strong> <strong>Published Date: 03-</strong><strong> January- 2023</strong> <strong>DOI: https://doi.org/10.5281/zenodo.7501099</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.noveltyjournals.com/upload/paper/Investigating%20the%20Evidence%20of%20the%20Philips%20Curve-03012023-1.pdf</strong>

In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust regression techniques for the estimation of parameters. In this paper, we evaluate various ridge-type robust estimators in the cases where there are multicollinearity and outliers during the analysis of mixture experiments. Also, for selection of biasing parameter, we use fraction of design space plots for evaluating the effect of the ridge-type robust estimators with respect to the scaled mean squared error of prediction. The suggested graphical approach is illustrated on Hald cement data set.

The Brazilian Legal Amazon (BLA) is the largest administrative unit in Brazil. The region has undergone a series of territorial policies that have led to specific conditions of occupation of the land and particular urban environments. This plurality expresses specific physical relations with the environment and infrastructure, which require innovative methods for detecting and profiling human settlements in this region. The aim of this work is to demonstrate how angular composites of nighttime lights can be associated with specific profiles of urban infrastructure, sociodemographic parameters, and mining sites present in the BLA. We make use of sets of yearly VNP46A4 angular composites specifically associated with the narrowest ranges of observations across the year, i.e., observations right below the sensor’s pathway (near-nadir range) and observations in between the oblique range (off-nadir), to identify urban typologies that expose the presence of structures such as vertical buildings, industrial sites, and areas with different income levels. Through a non-parametric evaluation of the simple difference in radiance values ranging from 2012 to 2021, followed by an ordinary least squares regression (OLS), we find that off-nadir values are persistently higher than near-nadir values except in areas where obstructing structures and particular anisotropic characteristics are present, generally changing trends of the so-called angular effect. We advocate that relational metrics can be extracted from the angular annual composites to provide additional information on the current urban structural state. By calculating the simple difference (DIF), the relative difference (REL), and the residual values of the linear regression formula estimated for the off-nadir and near-nadir composites (RES), it is possible to differentiate urban environments by their physical aspects, such as high-mid income areas, low-income settlements with different levels of density, industrial sites, and verticalized areas. Moreover, pixels that were exclusively found in one of the angular composites could be spatially associated with phenomena such as the overglow effect for the exclusive off-nadir samples and with the wetlands of the northwest portion of the Amazon Forest for the near-nadir samples. This work deepens our current understanding of how to optimize the use of the VNP46A4 angular series for monitoring human activities in the Amazon biome and provides further directions on research possibilities concerning nighttime light angular composites.

В настоящее время разработка и оценка качества биологически активных добавок с использованием растительного сырья является перспективным направлением развития пищевой промышленности. Актуально создание компонентов питания с высокой антиоксидантной активностью. В работе представлены последовательные этапы разработки и оценки качества биологически активной добавки с веществами антиоксидантного ряда. В качестве активного компонента добавки выбран лист зеленого чая. Экспериментальным путем установлено, что лист зеленого чая является источником фенольных соединений. 1 грамм сухого зеленого чая восполняет суточную потребность во флаван-3-олах в среднем на 70,5 %. Эффективным способом экстракции катехинов из листа зеленого чая является ультразвуковая технология, которая позволяет увеличить антиоксидантную активность в 8 раз. Для защиты катехинов от деградации и для более качественного применения их в составе пищевых продуктов в работе используется метод микроинкапсулирования чайных катехинов со смесью полисахаридов (гуммиарабика и мальтодекстрина). Преимущество технологии микроинкапсулирования заключается в защитных свойствах ядра микрокапсул матрицей оболочки. Микроинкапсулирование катехинов и полисахаридов реализовано путем распылительной и лиофильной сушек. Методом сканирующей электронной микроскопии был проведен анализ качества материалов, полученных в результате высушивания суспензии. Более эффективным способом инкапсулирования оказалась лиофильная сушка по следующим индикаторам качества: эффективность микрокапсулирования, сохранность катехинов и выход добавки. Готовая микроинкапсулированная добавка представляет собой однородный, мелкодисперсный порошок светло-зеленого цвета со слабо выраженным терпким вкусом и запахом зеленого чая. Добавка прошла доклинические исследования и может быть использована для разработки функциональных пищевых продуктов. Разработанная биологически активная добавка не проявляет отрицательного воздействия на обменные процессы жизнедеятельности лабораторных животных. Development and quality evaluation of plant-based dietary supplements is currently a prospective direction in the development of the food industry. Development of highly antioxidative nutritional components is a relevant task. In this work consequent stages of development and quality evaluation of a dietary supplement with antioxidative compounds are presented. Green tea leaf was selected as the active component. It has been experimentally established that green tea is a source of phenolic components. 1 g dry green tea fills on average 70.5 % of the daily value of flavan-3-ols. An efficient method of extraction is the ultrasonic technology, which provides an eight-time increase in antioxidative activity. In order to preserve catechins from degradation and improve quality of use of those in food products, the method of encapsulating tea catechins with a mixture of polysaccharides (gum arabic and maltodextrin) was used in the research. The advantage of microencapsulation technology is preservation of the capsules’ core by the matrix of the membrane. Microencapsulation of catechins and polysaccharides was performed via spray drying and lyophilization. Analysis of the materials derived as the result of drying of the suspension was performed via scanning electron microscopy. Lyophilization was determined as the more efficient method of encapsulation, demonstrating higher levels of quality in the following quality parameters: microencapsulation effectiveness, catechins preservation and output of the supplement. The prepared microencapsulated supplement is a homogenous finely-dispersed light-green powder with a subtle astringent taste and green tea aroma. The supplement has undergone preclinical trials and can be used for development of functional food products. The developed dietary supplement does not have a negative effect on the metabolic processes of laboratory animals.

We study the impact that financial intermediation can have on productivity through the alleviation of credit constraints in occupation choice and/or an improved allocation of risk, using both static and dynamic structural models as well as reduced-form OLS and IV regressions. Our goal in this paper is to bring these two strands of the literature together. Even though, under certain assumptions, IV regressions can accurately recover the true model-generated local average treatment effect, this is quantitatively different, in order of magnitude and even sign, from other policy impact parameters (e.g., ATE and TT). We also show that laying out clearly alternative models can guide the search for instruments. On the other hand, adding more margins of decision, that is, occupation choice and intermediation jointly, or adding more periods with promised utilities as key state variables, as in optimal multiperiod contracts, can cause the misinterpretation of IV as the causal effect of interest.

Incidence ( infected leaves) and severity (number of lesions/leaf) of olive leaf spot disease caused by Spilocaea oleagina were assessed every 2 weeks on 20 trees in a Canterbury olive grove for 12 weeks during summer 2003/04 All the trees were infected by olive leaf spot disease (OLS) and although disease incidence and severity varied between trees (Plt;0001) it did not vary between branches over time (P0088) There was a strong correlation (R20869) between disease incidence and severity It was estimated that at least five trees and 50 leaves/tree were required to correctly estimate the mean values of the parameters measured Throughout the duration of the experiment no new leaf lesions formed and although old lesions increased in size (Plt;0001) spore numbers decreased from 5104 to 1102 conidia/cm2 of lesion and viability of conidia declined from 55 to 10

Decent work is considered to be crucial in the process of inclusive development and poverty alleviation in economies dominated by informal employment. This study is an attempt to understand decent work achievements of rural and urban informal workers of Hooghly district, West Bengal, India. The study uses the theoretical framework of seven work-based security dimensions from People’s Security Survey (by International Labour Organization) and constructs seven individual-level sub-indices and one composite individual-level decent work index using primary survey data. Then, it investigates the effect of the supply-side parameters on decent work using simple OLS regressions. The findings indicate ineffectiveness of education to improve decent work condition of informal workers in the absence of adequate skill-building initiatives. It also reveals the poor work condition of rural informal workers and self-employed workers in general. The study emphasises the need of vocationalisation of education and upgrading the quality of informal employment to achieve decent work.

Abstract Background The degree of plasma cell (PC) infiltration in the bone marrow (BM) is an important diagnostic and prognostic marker in multiple myeloma. An infiltration of 60% or more has been included into the new criteria of the IMWG defining myeloma. PC infiltration can vary significantly within and among individual patients regarding growth patterns (focal, diffuse or mixed), bone destruction (best visible in CT), which may or may not be concomitantly present, and levels of PC metabolism (best detected by PET). Usually, BM examinations are performed by random biopsy and aspirate from the pelvis. It is up for debate whether the PC infiltration at this location is representative for the whole BM compartment or merely represents a local picture detail of the disease. In this prospective study we evaluated PC infiltration of osteolytic lesions (OL) and random BM biopsies and aspirates (RA) at the iliac crest with local parameters whole-body imaging with PET/CT. Patients and Methods 64 transplant-eligible patients with newly diagnosed multiple myeloma (NDMM) were enrolled in this ongoing prospective study to investigate the genetic heterogeneity of malignant cells from OL in different parts of the BM compared with a RA of the pelvis. Target OLs were identified by low-dose whole-body CT scan. Sample pairs (n=64) were obtained by CT-guided biopsies of OLs as well as simultaneous RAs of the iliac crest at diagnosis and before maintenance therapy (n=19). To analyze differences between PC infiltration of the BM in RA compared to OL, we performed immunohistochemistry (IHC) on trephines of the iliac crest and on samples from OL. Whole-body 18F-FDG PET/CT was performed at diagnosis (n=53) and before initiation of maintenance therapy (n=42) assessing PET/CT characteristics like uptake patterns, number of focal lesions, maximal Standardized Uptake Value (SUVmax) of the respective lesion, SUVmax of normal BM as reference and delta SUVmax (SUVmax lesion-SUVmax reference) at diagnosis and before maintenance therapy. Results and Discussion: At baseline, samples from OLs were obtained in the pelvis (47 patients), in the spine (18) or in the extremities (4). PET/CT at diagnosis showed 3 different infiltration patterns: focal lesions in 11 patients, diffuse infiltration in 11 patients, and a mixed pattern in 31 patients. The median number of focal lesions per patient was 7 (range, 0 to &gt;20). PET/CT-detectable lesions were most frequent in patients with a mixed pattern (median, 8 OL, 14/31 patients had &gt;10 lesions). Patients with a focal pattern had a median number of 3 focal lesions; only one patient had &gt;10 OLs. Interestingly, the number of PET/CT-detectable focal lesions at diagnosis neither correlates with ISS stage of the patients nor with their response to therapy. At diagnosis, PC infiltration in OL was significantly higher in comparison to PC in random samples of the iliac crest (p=0.001). In 23 of 36 patients with a PC percentage in OL &gt;=60%, the respective PC infiltration in RA of the iliac crest was &lt;60%. The size of lesions (max. axial diameter measured in the accompanying CT scan) correlated with the extent of PC infiltration in IHC of OL (p=0.00014). However, comparing estimates of cellularity in CT and PET/CT, neither Hounsfield units (HU) nor SUV showed any correlation with PC infiltration of OL samples. In a preliminary follow-up analysis of 19 patients, neither PC infiltration, size, HU nor SUV of OL showed any significant association with the outcome seen at the time of imaging analysis. However, our analysis showed that after induction therapy and ASCT, 9 of 10 patients with remaining PET-CT-detectable, 18F-FDG avid OLs would progress within 12 months (90%, 4 patients with focal, 6 patients with mixed patterns at baseline). Conclusion Our data suggests that the routine assessment of PC infiltration in RA of the iliac crest might underestimate the degree of PC infiltration in the whole skeleton of NDMM. PC infiltration correlated significantly with the size of the lesion in CT but neither with HU nor SUVmax of OL in PET-CT. This raises the question whether the imaging techniques being used will pick up signatures of non-viable tumor, such as necrotic tissue or inflammation, instead of or in addition to malignant plasma cells. Interestingly, patients with PET-detectable, 18F-FDG avid residual lesions after therapy were at high risk of progression within 12 months. Disclosures Goldschmidt: Amgen: Consultancy, Research Funding; Bristol Myers Squibb: Consultancy, Honoraria, Research Funding; Janssen: Consultancy, Honoraria, Research Funding; Adaptive Biotechnology: Consultancy; Celgene: Consultancy, Honoraria, Research Funding; Sanofi: Consultancy, Research Funding; Novartis: Honoraria, Research Funding; Mundipharma: Research Funding; Chugai: Honoraria, Research Funding; Takeda: Consultancy, Research Funding; ArtTempi: Honoraria. Hillengass:Celgene: Consultancy, Honoraria, Other: Advisory Board, Research Funding; Sanofi: Research Funding; BMS: Honoraria, Other: Advisory Board; Novartis: Honoraria, Other: Advisory Board; Takeda: Honoraria, Other: Advisory Board; Janssen: Honoraria, Other: Advisory Board; amgen: Consultancy, Honoraria, Other: Advisory Board.

The aim of the present study was to evaluate microwave-assisted (MAE) and pressurized liquid extraction (PLE) for the recovery of polyphenols from blackcurrant and bilberry leaves and the preservation of their antioxidant activity. The extractions were carried out varying the solvent/solid (SS) ratio, temperature and time. During MAE, increasing the SS ratio increased the polyphenol concentration in the extracts from blackcurrant and bilberry leaves, while increasing the temperature had a positive effect only on bilberry polyphenols. During PLE, only a temperature increase was a determining factor for the isolation of blackcurrant leave polyphenols. Based on polyphenol recovery, optimal extraction parameters were established resulting in a yield of 62.10 and 56.06 mg/g dw in the blackcurrant and bilberry MAE extracts and 78.90 and 70.55 mg/g dw in the PLE extracts. The optimized extracts were profiled by UPLC ESI MS2, and their antioxidant capacity was evaluated through FRAP, DPPH, ABTS and ORAC assays. The characterization of the extracts by UPLC ESI MS2 confirmed flavonols as the predominant compounds in both blackcurrant and bilberry leaves, while flavan-3-ols and procyanidins were the main compounds responsible for high antioxidant capacity as confirmed by the ABTS and ORAC assays. Due to the extract composition and antioxidant capacity, PLE proved to be a technique of choice for the production of blackcurrant and bilberry leave extracts with high potential for use as value-added ingredients in the food and nutraceutical industry.

Rapid urbanization rates impact significantly on the nature of Land Cover patterns of the environment, which has been evident in the depletion of vegetal reserves and in general modifying the human climatic systems (Henderson, et al., 2017; Kumar, Masago, Mishra, &amp; Fukushi, 2018; Luo and Lau, 2017). This study explores remote sensing classification technique and other auxiliary data to determine LULCC for a period of 50 years (1967-2016). The LULCC types identified were quantitatively evaluated using the change detection approach from results of maximum likelihood classification algorithm in GIS. Accuracy assessment results were evaluated and found to be between 56 to 98 percent of the LULC classification. The change detection analysis revealed change in the LULC types in Minna from 1976 to 2016. Built-up area increases from 74.82ha in 1976 to 116.58ha in 2016. Farmlands increased from 2.23 ha to 46.45ha and bared surface increases from 120.00ha to 161.31ha between 1976 to 2016 resulting to decline in vegetation, water body, and wetlands. The Decade of rapid urbanization was found to coincide with the period of increased Public Private Partnership Agreement (PPPA). Increase in farmlands was due to the adoption of urban agriculture which has influence on food security and the environmental sustainability. The observed increase in built up areas, farmlands and bare surfaces has substantially led to reduction in vegetation and water bodies. The oscillatory nature of water bodies LULCC which was not particularly consistent with the rates of urbanization also suggests that beyond the urbanization process, other factors may influence the LULCC of water bodies in urban settlements.&#x0D; Keywords: Minna, Niger State, Remote Sensing, Land Surface Characteristics&#x0D; &#x0D; References &#x0D; Akinrinmade, A., Ibrahim, K., &amp; Abdurrahman, A. 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ABSTRACTIn linear regression models, the ordinary least squares (OLS) method is used to estimate the unknown regression coefficients. However, the OLS estimator may provide unreliable estimates in non‐orthogonal models. This article introduces a novel mixed‐biased estimator to address the challenges posed by the non‐orthogonal model. The proposed estimator is derived through a combination of two estimators, namely, the Stein and ridge estimators. The theoretical properties of the proposed estimator are discussed. Moreover, we suggest estimation methods to estimate the value of the shrinkage parameters for the proposed estimator. We compare the performance of the proposed estimator with the Stein estimator, the ridge estimator with standard and two best ridge parameters and the ordinary least square estimator. This evaluation is based on the mean squared error performance criterion, using both a simulation study and two practical applications related to cement and crock datasets. The simulation study and applications results show that the proposed estimator performs better than the other considered estimators.

Abstract Background Analysis of the outcomes of Ilizarov treatment of tibial nonunion shows functional deficits in the lower limbs of some patients. Biomechanical gait parameters are an important measure for assessing musculoskeletal disorder treatments that aim to restore normal gait. The purpose of our study was to compare the kinematic parameters in patients with tibial nonunion treated using the Ilizarov method and those in a control group of healthy volunteers. Methods The study population consisted of 23 patients (age 54.9 ± 16.4 years) who were treated for tibial nonunion using the Ilizarov method, as well as 22 healthy adult controls (age 52.7 ± 10.6 years). Kinematic parameters were measured using a Noraxon MyoMOTION System. We measured hip flexion and abduction, knee flexion, ankle dorsiflexion, inversion, and abduction during walking. Results Our analysis showed significant differences between the patients’ operated limbs (OLs) and the controls’ nondominant limbs (NDLs) in the ranges of hip flexion, hip abduction, and knee flexion. We observed no significant differences in knee flexion between the OL and the NOL in patients or between the dominant limb (DL) and NDL in controls. Our evaluation of the kinematic parameters of the ankle joint demonstrated significant differences between the patients’ OLs and the controls’ NDLs in the ranges of ankle dorsiflexion, ankle inversion, and ankle abduction. There were also significant differences in the range of ankle dorsiflexion and ankle abduction between the patients’ NOLs and the controls’ DLs. Conclusion Tibial nonunion treatment using the Ilizarov method does not ensure complete normalization of kinematic parameters assessed 24–48 months following the completion of treatment and rehabilitation.

BACKGROUND: In clinical practice, decisions often must be made rapidly; therefore, automated software is useful for diagnostic support. Perfusion computed tomography and follow-up evaluation of perfusion data are valuable tools for selecting the optimal recanalization therapy in patients with acute ischemic stroke. OBJECTIVE: This study aimed to compare commercially available software used to evaluate stroke patients prior to thrombectomy. METHODS: The performance of Olea Sphere (OlS) software vs. CT Neuro Perfusion from Syngo (Sy), as well as the electronic Alberta Stroke Program Early Computed Tomography Score (e-ASPECTS) software vs. an experienced radiologist, were compared using descriptive statistics including significance analysis, Spearman’s correlation, and the Bland-Altman agreement analysis. For this purpose, 43 data sets of patients with stroke symptoms related to the middle cerebral artery territory were retrospectively post-processed with both tools and analyzed. RESULTS: The automatic e-ASPECTS showed high agreement with an expert rater assessment of the ASPECTS. Using OlS and Sy, we compared the parameters for the ischemic core (relative cerebral blood flow), Time to maximum (Tmax) for the penumbra, and the relative mismatch between these two values. Overall, both software tools achieved good agreement, and their respective values correlated well with each other. However, OlS predicted significantly smaller infarct core volumes compared with Sy. CONCLUSIONS: Although the absolute values have a certain degree of variation, both software programs have good agreement with each other.

Olive leaves (OLs) are well known for being rich in oleuropein, their main bioactive molecule which has recently been attracting great interest from the scientific community due to its antiviral properties, including Covid-19 disease. Furthermore, the high-temperature/short-time drying process has found applications for various plants and food processing, which might be also implemented for the drying of OLs. This study focuses on: 1. the mathematical modeling of thin-layer high-temperature-drying (HTD) kinetic of olive (var. Chemlal and Oleaster) leaves, and 2. the determination of HTD effect on some physicochemical properties (oleuropein, chlorophylls, and CIELab color parameters) of the dried olive leaves (DOLs). For this, four drying temperatures (100, 120, 140, and 160 °C) were applied. For comparison purposes, low-temperature DOL samples were also prepared. The obtained data have shown that among the tens tested mathematical models, the Midilli et al. model describes more correctly experimental data for all drying temperatures and for both olive leaf varieties (R2 = 0.9960, SEE = 0.0085, RMSE = 0.0165 and χ2 = 0.0006). Moreover, the results show that the HTD at 120 and 160 °C does not differ from freeze-drying in terms of oleuropein retention (p &lt; 0.05), highlighting the technological interest in the high-temperature/short-time drying process. Considering the biological value of oleuropein, in particular its antiviral activity, the study deserves further investigation in order to elucidate certain questions such as the storability of DOLs, and their valorization as fortification ingredient in food and pharmaceutical formulations, evaluation in vitro of their biological activities, etc.

This study introduces a novel bias estimator within the linear regression framework, specifically addressing models with correlated or heterogeneous errors. Recognizing the limitations of traditional estimation methods like Ordinary Least Squares (OLS) in the presence of multicollinearity and autocorrelated errors, the proposed estimator provides a robust alternative by leveraging bias corrections. The new estimator, termed Corrected Modified Unbiased Ridge Regression (CMURR), incorporates two parameters, 𝑘 and 𝑑, to enhance accuracy. The properties of CMURR are derived, including its mean squared error (MSE), which serves as a key metric for performance evaluation. The CMURR estimator is rigorously compared against existing estimators, including the Modified Almost Unbiased Liu Estimator (MAULE), the Modified Almost Unbiased Two-Parameter Estimator (MAUTP), and the Mustafa Unbiased Ridge Regression (MURR). Simulation studies, conducted under varying degrees of multicollinearity and heteroscedasticity, demonstrate the superior performance of CMURR in reducing MSE across diverse conditions. Additionally, a numerical example utilizing real-world data from economic indicators underscores its practical applicability. Results indicate that the proposed estimator consistently outperforms others, particularly in scenarios involving high multicollinearity or correlated errors. The findings contribute to the ongoing advancement of statistical methods in regression analysis, providing a reliable tool for researchers handling complex error structures in data.

Monitoring the quality of irrigation water can help in the maintenance of filters and irrigation systems, avoiding clogs and uniformity problems. The objective of this work was, thus, to evaluate the performance of sensor modules for monitoring irrigation water quality variables. For that, three sensors were evaluated, and their performance was rated from the adjustment of calibration equations, obtained through linear regression analysis (yi = b0 + b1xi + εi), using the ordinary least squares method (OLS) to estimate its parameters (β0 and β1). The first sensor evaluated was the Ph4502c for pH measurement. Direct methodology was used, using standard pH solutions (1.79; 4.5; 6.88; 12.13; and 13.99) and an electrode type BNC probe. The second evaluated sensor was turbidity model TSW30. To evaluate the total dissolved solids (TDS) sensor, the direct method was applied, using solutions with electrical conductivity of 0.50, 1.0, and 2.0 dS m-1. To investigate the assumptions of independence, homoscedasticity, and normality of the residuals of the linear regression models, the Durbin-Watson, Breusch-Pagan, and Kolmogorov-Smirnov tests were respectively used. In the evaluation of the statistical performance, the indicators of the root-mean-square error, coefficient of determination, correlation coefficient, confidence index, and index of agreement were adopted. The ordinary least squares method did not produce the best unbiased linear estimators for the calibration equations of the pH, turbidity, and TDS sensors, due to the violation of the regression assumptions. The adjustments showed good accuracy for water quality assessment, according to high performance statistics and models classified as ‘Excellent’.

Background: Since women spend about one-third of their lifespan in menopause, accurate prediction of the age of natural menopause and its effective parameters are crucial to increase women’s life expectancy.&#x0D; Objective: This study aimed to compare the performance of generalized linear models (GLM) and the ordinary least squares (OLS) method in predicting the age of natural menopause in a large population of Iranian women.&#x0D; Materials and Methods: This cross-sectional study was conducted using data from the recruitment phase of the Shahedieh Cohort Study, Yazd, Iran. In total, 1251 women who had the experience of natural menopause were included. For modeling natural menopause, the multiple linear regression model was employed using the ordinary least squares method and GLMs. With the help of the Akaike information criterion, rootmean- square error (RMSE), and mean absolute error, the performance of regression models was measured.&#x0D; Results: The mean age of menopausal women was 49.1 ± 4.7 yr (95% CI: 48.8-49.3) with a median of 50 yr. The analysis showed similar Akaike criterion values for the multiple linear models with the OLS technique and the GLM with the Gaussian family. However, the RMSE and mean absolute error values were much lower in GLM. In all the models, education, history of salpingectomy, diabetes, cardiac ischemic, and depression were significantly associated with menopausal age.&#x0D; Conclusion: To predict the age of natural menopause in this study, the GLM with the Gaussian family and the log link function with reduced RMSE and mean absolute error can be a good alternative for modeling menopausal age.&#x0D; Key words: Menopause, Etiology, Statistics, Numerical data.

The study proposed an Adaptive Neuro-Fuzzy Inference Systems (ANFIS) model capable of predicting sediment deposited in a dam and sediment loss-in-transit (SLIT) using the potential of a formulated mathematical relation. The input parameters consist of five members viz: the rainfall, the slope, the particle size, the velocity, and the computed total volume of sediment exited from two prominent gullies for 2017, 2018, and 2019. The outputs are the total volume of sediment deposited at the adjoining Ikpoba dam for 2017, 2018, and 2019, respectively. The Ordinary Least Square (OLS) regression model on sediment volume retained all covariates with p&lt;0.05, explaining 93.8% of the variability in the dataset. The multicollinearity effect on the dataset was assessed using the Variance Inflation Factor (VIF) which was found not to pose a problem for (VIF&lt;5). The model was validated using the (MSE), the (MAE), and the correlation coefficient (r). The best prediction was obtained as: (RMSE = 0.0423; R2 = 0.947). The predicted volume of sediment was 842,895.8547m3 with an error of -0.3295344% and the predicted volume of SLIT was 57,787.98m3 which is an indication that ANFIS performs satisfactorily in predicting sediment volume for the gullies and the dam respectively

AbstractInterrupted time series (ITS) are often meta‐analysed to inform public health and policy decisions but examination of the statistical methods for ITS analysis and meta‐analysis in this context is limited. We simulated meta‐analyses of ITS studies with continuous outcome data, analysed the studies using segmented linear regression with two estimation methods [ordinary least squares (OLS) and restricted maximum likelihood (REML)], and meta‐analysed the immediate level‐ and slope‐change effect estimates using fixed‐effect and (multiple) random‐effects meta‐analysis methods. Simulation design parameters included varying series length; magnitude of lag‐1 autocorrelation; magnitude of level‐ and slope‐changes; number of included studies; and, effect size heterogeneity. All meta‐analysis methods yielded unbiased estimates of the interruption effects. All random effects meta‐analysis methods yielded coverage close to the nominal level, irrespective of the ITS analysis method used and other design parameters. However, heterogeneity was frequently overestimated in scenarios where the ITS study standard errors were underestimated, which occurred for short series or when the ITS analysis method did not appropriately account for autocorrelation. The performance of meta‐analysis methods depends on the design and analysis of the included ITS studies. Although all random effects methods performed well in terms of coverage, irrespective of the ITS analysis method, we recommend the use of effect estimates calculated from ITS methods that adjust for autocorrelation when possible. Doing so will likely to lead to more accurate estimates of the heterogeneity variance.

The availability and quality of instrumental variables (IV) are frequent concerns in empirical management research when trying to overcome endogeneity problems. For endogeneity that does not arise from sample selection, management scholars have recently started to apply the Gaussian Copula (GC) approach as an alternative to IV regression. Although the GC approach has various promising features, its limitations and usefulness in a management context are still not fully understood. We discuss the GC approach as a flexible, instrument-free approach to correct for endogeneity and examine its suitability for applied management research. We use simulations to explore the limitations and practical usefulness of the GC approach relative to ordinary least squares (OLS), IV regression, and a Higher Moments (HM) estimator by simulating the impact of different degrees of violation of the key underlying assumptions of the GC approach. We show that the GC approach can recover the true parameters remarkably well if all of its assumptions are met but that its absolute and relative performance in terms of parameter recovery and estimation precision can deteriorate quickly if these assumptions are violated. This is of particular concern as some of these assumptions are not testable and violations of them are likely in many empirical management contexts. Based on our results, we provide a series of recommendations and practical guidelines for scholars who consider using the GC approach when dealing with endogeneity.

Research background. The motivation of this study is to emphasize the importance of artificial intelligence (AI) and causality modelling of food quality and analysis with “big data”. AI with structural causal modelling (SCM), based on Bayes networks and deep learning, enables the integration of theoretical field knowledge in food technology with process production, physical-chemical analytics, and consumer organoleptic assessments. Food products have complex nature and data are highly dimensional, with intricate interrelations (correlations) and are difficult to relate to consumer sensory perception of food quality. Standard regression modelling techniques such as multiple ordinary least squares (OLS) and partial least squares (PLS) are effectively applied for the prediction by linear interpolations of observed data under cross-sectional stationary conditions. Upgrading linear regression models by machine learning (ML) accounts for nonlinear relations and reveals functional patterns, but is prone to confounding and fails predictions under unobserved nonstationary conditions. Confounding of data variables is the main obstacle to applications of the regression models in food innovations under previously untrained conditions. Hence, this manuscript focuses on applying causal graphical models with Bayes networks to infer causal relationships and intervention effects between process variables and consumer sensory assessment of food quality. Experimental approach. This study is based on the literature available data on the process of wheat bread baking quality, consumer sensory quality assessments of fermented milk products, and professional wine tasting data. The data for wheat baking quality are regularized by the least absolute shrinkage and selection operator (LASSO elastic net). Applied is Bayes statistics for evaluation of the model joint probability function for inferring the network structure and parameters. The obtained SCM models are presented as directed acyclic graphs (DAG). D-separation criteria is applied to block confounding effects in estimating direct and total causal effects of process variables and consumer perception on food quality. Probability distributions of causal effects of the intervention of individual process variables on quality are presented as partial dependency plots determined by Bayes neural networks. In the case of wine quality causality, the total causal effects determined by SCM models are positively validated by the double machine learning (DML) algorithm. Results and conclusions. Analysed is the data set of 45 continuous variables corresponding to different chemical, physical and biochemical variables of wheat properties from seven Croatian cultivars during two years of controlled cultivation. LASSO regularization of the data set yielded the ten key predictors, accounting for 98 % variance of the baking quality data. Based on the key variables derived is the quality predictive random forest model with 75 % cross-validation accuracy. Causal analysis between the quality and key predictors is based on the Bayes model depicted as a DAG graph. Protein content shows the most important direct causal effect with the corresponding path coefficient of 0.71, and THMW (total high molecular glutenin subunits) content is an indirect cause with a path coefficient of 0.42, and protein total average causal effect (ACE) is 0.65. The large data set of quality fermented milk products includes binary consumer sensory data (taste, odour, turbidity), continuous physical variables (temperature, fat, pH, colour), and three grade classes of consumer quality assessment. Derived is a random forest model for the prediction of the quality classification with an “out of box” (OOB) error of 0.28 %. The Bayes network model predicts that the direct causes of the taste classification are temperature, colour, and fat content, while the direct causes for the quality classification are temperature, turbidity, odour, and fat content. Estimated are the key quality grade average causal effects (ACE) of temperature -0.04 grade/°C and 0.3 quality grade/fat content. The temperature ACE dependency shows a nonlinear type as negative saturation with the “breaking” point at 60 °C, while for fat ACE has a positive linear trend. Causal quality analysis of red and white wine is based on the large data set of eleven continuous variables of physical and chemical properties and quality assessments classified in ten classes, from 1 to 10. Each classification is obtained in triplicates by a panel of professional wine tasters. A non-structural double machine learning algorithm (DML) is applied for total ACE quality assessment. The alcohol content of red and white wine has the key positive ACE relative factor of 0.35 quality/alcohol, while volatile acidity has the key negative ACE –0.2 quality/acidity. The obtained ACE predictions by the unstructured DML algorithm are in close agreement with the ACE obtained by the structural SCM models. Novelty and scientific contribution. Presented are novel methodologies and results for the application of causal artificial intelligence models in the analysis of consumer assessment of the quality of food products. The application of Bayes network structural causal models (SCM) enables the d-separation of pronounced effects of confounding between parameters in noncausal regression models. Based on SCM, inference of average causal effects (ACE) provides substantiated and validated research hypotheses for new products and support for decisions of potential interventions for improvement in product design, new process introduction, process control, management, and marketing.

IntroductionLight’s non-visual effects on the biological clock, cognitive performance, alertness, and mental health are getting more recognized. These are primarily driven by blue light, which triggers specific retinal cells containing melanopsin. Traditionally, research on light has relied on correlated color temperature (CCT) as a metric of its biological influence, given that bluer light corresponds to higher Kelvin values. However, CCT proves to be an inadequate proxy of light’s biological effects. A more precise metric is melanopic Equivalent Daylight Illuminance (mel-EDI), which aligns with melanopsin spectrum. Studies have reported positive cognitive impacts of blue-enriched white light. It’s unclear if the mixed results are due to different mel-EDI levels since this factor wasn’t assessed.MethodGiven recent recommendations from experts to aim for at least 250 mel-EDI exposure daily for cognitive benefits, our aim was to assess if a 50-minute exposure to LED light with 250 mel-EDI could enhance concentration and alertness, without affecting visual performance or comfort compared to conventional lighting producing around 150 mel-EDI. To ensure mel-EDI’s impact, photopic lux levels were kept constant across conditions. Conditions were counterbalanced, parameters included subjective sleepiness (KSS; Karolinska Sleepiness Scale), concentration (d2-R test), visual performance (FrACT; Freiburg Visual Acuity and Contrast Test), general appreciation (VAS; Visual Analogous Scale), preferences and comfort (modified OLS; Office Lighting Survey).ResultsThe experimental light significantly reduced sleepiness (p = 0.03, Cohen’s d = 0.42) and also decreased contrast sensitivity (p = 0.01, Cohen’s d = 0.50). The conventional light was found to be more comfortable (p = 0.002, Cohen’s d = 0.62), cheerful (p = 0.02, Cohen’s d = 0.46) and pleasant (p = 0.005, Cohen’s d = 0.55) while the experimental light was perceived as brighter (p = 0.004, Cohen’s d = 0.58) and tended to be more stimulating (p = 0.10). Notably, there was a preference for conventional lighting (p = 0.004, Cohen’s d=0.56) and concentration was equally improved in both conditions.DiscussionDespite the lack of further improvement in concentration from exposure to blue-enriched light, given the observed benefits in terms of vigilance, further research over an extended period would be justified. These findings could subsequently motivate cognitive optimization through lighting for workers that would benefit from artificial lighting such as in northern regions.

<strong>Gyeongsang University Turnitin Trash Files</strong> <strong>HUMAN CAPITAL NEXUS AND GROWTH OF NIGERIA ECONOMY</strong> <strong>CHAPTER ONE</strong> <strong>INTRODUCTION</strong> <strong>Background to the Study </strong> Government expenditure equally known as public spending simply refers to yearly expenditure by the public sector (government) in order to achieve some macroeconomic aims notably high literacy rate, skilled manpower, high standard of living, poverty alleviation, national productivity growth, and macro-economic stability. It is also expenditure by public authorities at various tiers of government to collectively cater for the social needs of the people. Generally, it has been revealed that public expenditure plays a key role in realizing economic growth. This is because providing good education to individuals is one of the principal avenues of improving human resource quality in any economy. From this perspective, advancing school enrolment may subsequently lead to economic growth. Therefore, education remains the effective way to subdue poverty, illiteracy, underfeeding and accelerate economic growth in the long-term. Much attention has been channeled towards clarifying the relationship between education and economic growth, and so, has led to series of studies by economists over the past 30 years. There is substantial literature to back the fact that correlation exists between the two. (Sylvie, 2018). In line with the views of Hadir and Lahrech (2015), the fact that humans are the most worthy assets remains undisputable in both developed and developing countries. Therefore efficiency in human resource management is pertinent if development must be realized. In this sense, the major gateway to development is adequate investment in human capital which may be described as an individual&rsquo;s potential economic value in terms of skills, knowledge, and other intangible assets. In order to realize the well-known macroeconomic objective of economic growth, Nigeria being a developing country embarked on some programs in the educational sector with the aim of boosting human capital development. However, these programs have only served as conduits for enriching the corrupt political elite. Given the high prospects of achieving economic growth in Nigeria and the place of human capital development in its actualization, education, therefore, remains a top priority for the Nigeria government as well as concerned researchers. Thus, this study is one among other concerned studies that will attempt to examine economic growth and human capital nexus in Nigeria through education variables. In particular, using education as a measure of human capital, it will attempt to explore the impact of education variables on the growth of Nigeria&rsquo;s economy. According to Wamboye, (2015), education makes way for vital knowledge, skills, techniques and information for individuals to function in family and society. Education can groom a set of educated leaders to take on jobs in government services, public and private firms, and domestic and foreign firms. The growth of education can provide all kinds of grooming that would foster literacy and basic skills. Though alternative investments in the economy could generate more growth, it must not deviate from the necessary contributions; economic as well as non-economic, that education can make and has made to expediting macroeconomic growth (Clark, 2015). Todaro and Smith in Clark (2015), likewise called attention to the fact that, extension of education lead to an increasingly gainful labor force and provide it with expanded information and abilities, and boost employment and income-earning avenues for educators, schools, and employees. Economic growth, proxied by Gross Domestic Product (GDP), gives numerous advantages which include increasing the general living standard of the masses as estimated by per capita pay (income), making the distribution of income simpler to accomplish, thus, shortening the time span needed to achieve the fundamental needs of man to a considerable majority of the masses. The main source of per capita yield (output) in any nation, regardless of whether it is advanced or developing, is really increment in &#39;human productivity&#39;. Per capita yield (output) growth is notwithstanding a significant aspect of economic prosperity (Abramowitz, 1981). For the most part, it has been uncovered that individuals are the most important source of productivity growth and economic prosperity. Technology and technological hardware are the results of human inventions and innovativeness. The suggestion of UNESCO, that 26% of yearly planned expenditure (budget) in developing nations should be dedicated to education has become intangible, particularly in Nigeria. Planned expenditure on education in Nigeria ranges from only 5%-7% of total planned expenditure. The impact of the above situation on the economic prosperity of the nation as it concerns human capital development, capacity building, infrastructural advancement, etc, is troubling. On this note, the necessity of a well-thought out plan for rectifying this unwanted situation can&#39;t be over stressed. &nbsp; <strong>1.2 Statement of the Problem </strong> Sikiru (2011) as cited in Ajibola (2016) rightly pointed out that the role of education in any economy is no longer business as usual because of the knowledge based globalized economy where productivity greatly depends on the quantity and quality of human resource, which itself largely depends on investment in education. Governments continue to increase spending on education with a view toward enhancing the standard of education, build human capacity and attainment of economic growth. Ironically, this effort by government is still a far cry of UNESCO&rsquo;s recommendation of 26% total annual budget to education, and so, has not yielded the expected results. Thus, researchers sought to understand the relationship between government expenditure on education and economic growth and how they influence each other. These researches on the above subject matter, have given rise to divergent school of thoughts. Over time, Nigeria has indicated willingness to develop&nbsp; education in order to curtail illiteracy and quicken national development. Anyway regardless of the irreproachable evidence that education is key to the improvement of the economy; there exists a wide loop-hole in accessibility, quality and fairness (equity) in education (Ayo, 2014). Empirically verifiable facts in recent years have indicated that the Nigeria&nbsp;education system has continuously turned-out graduates who overtime have defaulted in adapting to evolving techniques and methods of production; due to inadequate infrastructure, underfunding, poor learning aids, outmoded curriculum, dearth of research and development. This has resulted to drastic reduction in employment and the advent of capacity underutilization. This paper assesses growth of Nigeria economy in relation to government expenditure on education and school enrollment from 1981 to 2018. Frequent adjustments and changes in education system in Nigeria, points to the fact that, all is not well with the countries education system. Government have experimented 6-3-3-4, 9-3-4 systems of education, among others. Enrollment in schools forms the main part of investment in human capital in most of the world&rsquo;s societies (Schultz, 2002). There are several explanations concerning why improvement in scholastic quality is not forthcoming in Nigeria as regards the above subject matter. Researchers disagree on whether changes in education attainment levels alters economic growth rate in the long-term. &nbsp;&ldquo;In Nigeria, average public education expenditure to total government expenditure between 1981 and 2018 is 5.68 per cent. It ranged between 0.51 and 10.8 per cent during the period under review&rdquo; (CBN Statistical Bulletin, 2019). However, the major problem therefore, is that despite an increase in the numeric value of budgetary allocation to education in Nigeria over the years, they still fall short of 26 % UNESCO,S recommendation. For instance, 2014, 10.6%; 2015, 9.5%; 2016, 6.1%, 2017, 5.41%, 2018, 7.0% and 2019, 7.2% percent respectively of total annual budget to education. The statistics presented above indicates that investment in education has not produced the desired level of human capital and economic growth in Nigeria. These uncertainties as it relates to government expenditure on education, school enrollment and growth of Nigeria economy gave birth to this research work. Furthermore, most studies relating to the subject matter, conducted analysis on times series data without subjecting these data sets to structural breaks, thereby giving rise to spurious results and therefore, unreliable recommendations. For instance, unit root test with structural breaks were not employed in majority of these studies. <strong>1.3 Research Questions </strong> The issues raised above have provoked series of questions which this study attempts to provide answers. These questions include; i. To what extent does government expenditure on education affect growth of Nigeria economy? ii. To what extent does primary school enrollment affect growth of Nigeria economy? iii. To what extent does secondary school enrollment affect growth of Nigeria economy? iv. To what extent does tertiary school enrollment affect growth of Nigeria economy? <strong>1.4 Objectives of the Study </strong> The main objective of the study is to access the effect of government expenditure on education and growth of Nigeria economy. Specific objectives of the study are to; i. Access the effect of government expenditure on growth of Nigeria economy. ii. Access the effect of primary school enrollment on growth of Nigeria economy. iii. Access the effect of secondary school enrollment on growth of Nigeria economy. iv. Access the effect of tertiary school enrollment on growth of Nigeria economy. <strong>1.5 Hypotheses of the Study </strong> The following hypotheses were tested in this study. i. Government expenditure on education has no significant effect on growth of Nigeria economy. ii. Primary school enrollment has no significant effect on growth of Nigeria economy. iii. Secondary school enrollment has no significant effect on growth of Nigeria economy. iv. Tertiary school enrollment has no significant effect on growth of Nigeria economy. <strong>1.6 Scope of the Study </strong> The study covers the time series analysis of government expenditure on education, school enrolment; primary, secondary and tertiary, and growth of Nigeria economy from 1981 to 2018. Based on available data. Justification for this study is on the premise that, time series data used for the study is a current data on government expenditure on education, education enrolment and economic growth in Nigeria. This study used annual data for the period 1981-2018, collected from the CBN Statistical Bulletin (2019) and World Bank databank. Variables employed for the study include; Real GDP Per Capita, government expenditure on education, primary, secondary and tertiary school enrolment. <strong>1.7 Significance of the Study </strong> Models of economic growth provide useful predictions that inform decisions made by policy makers. Agreeing with policy options based on inaccurate research studies could undermine government intervention particularly in the education sector. A good perception of the interaction among investment in education, its outcome, school enrolment and economic growth is appropriate policy measure, guarantees human capital development. Thus, a representative model that take cognisance of inter-play among public education expenditure, school enrolment and growth of the economy will lead to adequate disbursement and utilization of government funds. The outcome of this research will serve as a tool for policy makers in the Ministries of Finance, Education and the National Planning Commission including regulatory agencies not mentioned here. It will also serve as a reference material for subsequent research work in this field. <strong>1.8 Limitation of the Study </strong> This research x-rays Government Expenditure on Education, school (primary, secondary and tertiary) enrolment as they relate to Growth of Nigeria Economy. Time series data covering the period 1981 to 2018 is used for this study. A study undertaken in 2020, but can not access 2019 data on the variables used, stand as one of the limitations, since lag periods are essential in policy implementation. Data availability, genuineness and accuracy of same, time and financial constraints, constitute limitations to this research work. Effect of corruption on government expenditure and outbreak of Corona virus, resulting to closure of tertiary institutions in Nigeria, also constitute limitation to this study. <strong>1.9 Organization of the Study </strong> This research work comprises of five (5) chapters, these includes; Chapter one: this consists of background to the study, Problem Statement, research questions, research hypothesis and scope of the study. Chapter two: consisting of conceptual framework, theoretical review, review of related literatures and theoretical framework. Chapter three: explained the methodology this research adopted. Chapter four: presentation of results and discussion of findings. Chapter five: consists of summary of findings, conclusion, policy recommendation, contribution to knowledge and suggestion for further studies.&nbsp; <strong>CHAPTER TWO</strong> <strong>LITERATURE REVIEW AND THEORITICAL FRAMEWORK</strong> <strong>2.1 Conceptual Review</strong> <strong>2.1.1 Government&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </strong> Government is the sector of the economy focusing on giving different public services. Its structure differs by nation, yet in many nations, government involves such services as infrastructure, military, police, public travel, government provided education, alongside medical services and those working for the public sector itself, like, elected authorities. The government may offer types of assistance that a non-taxpayer can&#39;t be barred from, (for example, street lighting), goods which aids all of society instead of benefiting only one person. Finances for government goods and services are generally obtained through various techniques, including taxes, charges, and through monetary transfers from different tiers of government (for example from federal to state government). Various governments from around the globe may utilize their own strategies for financing public goods and services. <strong>2.1.2 Government Expenditure</strong> Government Expenditure refers to government spending both capital and recurrent. For the purpose of this study we limited our scope to government educational expenditure in Nigeria. The theory of government expenditure is the theory of the costs of availing goods and services through planned spending (budget). There are two ways to deal with the subject of growth of government, precisely, the expansion in total size of government spending and the expansion of government in terms of economic magnitudes. Government expenditure is spending made by the public sector (government) of a nation on aggregate needs and wants, for example, pension and arrangement of infrastructure, among others. Until the nineteenth century, government speding was constrained, as free enterprise theorists believed that financial resources left in the private sector could lead to higher returns. In the twentieth century, John Maynard Keynes advocated the job of government spending in influencing levels of wages and income distribution in the economy. From that point forward government spending has demonstrated an expanding pattern. The public expenditure trend of the government of a nation is essentially the manner in which assets (resources) are distributed to the various segments of the economy where spending is required. It is exemplified in the government&rsquo;s ways of spending money. In analyzing the trend of government spending hence, it is critical to realize that under a federal system of administration, government job in dealing with the economy is the joint duty of the different tiers of government (Eze and Ikenna 2014). <strong>2.1.3 Human Capital </strong> By and large, human capital is characterized as all skills that are indistinguishably helpful to numerous organizations, including the training organization. Industry-specific skills, conversely, foster efficiency (productivity) just in the industry in which the skills were obtained. In a serious market setting, laborers consistently get a pay that approaches their minor profitability and in this manner, on account of general human capital, laborers win a similar compensation any place they work. <strong>2.1.4 Economic Growth</strong> As per Haller (2012), economic growth or economic expansion means the way toward expanding the size of a country&rsquo;s economy, its macro-economic indicators, particularly the per capita GDP, in an incremental yet not mandatorily linear course, with beneficial outcomes on the socio-economic sector. IMF (2012) perceives economic expansion as the expansion in the market worth of commodities created in a country over a period of time after discounting for inflation. The rate of increment in real Gross Domestic Product is often used as an estimate of economic expansion. In the perspectives of Kimberly (2012), economic expansion is an expansion in the creation of commodities. Any expansion in the worth of a nation&rsquo;s created commodities is likewise characterized as economic expansion. Economic expansion means an expansion in real GNP per unit of labor input. This relates to labor efficiency variation with time. Economic expansion is routinely estimated with the pace of increment in GDP. It is often estimated in real terms (deducting the impact of inflation on the cost of all commodities created). Growth improves the living standard of the individuals in that specific nation. As per Jhingan (2004), one of the greatest aims of money policy approach as of late has been quick macroeconomic expansion. He thus, characterized economic prosperity (growth) as the event whereby the real per capita earnings (income) of a nation increments over a significant stretch of time. Economic expansion is estimated by the expansion in the quantity of commodities created in a nation. An expanding economy creates more commodities in each subsequent timespan. In this manner, growth happens when an economy&#39;s capacity to produce increases which in turn, is utilized to create a greater quantity of commodities. In a more extensive perspective, economic expansion means increasing the living standard of individuals, and reducing disparities in earnings. &nbsp; <strong>2.1.5 </strong><strong>Gross Domestic Product</strong> - GDP Investopedia designates Gross Domestic Product (GDP) as the financial worth of marketable commodities created in a nation during any given duration of time. It is normally computed on a yearly or a quarterly premise. It comprises household and government consumption, government pay-outs, investments and net exports that exist in a sovereign territory. Set forth plainly, GDP is a broad estimation of a country&#39;s aggregate economic activity. &nbsp; <strong>2.1.6 Education</strong> There is no singular meaning of education and this is on the grounds that it indicates various things to various individuals, cultures and societies (Todaro and Stephen, 1982). Ukeje (2002), considers education to be a process, a product and a discipline. When viewed as a process, education is a group of activities which involves passing knowledge across age-groups (generations). When viewed as a product, education is estimated by the characteristics and attributes displayed by the educated individual. Here, the informed (educated) individual is customarily considered to be an informed and refined individual. While as a discipline, education is perceived in terms of the pros of well-structured knowledge which learners are acquainted with. Education is a discipline concerned with techniques of giving guidance and learning in institutions of learning in lieu of informal socialization avenues like rural development undertakings and education via parent-child interactions). It comprises both inherent (intrinsic) and instrumental worth. It is attractive for the person as well as for the general public. Education as private commodity directly aids the individuals who get it, which thusly influences the person&#39;s future pay (income) stream. At the macroeconomic level, a workforce that is superior in terms of education is thought to expand the supply of human capital in the economy and increment its efficiency (productivity). Considering the externalities pervasive in education, it is broadly acknowledged that the state has a key task to carry out in guaranteeing fair distribution of educational chances (opportunities) to the whole populace. This is especially critical in developing nations, for example, Nigeria that experiences the ill effects of elevated poverty levels, inequality and market imperfections. Enrolment might be viewed as the process of commencing participation in a school, which is the number of learners (students) adequately registered as well as participating in classes (Oxford dictionaries). 2.1.7 Primary Education Pupils usually commence learning at the elementary level when they are as old as 5 years or more. Pupils go through 18 terms equivalent to 6 years at the elementary level and may be awarded a first school leaving certification upon successful completion of learning. Subjects treated at the elementary stage comprise arithmetic, foreign and indigenous languages, culture, home economics, religious studies, and agric science. Privately owned institutions of learning may opt to treat computer science, and fine arts. It is mandatory to participate in a Common Entrance Examination in order to meet requirements for induction into secondary institutions of learning. <strong>2.1.8 Secondary Education In Nigeria</strong> Decades after the advancement of elementary education, government gave attention to secondary education, because of the requirement for pupils to advance their education in secondary schools. Secondary education is defined as the completion of fundamental education that started at the elementary level, and seeks to establish the frameworks for long-term learning and human development, by providing subject and skill-centred guidance. It is equally a link between elementary learning and tertiary learning. It is given in two phases, junior and senior levels of three years each and it is six-year duration. It was only in 1909 that the colonial administration began to supplement the endeavors of the Christian Missions in giving secondary education. This was when King&#39;s College was established in Lagos as the colonial government&#39;s secondary institution of learning. As per Adesina and Fafunwa , numerous laws were enacted to improve the condition of secondary education in Nigeria. For the duration of the time the nation was under Colonial Governments, there were scarcely any secondary schools to give secondary education to those that were then ready to gain it. 2.1.9 Tertiary Education Institutions of tertiary learning comprise universities, colleges of education, polytechnics and monotechnics. Government has dominant control of university education, and regulates them through National Universities Commission (NUC). At the university level, first year selection criteria include: At least 5 credits in not more than two sittings in WAEC/NECO; and a score above the 180 benchmark in the Joint Admission and Matriculation Board Entrance Examination (JAMB). Prospective entrants who hold satisfactory national certificates of education (NCE) or national diplomas (ND) having 5 or more ordinary level credits may gain direct entry into universities at the undergraduate level. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <strong>2.2 Theoretical Review</strong> <strong>2.2.1 Wagner&rsquo;s Law of Expending State Activity </strong> Public expenditure has one its oldest theories rooted in Adolph Wagner&rsquo;s (1883) work. A German economist that came up with a fascinating hypothesis of development in 1883 which held that as a country builds its public sector up, government spending will consequently become more significant. Wagner built up a &ldquo;law of increasing state activity&quot; after empirical investigation on Western Europe toward the conclusive part of the nineteenth century. Wagner&#39;s Law as treated to in Likita (1999) contended that government administration development is a product of advancement in industrialization and economic development. Wagner believed that during industrialization, the expansion of real earnings per capita will be accompanied by increments in the portion of government spending in total spending. He stated that the coming of industrial communities can bring about greater political impetus for social advancement and expanded earnings. Wagner (1893) stated three central reasons for the expansion in state spending. To start with, activities in the public sector will supplant non-private sector activities during industrialization. State duties like authoritative and defensive duties will increment. Furthermore, governments will be expected to give social services and government assistance like education, and public health for the elderly, subsidized food, natural hazards and disaster aids, protection programs for the environment and social services. Thirdly, industrial expansion will lead to novel&nbsp; technology and erode monopoly. Governments will need to balance these impacts by offering public goods through planned spending. Adolf Wagner in Finanzwissenschaft (1883) and Grundlegung der politischen Wissenschaft (1893) identified state spending as an &ldquo;internal&rdquo; factor, controlled by the development of aggregate earnings. Thus, aggregate earnings give rise to state spending. Wagner&#39;s may be viewed as a long-term phenomenon which is best observed with lengthy time-series for better economic interpretation and factual (statistical) derivations. This is because these patterns were expected to manifest after 5 or 10 decades of present day industrial community. The hypothesis of public spending is the hypothesis of the costs of availing commodities through planned government spending as well as the theory of policies and laws enacted to bring about private spending. Two ways to deal with the topic of the growth of the government sector are, namely, the expansion in volume of non-private spending and the expansion of non-private sector. Okafor and Eiya (2011) investigated the factors responsible for increment of government spending utilizing BLUE-OLS estimator. They discovered that population, government borrowing, government income, and inflation significantly affected government at the 5% level, while inflation most certainly did not. Further, Edame (2014) examined the predictive factors of state infrastructure spending in Nigeria, utilizing error correction modeling. In this study, it was found that growth-pace of urbanization, public income, density of population, system of government, and foreign reserves collectively or separately impact Nigeria&rsquo;s state infrastructure spending. &nbsp; <strong>2.2.3</strong><strong>The Classical Theory of Economic Growth</strong> This theory signifies the underlying structure of economic reasoning and Adam Smith&#39;s &quot;The Wealth of Nations&quot; (1776) typically paves the way for classical economics. Prominent and remarkable advocates of the classical school are: Adam Smith (1723-1790), David Ricardo (1772-1823), Thomas Malthus (1766-1834), Karl Marx (1818-1883), John Stuart Mill (1808-1873), Jean-Baptiste Say (1767-1832) and so on. Basically Smith&#39;s theory says that the endowment of countries was put together not with respect to gold, but with respect to commerce: As when two economic agents trade valuable commodities, in order to reap the benefits of trade, endowment grows. The classicalists see that markets are self-regulating, when liberated from compulsion. The classicalists termed this figuratively as the &quot;invisible hand&quot;, which establishes equilibrium, when consumers choose among various suppliers, and failure is allowed among firms that fail to compete successfully. The classicalists often warned against the risks of &ldquo;trust&rdquo;, and emphasized on free market economy (Smith, 1776). Adam Smith connected the expansion in endowment of individuals to the expansion of the yield of production factors, which manifests in the improvement of productivity of labor and an expansion in the quantity of working capital. Much scrutiny was given to population expansion, to the expansion in the portion of laborers in material production, to investment and geographical findings, which added to far-reaching prosperity. The perspectives of Thomas Malthus on economic expansion, portraying the expansion of populace and the expansion in production appeared pessimistic. As per Malthus, when the proportion between population expansion and subsistence methods&nbsp; remains, when the populace is expanding increasingly, and subsistence methods expand steadily, the aftermath will be inadequate earth resources (land), and consequently a severe battle for few resources, the prevalence of wars, plagues, hunger, mass illness, etc (Ojewumi and Oladimeji, 2016). As a solution to this issue, Malthus proposed to limit the growth of the populace by the &quot;call to prudence&quot;, particularly the impoverished, and the birth of children on the bases that they were to be provided with decent means of subsistence. One among the most compelling classicalists was David Ricardo (1772 &ndash; 1823). Apparently, the hypothesis of comparative advantage which recommends that a country should engage exclusively in internationally competitive businesses and trade with different nations to acquire commodities lacking domestically is his most notable contribution. He contended the possibility of the presence of a natural market wages and expected that new technologies will result to a fall in the demand for labor. John Stuart Mill (1808-1873) to a great extent summarized the past ideologies of the classicalists. Specifically, he finished the classicalists&rsquo; hypothesis of economic dynamics that considers long-term economic patterns. At the core of this idea is the unceasing amassing of capital. As indicated by the hypothesis, the expansion in capital prompts an increment in the need for labor, and zero population growth gives rise to increment in real earnings, and therefore gives rise to population expansion in the long-run. When the amassing of capital is quicker than the expansion in the workforce, both of these processes can, in principle, remain forever. Increment in the quantity of laborers means having more &quot;mouths&quot;, hence the expansion in the demand for consumption and particularly for food. Food created in agribusiness, which, as we know, characterized by diminishing returns to scale. Therefore, issues of diminishing marginal productivity of capital emerge and the fall of incentives to invest. <strong>2.2.4 The Keynesian Approach of Public Expenditure </strong> John M. Keynes (1936), a British Economist and the pioneer of macroeconomics contended that public spending is a crucial determinant of economic posperity. Keynes hypothesis clearly stated that fiscal policy instrument (for example government expenditure) is a significant apparatus for obtaining stability and better economic expansion rate in the long-term. To obtain stability in the economy, this hypothesis endorses government action in the economy through macroeconomic policy especially fiscal policy. From the Keynesian view, government spending will contribute incrementally to economic expansion. Keynes contended that it is necessary for government to mediate in the economy since government could change financial downturns by raising finances from private borrowing and afterward restoring the funds to the private sector through several spending programs. Likewise, government capital and recurrent spending in the structure provision of class rooms, research centers, acquisition of teaching and learning aids including PCs and payment of salary will have multiplier effects on the economy. Spending on education will boost productivity as well as advancement by improving the quality of labour. It will likewise help in developing a stream of educated administrators in both the private and public sectors of the economy. Keynes classified public spending as an exogenous variable that can create economic prosperity rather than an endogenous phenomenon. In summary, Keynes acknowledged the functioning of the government to be significant as it can prevent economic downturn by expanding aggregate demand and in this manner, switching on the economy again by the multiplier effect. It is an apparatus that proffers stability the short-term yet this should be done carefully as excessive government spending leads to inflation while lack of spending aggravates unemployment. &nbsp; <strong>2.2.5 </strong><strong>Human Capital Theory</strong> Human capital theory, at first developed by Becker (1962), contends that workers have a set of abilities which they can improve or acquire by learning and instruction (education). Be that as it may, human capital hypothesis often assume for the most part expect that experiences are converted into knowledge and skills. It helps us comprehend the training activities of organizations. It (re-)introduced the view that education and training add up to investment in future efficiency (productivity) and not only consumption of resources. From this viewpoint, both firms and labourers rely upon investment in human capital to foster competitiveness, profitability, and earnings. In spite of the fact that these advantages are self-evident, these investments are tied to some costs. From the firm&#39;s perspective, investment in human capital contrast from those in physical capital, because the firm doesn&#39;t gain a property right over its investment in skills, so it and its employees need to agree on the sharing of costs and benefits derived from these investments. While investment in physical capital are solely the organization&#39;s own choice, investment in the abilities (skills) of its workforce include interaction with the workers to be groomed. In the basic formulation, Becker, assuming that commodity and labour markets are perfectly competitive, introduced the distinction between firm-specific and general human capital to answer the question: who bears the expenses of training? &nbsp; <strong>2.2.6 Neoclassical Growth Theories </strong> The neoclassical development hypotheses arose in the 1950s and 1960s, when regard for the issues of dynamic equilibrium declined and the issue of actualizing growth potentials through the adoption of novel technology, boosting productivity and improving the organization of production gained popularity. The principle advocates of this school are Alfred Marshall (1842-1924), Leon Walras (1834-1910), William Stanley Jevons (1835-1882), Irving Fisher (1867-1947) and others. The American economist Robert Solow (1924-present) along with other economists opposed the state&#39;s participation and rather supported the notion of permitting firms to competitively grow by utilizing the majority of the assets accessible to them. They hinged on the production theory and marginal productivity theory from the classical school, according to which, the earnings obtained production factors depend on their marginal products. Neoclassical scholars disagreed with neo-Keynesian views on growth on three grounds (UN, 2011): Firstly, in light of the fact that they are centered around capital accumulation, overlooking land, labour, technology and so on; On the second note, owing to the fact that they are rooted in the unchanging nature of capital share in earnings (income); On the third note, while the neoclassicists recognized the self-restoring equilibrium of the market mechanism, the former overlooked it. On this premise, they identified inflationary government spending as a source of instability in the economy. <strong>2.2.7 The Endogenous Growth Theory</strong> This was created as a response to exclusions and inadequacies in the Solow-Swan model. This theory throws light on long-term economic expansion pace based on the pace of population expansion and the pace of technical advancement which is autonomous with regards to savings rate. Since long-term economic expansion rate depended on exogenous factors, Romer (1994) saw that the neoclassical hypothesis had hardly limited implications. As per Romer, in models with exogenous technical change and exogenous population expansion, it never truly made a difference what the public administration did. The new growth theory doesn&#39;t rebuff the neoclassical growth theory. Perhaps it broadens the neoclassical growth hypothesis by incorporating endogenous technical advancement in growth models. The endogenous development models have been improved by Kenneth J. Arrow, Paul M. Romer, and Robert E. Lucas. The endogenous development model highlights technical advancement arising from pace investment, quantity of capital, and human capital supply. Romer saw natural assets as a lower priority than ideas. He refers to case of Japan which has limited natural assets but welcomed novel ideas and technology from the West. These included improved plans for production of producer durable goods for final production. Accordingly, ideas are key in economic prosperity. With respect to endogenous growth theory, Chude and Chude (2013) submitted that the major improvement in the endogenous growth hypothesis in relation to the past models lies in the fact that it treats the determinants of technology. That is, it openly attempts to model technology instead of expecting it to be exogenous. Momentously, it is a statistical clarification of technological improvement that introduced a novel idea of human capital, knowledge and abilities (skills) that empower employees to be increasingly productive. More often than not, economic expansion is a product of progress in technology, arising from effective utilization of productive resources through the process of learning. This is because human capital development has high rate or increasing rate of return. Therefore, the rate of growth depends heavily on what (the type of capital) a country invests in. Thus to achieve economic expansion, public expenditure in human capital development especially education spending must be increased. At the same time, the theory predicts unexpected additional benefits from advancement of a substantial valued-added knowledge economy, that can develop and preserve a competitive advantage in expanding industries. <strong>2.3 Empirical Review</strong> Bearing in mind the sensitive nature of the field being studied, many investigations had been conducted with the aim of clarifying the divergent ideological schools. For example, Amadi, and Alolote, (2020) explored government infrastructural spending and Nigeria&rsquo;s economic advancement nexus. The investigation uncovered that public spending on transport, communication, education and medical infrastructure significantly affect economic expansion, while spending on agric and natural resources infrastructure recorded a major adverse impact on economic expansion. Despite the fact that the investigation is recent, the time series variables were not exposed to unit root tests with breaks, and thus will yield misleading outcomes. Shafuda and Utpal (2020) explored government spending on human capital and Namibia&rsquo;s economic prosperity (growth) nexus from 1980 to 2015. The examination utilized human development indicators like healthcare outcomes, educational accomplishments and increment in national earnings in Namibia. The investigation uncovered huge effects of government spending on medical care and education on GDP expansion over the long-term. Study conducted in 2020 that utilized data from 1980-1915, comprises a setback to this work. Ihugba, Ukwunna, and Obiukwu (2019) explored government education spending and Nigeria&rsquo;s elementary school enrolment nexus by applying the bounds testing (ARDL) method of cointegration during the time of 1970 to 2017. The model utilized for the investigation attempted to recognize the interaction between two variables and their relationship with control variables; per capita earning (income), remittances, investment and population expansion. The bounds tests indicated that the variables that were studied are bound together over the long-term, when elementary school enrolment is the endogenous variable. The investigation saw that an inconsequential relationship exists between government education spending on elementary school enrolment while a positive relationship exists among remittances and primary school enrolment. Sylvie (2018) explored education and India&rsquo;s economic expansion nexus. The investigation inspected the connection among education and economic prosperity in India from 1975 to 2016 by concentrating on elementary, secondary and tertiary levels of education. It used econometric estimations with the Granger Causality Method and the Cointegration Method. The study indicated that there is convincing proof demonstrating a positive association between education levels and economic expansion in India which may impact government activities and shape the future of India. Ayeni, and Osagie (2018), explored education spending and Nigeria&rsquo;s economic expansion nexus from 1987 to 2016. The investigation uncovered that education spending was inconsistent with education sectoral yield (output), while recurrent education spending had meaningful relationship with real gross national output (or GNP), conversely, capital spending on education was weak. Ogunleye, Owolabi, Sanyaolu, and Lawal, (2017), utilized BLUE-OLS estimator to study the effect of advancement in human capital on Nigeria&rsquo;s economic expansion from 1981 to 2015. The empirical outcomes indicated that human capital development has strong effects on economic expansion (growth). Likewise, human capital development variables; secondary school enrolment, tertiary enrolment, aggregated government spending on health and aggregated government spending on education displayed positive and strong effect on economic expansion of Nigeria. Glylych, Modupe and Semiha (2016) explored education and Nigeria&rsquo;s economic expansion nexus utilizing BLUE-OLS estimator to unveil the interaction between education as human capital and real Gross Domestic Product. The investigation found a strong connection between GDP and different indicators (capital spending on education, recurrent spending on education, elementary school enrolment and secondary school enrolment) utilized in the investigation except for elementary school enrolment (PRYE). Lingaraj, Pradeep and Kalandi (2016) explored education expenditure and economic expansion nexus in 14 major Asian nations by utilizing balanced panel data from 1973 to 2012. The co-integration result indicated the presence of long-run relationships between education spending and economic expansion in all the nations. The findings additionally uncovered a positive and significant effect of education training on economic advancement of all the 14 Asian nations. Further, the panel vector error correction showed unidirectional Granger causality running from economic expansion to education spending both in the short and long-run, however, education spending only Granger causes long-run economic expansion in all the nations. The findings likewise demonstrated a positive effect of education spending on economic expansion. The study contended that education sector is one of the significant elements of economic expansion in each of the 14 Asian nations. A significant portion of government spending ought to be made on education by upgrading different essential, senior and technical educations in the respective countries to make available the skilled labour for long-term economic advancement. Ojewumi and Oladimeji (2016) explored government financing and Nigeria&rsquo;s education nexus. In the research work, public spending on education was arranged into two classes (recurrent and capital spending). The data covered the period 1981 to 2013 and were secondary in nature. The data were gotten for the most part from the publications of the World Bank, Central Bank of Nigeria and National Bureau of Statistics. BLUE-OLS estimator was utilized to study the data. The main results indicated that the effect of both capital and recurrent spending on education expansion were negative during the examination time frame. The study suggested that the elevated level of corruption common in the educational sector ought to be checked to guarantee that finances ear-marked for education particularly capital spending in the sector are prudently appropriated. Government at various levels ought to likewise increment both capital and recurrent spending to support the educational sector up to the United Nations standard. Obi, Ekesiobi, Dimnwobi, and Mgbemena, (2016) explored government education spending and Nigeria&rsquo;s education outcome nexus from 1970 &ndash; 2013. The investigation utilized BLUE-OLS estimator, and demonstrated that government spending on education has a cordial and notable impact on education. Public health spending and urban population expansion were likewise found to positively affect education outcome but are insignificant in influencing education outcome. Omodero, and Azubike, (2016), explored government spending on education and Nigeria&rsquo;s economic advancement nexus from 2000&ndash;2015. Multiple regression analysis and student t-test were applied for investigation. The outcome of the investigation showed that education spending is significant and affects the economy. Additionally, education enrolment demonstrated a significant relationship with GDP but minor effect on the economy. Muhammad and Benedict (2015) explored education spending and Nigeria&rsquo;s economic expansion nexus during the time covering 1981-2010. Co-joining and Granger causality tests were utilized so as to unveil the causal nexus between education spending and economic expansion. They found that there is co-integration between real growth rate of GDP, aggregated government spending on education, recurrent expenditure on education and elementary school enrolment. Adeyemi and Ogunsola (2016) explored advancement in human capital and Nigeria&rsquo;s economic expansion nexus from 1980-2013 on secondary school enrolment, life expectancy rate, government spending on education, gross capital formation and economic expansion rate. ARDL cointegration approach was utilized in the investigation and it uncovered a positive since a long-run nexus among secondary school enrolment, life expectancy rate, government spending on education, gross capital formation and economic expansion rate. Olalekan (2014) explored human capital and Nigeria&rsquo;s economic expansion nexus utilizing yearly data on education and health, from 1980 to 2011. The investigation made use of Generalized Method of Moment (GMM) techniques in the research and the estimated outcomes gave proof of positive connection between human capital and economic expansion. Oladeji (2015) explored human capital (through education and effective services in healthcare) and Nigeria&rsquo;s economic expansion nexus from 1980 to 2012. The investigation utilized BLUE-OLS estimator and uncovered that there is a significant functional and institutional connection between the investment in human capital and economic expansion. The work indicated that a long-term nexus existed between education and economic expansion rate. Hadir and Lahrech, (2015) explored human capital advancement and Morocco&rsquo;s economic expansion nexus utilizing yearly data from 1973 to 2011. The BLUE-OLS estimator was incorporated utilizing aggregated government spending on education and health, the enrolment data of tertiary, secondary and elementary educational institutions as a measure for human capital. The research uncovered a positive nexus between aggregated government spending on education, aggregated government spending on health, elementary education enrolment, secondary education enrolment and tertiary education enrolment. Obi and Obi (2014) explored education spending and Nigeria&rsquo;s economic expansion nexus as a method for accomplishing ideal socio-economic change required from 1981 to 2012. The Johansen co-integration method and BLUE-OLS estimator econometric methods were utilized to closely study the connection between GDP and recurrent education spending. The results showed that regardless of the fact that a positive relationship was obtainable between education spending and economic expansion, a long-term nexus was not obtainable over the period under examination. Jaiyeoba (2015) explored investment in education/health and Nigeria&rsquo;s economic expansion nexus from 1982 to 2011. He utilized trend analysis, the Johansen cointegration and BLUE-OLS estimator. The outcomes demonstrated that there was long-term connection between government spending on education, health and economic expansion. The factors: health and education spending, secondary and tertiary enrolment rate and gross fixed capital formation carried the speculated positive signs and were notable determinants (apart from government spending on education and elementary education enrolment rate). Sulaiman, Bala, Tijani, Waziri and Maji (2015) explored human capital /technology and Nigeria&rsquo;s economic expansion nexus. They utilized yearly time series covering 35 years (1975-2010) and applied autoregressive distributed lag method of cointegration to look at the connection between human capital, technology, and economic expansion. Two measures of human capital (secondary and university enrolment) were utilized in two different models. Their outcome uncovered that all the factors in the two separate models were cointegrated. Besides, the findings from the two assessed models indicated that human capital in measured by secondary and tertiary education enrolments have significant positive effect on economic expansion. Borojo and Jiang (2015) explored education/health (human capital) and Ethiopia&rsquo;s economic expansion nexus from 1980 to 2013. Human capital stock is measured by elementary, secondary and tertiary education enrolment. Human capital investment is proxied by spending on health and education. The Augmented Dickey Fuller test and Johansen&#39;s Co-integration method were utilized to test unit root and to ascertain co-integration among factors, respectively. Their investigation indicated that public spending on health as well as education and elementary as well as secondary education enrolments has positive and significant impacts on economic expansion both in the short-term and the long-term. Ekesiobi, Dimnwobi, Ifebi and Ibekilo (2016) explored public education investment and Nigeria&rsquo;s manufacturing yield nexus. The investigation utilized Augmented Dickey Fuller (ADF) unit root test and BLUE-OLS estimator to examine the connection between public educational spending, elementary school enrolment rate, per capita income, exchange rate, FDI and manufacturing yield (output) rate. The investigation discovered that public education spending has a positive but inconsequential impact on manufacturing yield (output) rate. Odo, Nwachukwu, and Agbi (2016) explored government spending and Nigeria&rsquo;s economic expansion nexus. Their finding demonstrated that social capital had inconsequential positive effect on economic expansion during the period under consideration. Jiangyi, (2016) explored government educational spending and China&rsquo;s economic expansion nexus bearing in mind the spatial third-party spill-over effects. The findings uncover that public educational spending in China has a significant positive effect on economic expansion, but spending in various educational level shows varying outcomes. Public educational spending beneath high-education is positively related with domestic economic expansion, while the impact of educational spending in high-education is inconsequential. Lawanson (2015) explored the importance of health and educational elements of human capital to economic expansion, utilizing panel data from sixteen West African nations over the period 1980 to 2013. He utilized Diff-GMM dynamic panel procedure. The empirical results show that coefficients of both health and education have positive and significant impacts on GDP per capita. The paper ascertains the importance of human capital to economic expansion in West Africa. He suggested that more assets and policies to persuade and improve access to both education and health by the populace ought to be sought after by policy makers. Ehimare, Ogaga-Oghene, Obarisiagbon and Okorie (2014), explored the connection between Nigerian government Expenditure and Human Capital Development. The level of human capital development, which is a measure of the degree of wellbeing (health) and educational achievement of a country influence the level of economic activities in that country. The unit root test was employed to ascertain if the stationary or non-stationary with the Phillip Peron test. So as to measure the efficiency of government spending on human capital development, the data analysis was performed with Data Envelopment Analysis including Input Oriented Variable Return to Scale. The discoveries of the study uncovered that there has been substantial decrease in the efficiency of government spending since 1990 up till 2011 which has been diminishing. Ajadi and Adebakin (2014), investigated the nature of association between human capital development and economic expansion. The descriptive survey method of research was incorporated and multi&ndash;stage sampling method was utilized to choose a size of 200 respondents utilized for the research. An adopted questionnaire with 0.86 reliability index was utilized for information gathering. Data gathered were examined utilizing the Pearson&#39;s Product Moment Correlation Coefficient. The results demonstrated that education has a predictive r-value of 0.76 on individual personal earnings and the type of occupation (job) is linked with individual personal earnings (r=0.64). It, subsequently, concluded that economic expansion rate is influenced by individual personal earnings and suggested that government ought to create adequate educational policy to avail the human capital need of the populace for economic prosperity. Harpaljit, Baharom and Muzafar (2014) examined the connection between education spending and economic expansion rate in China and India by utilizing yearly data from 1970 to 2005. This investigation used multi econometric methods including co-integration test, BLUE-OLS estimator, and VECM. The result uncovered that there is a long-term nexus between earnings (income) level, Gross Domestic Product per capital and education spending in both China and India. Also, a unidirectional causal relationship was obtained for the two nations, running from earnings (income) level to education spending for China, while for India, education spending Granger causes the level of earnings. Urhie (2014) analyzed the impacts of the components of public education spending on both educational achievement and Nigeria&rsquo;s economic expansion rate from 1970 to 2010. The investigation utilized Two Stage Least Squares estimation procedure to analyze the hypotheses. The result uncovered that both capital and recurrent spending on education affect education achievement and economic expansion rate differently. Recurrent spending negatively affected education while capital spending was found to have a positive effect. Conversely, recurrent education had a positive and notable effect on economic expansion while capital spending had a negative effect. Chude and Chude (2013) explored the impacts of public education spending on Nigeria&rsquo;s economic expansion over a time frame from 1977 to 2012, with particular focus on disaggregated and sectorial spending analysis. Error correction model (ECM) was utilized. The result uncovered that over the long-term, aggregated education spending is significant and has a positive relationship on economic expansion. Abdul (2013), analyzed Education and Economic expansion in Malaysia given the fact human capital or education has is now one of the focal issues in the research of economic advancement. The researcher contended that the current studies showed that human capital, particularly education, is a significant ingredient of economic expansion. Thus the researcher investigated the issue of Malaysia education data. Notwithstanding a few issues and data quality issues, Malaysian education datasets are heavily correlated for both secondary and tertiary education. The researcher further tests the impact of various datasets on education and economic expansion relationship. The results were fundamentally the same thereby indicating that Malaysian education datasets are not unreliable. The results were econometrically consistent irrespective of measure of education utilized. All datasets lead to the same conclusion; education is inversely associated with economic expansion. Alvina and Muhammad (2013), inspected the long-term connection between government education spending and economic expansion. The investigation utilized heterogeneous panel data analysis. Panel unit root test are applied for checking stationarity. The single equation approach of panel co-integration (Kao, 1999); Pedroni&#39;s Residual-Based Panel of co-integration Test (1997, 1999) was applied to ascertain the presence of long-term connection between public education spending and gross domestic production. Finally Panel fully modified OLS result uncovered that the effect of government public education on economic expansion is more prominent in developing nations as contrasted with the developed nations, which confirmed the &quot;catching-up effect&quot; in developing nations. Mehmet and Sevgi (2013), inspected the nexus between education spending and economic expansion in Turkey. The examination utilized econometric method as the principal investigation instrument. The result uncovered a positive connection between education spending and economic expansion in the Turkish economy for the period 1970-2012. Implying that, education spending in Turkey positively affected economic expansion. Edame (2014) researched the determinants of Nigeria&rsquo;s public infrastructure spending, utilizing ECM. He found that pace (rate) of urbanization, government income, population density, external reserves, and kind of government collectively or independently impact on public spending on infrastructure. Aregbeyen and Akpan (2013) examined the long-term determinants of Nigeria&rsquo;s government spending, utilizing a disaggregated approach. In their examination, they found that foreign aid is significantly and positively influencing recurrent spending to the detriment of capital spending; that income (revenue) is likewise positively influencing government spending; that trade transparency (openness) is adversely impacting government spending; that debt service obligation diminishes all parts of government spending over the long-term; that the higher the size of the urban population, the higher would be government recurrent spending on economic services; solid proof that Federal government spending is one-sided with regards to recurrent spending, which increments substantially during election times. In likewise manner, Adebayo et al. (2014) researched the effect of public spending on industrial expansion of Nigeria through co-integration and causality and discovered that public spending on administration, economic services, and transfers remained negatively related with industrial expansion while government spending on social services remained positively related in the long-term. They concluded in this manner that there is no crowding-out impact. From these studies reviewed, there is proof that all the investigations joined economic, social, and political determinants of government spending. Srinivasan (2013), analyzed the causal nexus between public spending and economic expansion in India utilizing co-integration approach and error correction model from 1973 to 2012. The co-integration test result uncovered the presence of a long-term equilibrium connection between public spending and economic expansion. The error correction model estimate indicated unilateral causality which runs from economic expansion to public spending in the short-term and long-term. Mohd and Fidlizan (2012), narrowed down on the long-term relationship and causality between government spending in education and economic expansion in Malaysian economy from 1970-2010. The investigation utilized Vector Auto Regression (VAR). The result indicated that economic expansion co-integrated with fixed capital formation (CAP), labour force participation (LAB) and government spending on education (EDU). The Granger cause for education variable and vice versa. In addition, the investigation demonstrated that human capital like education variable goes a long way in affecting economic expansion. Consensus from the above investigations demonstrates that government spending impacts positively on economic expansion. Notable theories that support this case include; Keynes, Wagner, Peacock and Wiseman. Keynes, in his hypothesis draws a connection between public spending and economic expansion and infers that causality runs from public spending to income, meaning that public sector spending is an exogenous factor and public instrument for expanding national income. Again, it holds that expansion in government spending prompts higher economic expansion. Wagner, Peacock and Wiseman and numerous economists have developed various theories on public spending and economic expansion. Wagner positioned public sector spending as a behavioral variable that positively indicates if an economy is prospering. Notwithstanding, the neo classical growth model created by Solow opined that the fiscal policy doesn&#39;t have any impact on the expansion of national income. These multifaceted results obtained from prior investigations show that in reality public spending and other inputs in the education system may have some innate heterogeneity, suggesting that what holds in a given area or country may not hold in another. In the light of the above, this investigation sees that it is necessary to revise the allotment of public spending on education, with regards to the type of impact this spending has on education outcomes. <strong>2.4 Theoretical Framework</strong> The endogenous growth theory has been adopted as the appropriate theoretical framework for this study. This owes much to the fact that, the theory emphasizes the critical role of human capital development, through public investments on education, as a major driver of aggregate productivity in the economy. This is also supported by the work of Ogunleye, Owolabi, Sanyaolu, and Lawal, (2017) who ascertained how economic expansion is influenced by advancement in human capital from 1981 to 2015. In this study it was discovered that economic expansion is greatly influenced by advancement in human capital. Also, economic expansion appeared to facilitated by secondary education enrolment, tertiary education enrolment, and aggregate spending on health and education by the government. <strong>2.5 Research Gap</strong> Though, so much research work has been carried out on the relationship between human capital development, Public Sector Expenditure on Education and Economic expansion in Nigeria, a lot still needed to be done to address some abnormities in these studies. Of note, is that methods adopted in most of these studies are faced with methodological limitations and policy carry-overs, not minding that no two economies are the same. This study therefore, seeks to fill these gaps created by previous researches. Importantly, time plays a vital role in research, making it imperative for continuous and up to date studies, so as to keep abreast with changes as quickly as possible. In the study carried out by Ojewumi and Oladimeji (2016), time series data covering from 1981-2013 was used, while Muhammad and Benedict (2015), used time series data from 1981-2010. These studies above used time series data of 1981 to 2013 and 1981 to 2010 respectively, while this study used updated data covering 1981-2018, thereby making the study current and up to date. &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <strong>Chapter Three</strong> <strong>Research Methods</strong> <strong>3.1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Research Design</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ex post facto research design and econometric procedures of analysis will be employed for empirical investigation. <strong>3.2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Model Specification</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Here, we specify a model which captures the relationship between real gross domestic product in per capita terms and the selected education enrolment variables. &nbsp; &nbsp; (3.1) In the above model, <em>Ln</em> denotes natural log, <em>PER_RGDP</em> denotes real gross domestic product in per capita terms,<em> PER_PEE</em> denotes public expenditure on education in per capita terms, <em>PENR</em> denotes percentage of primary education enrolment from population total, <em>SENR</em> denotes percentage of secondary education enrolment from population total, and <em>TENR</em> denotes percentage of tertiary education enrolment from population total. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; For further empirical analysis we can explicitly express the above model in the form of an autoregressive distributed lag (ARDL) model: &nbsp; &nbsp; (3.2) Here, based on economic theory and intuition all of the coefficients are expected to be positive. <strong>3.3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Estimation Procedure</strong> <strong>3.3.1&nbsp;&nbsp;&nbsp; Unit Root Test with Breaks</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Unlike the popularly used unit root tests (e.g. ADF and PP) which test the null of non-stationarity without accounting for possible breaks-points in data, the break-point unit root test of Peron (1989) tests the null of non-stationarity against other alternatives while accounting for a single break-point in the given data. The alternative hypotheses for this test are succinctly described in the following equations: &nbsp; &nbsp; (3.3) &nbsp; &nbsp; (3.4) &nbsp; &nbsp; (3.5) The first equation captures a break in the intercept of the data with the intercept-break dichotomous variable <em>I_t</em> which takes on values of 1 only when <em>t</em> surpasses the break-point <em>Br</em>; the second captures a break in the slope of the data with a regime-shift dichotomous variable <em>T_t*</em> which takes on values of 1 only when <em>t </em>surpasses the break-point <em>Br</em>; and the third equation captures both effects concurrently with the &ldquo;crash&rdquo; dichotomous variable <em>D</em> which takes on values of 1 only when <em>t</em> equals <em>Br</em>+1. <strong>3.3.2&nbsp;&nbsp;&nbsp; ARDL Bounds Cointegration Approach</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The popularly-used residual-based cointegration methods may not be very useful when the time-series under consideration attain stationarity at different levels. On the other hand, in addition to being econometrically efficient for small sample cases (<em>n</em> &lt; 30), the bounds cointegration method developed by Pesaran and Shin (1999) is particularly useful for combining time-series that attain stationarity at levels and first-difference. The bounds cointegration method makes use of upper bounds and lower bounds derived from 4 pairs of critical values corresponding to 4 different levels of statistical significance: the 1% level, the 2.5% level, the 5% level, and the 10% level. The null of &ldquo;no cointegration&rdquo; is to be rejected only if the computed bounds f-statistic surpasses any of the upper bounds obtained from a chosen pair of critical values, while the alternative hypothesis of cointegration is to be rejected only if the bounds f-statistic falls below any of the lower bounds obtained from a chosen pair of critical values. Therefore, in contrast to other cointegration tests, the bounds test can be inconclusive if the bounds f-statistic neither surpasses the chosen upper bound nor falls below the chosen lower bound. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; To obtain the bounds f-test statistic, an f-test is performed jointly on all of the un-differenced explanatory variables of the &ldquo;unrestricted&rdquo; error correction model (ECM) derived from any corresponding autoregressive distributed lag (ARDL) model such as the previously specified empirical ARDL model in (3.2). This takes the general form: &nbsp; &nbsp; (3.6) where &Delta;<em>i_t</em> denotes the chosen endogenous variable in first difference; &Delta;<em>j_t</em> and &Delta;<em>k_t</em> denote the chosen exogenous variables in first differences;&nbsp; and <em>e_t</em> denotes the stochastic component. Choosing the best lag-length to be included is made possible by information criteria such as the Akaike and the Schwarz Information Criterion. In the case where the bounds cointegration test disapproves the null, a &ldquo;restricted&rdquo; version of the error correction model can be estimated along-side a long-run model to capture the relevant short-run and long-run dynamics as seen in the following expressions: &nbsp; &nbsp; (3.7) &nbsp; &nbsp; (3.8) Here, the error correction term <em>_t</em>_-1 is non-positive and bounded between 0 and 1 (or 0 and 100) in order to capture the short-run rate of adjustment to long run equilibrium, while the coefficients <em>₁</em>,&hellip;,<em>_j</em>&nbsp; in (3.7) capture the state of long-run equilibrium and are obtained from <em>₁</em>=<em>b₂</em>/<em>b₁</em>,&hellip;, <em>_j</em>=<em>b_j</em>/<em>b₁</em> respectively. &nbsp; &nbsp; &nbsp; <strong>3.4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Model Evaluation Tests and Techniques</strong> <strong>3.4.1&nbsp;&nbsp;&nbsp; R² and Adjusted R²</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The R² and the adjusted R² both provide measures of goodness-of-fit. However, the adjusted R² is preferably used because it is robust against redundant regressors which inflate the conventional R². They involve the following statistics: &nbsp; &nbsp; (3.9) &nbsp; &nbsp; (3.10) where <em>SS_r</em> denotes the sum of squares of the regression residuals, <em>SS_t</em> denotes the total sum of squares of the dependent variable, <em>n</em> denotes the number of observations, and <em>k</em> denotes the number of regressors (Verbeek, 2004). <strong>3.4.2&nbsp;&nbsp;&nbsp; T-Test and F-Test</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The t-test and the f-test can be utilized to evaluate hypotheses pertaining to statistical significance of the parameters in a regression. Particularly, the t-test may be applied to a single parameter while the f-test may be applied to multiple parameters. They involve the following statistics: &nbsp; &nbsp; (3.11) &nbsp; &nbsp; (3.12) where <em>a_k</em> denotes a single parameter-estimate, <em>se </em>denotes its standard error, <em>R²</em> denotes the coefficient of determination of the regression, <em>N</em> denotes the number of observations, and <em>J</em> denotes the number of regressors. For the t-test, the statistical insignificance null hypothesis is to be rejected only if <em>t_i</em> exceeds its 5% critical-value, while for the f-test the joint statistical insignificance null hypothesis is to be rejected only if <em>f</em> exceeds its 5% critical-value at <em>N-J</em> and <em>J-1</em> degrees of freedom (Verbeek, 2004). <strong>3.4.3&nbsp;&nbsp;&nbsp; Residual Normality Test</strong> The Jarque-Bera test statistic (Jarque and Bera, 1987) is useful in determining whether the residuals of a regression are normally distributed. The Jarque-Bera statistic is computed as: &nbsp; &nbsp; (3.13) where <em>S</em> is the skewness, <em>K</em> is the kurtosis, and <em>N</em> is the number of observations. Under the null hypothesis of a normal distribution, the Jarque-Bera statistic is distributed as <em>X²</em> with 2 degrees of freedom. Therefore, the null hypothesis is to be accepted if the absolute value of the Jarque-Bera statistic exceeds the observed value under the null hypothesis. Contrarily, the null hypothesis is to be rejected if the absolute value does not exceed the observed value. <strong>Heteroskedasticity Test</strong> The Breusch-Pagan-Godfrey test (Breusch and Pagan, 1979; Godfrey, 1978) evaluates the null hypothesis of &ldquo;no heteroskedasticity&rdquo; against the alternative hypothesis of heteroskedasticity of the form , where is a vector of independent variables. The test is performed by completing an auxiliary regression of the squared residuals from the original equation on . The explained sum of squares from this auxiliary regression is then divided by to give an LM statistic, which follows a chi square <em>X² </em>distribution with degrees of freedom equal to the number of variables in <em>Z </em>under the null hypothesis of no heteroskedasticity. Therefore, the null hypothesis is to be accepted if the LM statistic exceeds the observed value under the null hypothesis. Contrarily, the null hypothesis is to be rejected if the LM statistic does not exceed the observed value. <strong>3.4.5&nbsp;&nbsp;&nbsp; Serial Correlation Test</strong> The Godfrey (1978) Lagrange multiplier (LM) test is useful when testing for serial correlation in the residuals of a regression. The LM test statistic is computed as follows: First, assuming there is a regression equation: &nbsp; &nbsp; (3.14) where <em>&beta;</em> are the estimated coefficients and <em>&epsilon;</em> are the errors. The test statistic for the lag order <em>&rho;</em> is based on the regression for the residuals <em>&epsilon; = y - XḂ</em> which is given by: &nbsp; &nbsp; (3.15) The coefficients <em>𝛾</em> and <em>𝛼</em><em>_&delta;</em>are expected to be statistically insignificant if the null hypothesis of &ldquo;no serial correlation&rdquo; is to be accepted. On the other hand, the null hypothesis cannot be accepted if the coefficients <em>𝛾</em> and <em>𝛼</em><em>_&delta;</em>are found to be statistically significant. <strong>3.4.6&nbsp;&nbsp;&nbsp; Model Specification Test</strong> The Ramsey (1969) Regression Error Specification Test (RESET) is a general test for the following types of functional specification errors: Omitted variables; some relevant explanatory variables are not included. Incorrect functional form; some of the dependent and independent variables should be transformed to logs, powers, etc. Correlation between the independent variables and the residuals. Ramsey (1969) showed that these specification errors produce a non-zero mean vector for the residuals. Therefore, the null and alternative hypotheses of the RESET test are: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3.16) The RESET test is based on an augmented regression which is given as: &nbsp; &nbsp; (3.17) The test of the null hypothesis of a well-specified model is tested against the alternative hypothesis of a poorly specified model by evaluating the restriction <em>𝛾</em><em> = 0</em>. The null hypothesis is to be accepted if <em>𝛾</em><em> = 0</em>, whereas the null hypothesis is to be rejected if <em>𝛾</em><em> &ne; 0</em>. The crucial factor to be considered in constructing the augmented regression model is determining which variable should constitute the <em>Z</em> variable. If <em>Z</em> is an omitted variable, then the test of <em>𝛾</em><em> = 0</em> is simply the omitted variables test. But if <em>y</em> is wrongly specified as an additive relation instead of a multiplicative relation such as <em>y =</em><em>𝛽</em><em>₀</em> X^𝛽¹X^𝛽² + 𝜖 then the test of <em>𝛾</em><em> = 0 </em>is a functional form specification test. In the latter case the restriction <em>𝛾</em><em> = 0 </em>is tested by including powers of the predicted values of the dependent variables in <em>Z</em> such that . <strong>3.4.7&nbsp;&nbsp;&nbsp; CUSUMSQ Stability Test</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; For the test of stability, cumulative sum of recursive residuals (CUSUM) and cumulative sum of recursive residuals squares (CUSUMSQ) tests as proposed by Brown, Durbin, and Evans (1975) was employed. The technique is appropriate for time series data and is recommended for use if one is uncertain about when a structural change might have taken place. The null hypothesis is that the coefficient vector &szlig; is the same every period. The CUSUM test is based on the cumulated sum of the residuals: &nbsp; &nbsp; &nbsp; (3.18) where &nbsp; &nbsp; (3.19) and &nbsp; &nbsp; (3.20) <strong>3.5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Sources of Data</strong> The Central bank of Nigeria served as the main source of data collection. This implies also that the study adopted secondary data. <strong>Chapter Four</strong> <strong>Empirical Results</strong> <strong>4.1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Descriptive Statistics</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Before going into cointegration analysis, we will attempt to briefly examine the properties of the data with descriptive statistics. Table 4.1 and Figures 4.1 to 4.5 will be acknowledged for this purpose. Table 4.1: Descriptive Statistics &nbsp; PER_RGDP PER_PEE PENR SENR TENR Mean 264316.01 635.72 23096192.94 5796345.78 787115.08 Median 232704.55 361.03 19747039.31 4410684.33 755776.70 Maximum 385349.04 2340.12 46188979.59 11840028.21 1648670.36 Minimum 199039.15 7.38 9554076.94 1846106.82 49626.49 Std. Dev. 66113.04 681.06 9425336.46 3142601.76 592505.50 Skewness 0.65 0.77 0.59 0.79 0.17 Kurtosis 1.83 2.43 2.27 2.15 1.36 Jarque-Bera 4.88 4.24 3.01 5.14 4.47 Probability 0.09 0.12 0.22 0.08 0.11 Observations 38 38 38 38 38 &nbsp; Figure 4.1: Trend of Real Gross Domestic Product (RGDP) Per Capita &nbsp; &nbsp; &nbsp; Figure 4.2: Trend of Public Expenditure on Education (PEE) Per Capita &nbsp; &nbsp; Figure 4.3: Trend of Primary School Enrolment (PENR) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Figure 4.4: Trend of Secondary School Enrolment (SENR) &nbsp; &nbsp; Figure 4.5: Trend of Tertiary School Enrolment (TENR) &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; From the second column of Table 4.1, RGDP per capita mean is NGN 264, 316.01 ($734.21). This critically lags behind RGDP per capita mean in all developed (OECD) countries and underscores the need for human and non-human capital development. Further, RGDP per capita maximum is NGN 385, 349.04 while its minimum is NGN 199, 039.15. Given that the trend of RGDP per capita is positively sloped as seen in Figure 4.1, the disparity between RGDP per capita maximum and its minimum indicates growth in RGDP per capita during the period under investigation. Lastly, the Jarque-Bera statistic (4.88) and probability value (0.09) of RGDP per capita simply suggest that it follows a normal distribution, with NGN 66, 113.04 as its standard deviation. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; From the third column of Table 4.1, PEE per capita mean is NGN 635.72 ($1.77). Just like RGDP per capita, this critically lags behind PEE per capita mean in all developed (OECD) countries and underscores the need for more government intervention in the education sector. Further, PEE per capita maximum is NGN 2, 340.12 while its minimum is NGN 7.38. Given that the trend of PEE per capita is positively sloped exponentially as seen in Figure 4.2, the disparity between PEE per capita maximum and its minimum indicates rapid growth in PEE per capita during the period under investigation. Lastly, the Jarque-Bera statistic (4.24) and probability value (0.12) of PEE per capita simply suggest that it follows a normal distribution, with NGN 681.06 as its standard deviation. From the fourth column of Table 4.1, PENR mean is 23096192.94. This represents about 18.33% of total population mean (126036036.63) and indicates high primary school enrolment during the period under investigation. Further, PENR maximum is 46188979.59 while its minimum is 9554076.94. Given that the trend of PENR is positively sloped linearly as seen in Figure 4.3, the disparity between PENR maximum and its minimum indicates consistent growth in PENR during the period under investigation. Lastly, the Jarque-Bera statistic (3.01) and probability value (0.22) of PENR simply suggest that it follows a normal distribution, with 9425336.46 as its standard deviation. From the fifth column of Table 4.1, SENR mean is 5796345.78. This represents about 4.60% of total population mean (126036036.63) and indicates relatively low secondary school enrolment during the period under investigation. Further, SENR maximum is 11840028.21 while its minimum is 1846106.82. Given that the trend of SENR is positively sloped exponentially as seen in Figure 4.4, the disparity between SENR maximum and its minimum indicates rapid growth in SENR during the period under investigation. Lastly, the Jarque-Bera statistic (5.14) and probability value (0.08) of SENR simply suggest that it follows a normal distribution, with 3142601.76 as its standard deviation. From the sixth column of Table 4.1, TENR mean is 787115.08. This represents about 0.63% of total population mean (126036036.63) and indicates very low tertiary school enrolment during the period under investigation. Further, TENR maximum is 1648670.36 while its minimum is 49626.49. Given that the trend of TENR is positively sloped concavely as seen in Figure 4.5, the disparity between TENR maximum and its minimum indicates slow growth in TENR during the period under investigation. Lastly, the Jarque-Bera statistic (4.47) and probability value (0.11) of TENR simply suggest that it follows a normal distribution, with 592505.50 as its standard deviation. From the descriptive statistics above, it is obvious that substantial disparities exist between the maximum and minimum values of the variables, especially for PEE per capita and TENR. This may distort the regression results of the cointegration analysis and may also lead to unnecessarily large regression coefficients. In order to avoid these problems, we have transformed the variables in two major ways. Firstly, we have reduced disparity among the variables by expressing PENR, SENR, and TENR as percentages of population total. Secondly, we have downsized all the variables to a smaller scale by expressing them in natural log form. Therefore instead of RGDP, PEE per capita, PENR, SENR, and TENR, we now have Ln_PER_RGDP, Ln_PER_PEE, Ln_PENR, Ln_SENR, and Ln_TENR respectively as our investigative variables. &nbsp; &nbsp; &nbsp; <strong>4.2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Break-Point Unit Root Test Results</strong> Table 4.2: Break-Point Unit Root Test Result Summary Variables Lags Included Specification Break Date ADF Test Statistic 5% Critical Value Summary <em>Ln_PER_RGDP</em><em>_t</em> 0 Intercept &amp; Trend 2001 -3.3506 -5.1757 Non-Stationary <em>∆Ln_PER_RGDP</em><em>_t</em> 2 Intercept &amp; Trend 2001 -5.4176 -5.1757 Stationary <em>Ln_PER_PEE</em><em>_t</em> 0 Intercept &amp; Trend 2004 -3.3665 -5.1757 Non-Stationary <em>∆Ln_PER_PEE</em><em>_t</em> 5 Intercept &amp; Trend 1995 -5.6226 -5.1757 Non-Stationary <em>Ln_PENR</em><em>_t</em> 7 Intercept &amp; Trend 2004 -7.6901 -5.1757 Stationary <em>Ln_SENR</em><em>_t</em> 3 Intercept &amp; Trend 1998 -5.0584 -5.1757 Non-Stationary <em>∆Ln_SENR</em><em>_t</em> 3 Intercept &amp; Trend 2016 -6.4199 -5.1757 Stationary <em>Ln_TENR</em><em>_t</em> 1 Intercept &amp; Trend 1998 -6.9768 -5.1757 Stationary Note(s): Lag selection based on Schwarz Information Criterion (SIC) &nbsp; As seen in the above table, there are different orders of integration for the time-series variables. Specifically, <em>Ln_PENR</em> and <em>Ln_TENR</em> are stationary at levels, while others are stationary only at the first difference. The bounds cointegration method is more appropriate in this case because it permits the combination of stationary and difference-stationary time series. <strong>4.3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ARDL Bounds Cointegration Test Results</strong> Table 4.3: Lag/Model Selection Criteria Table Number of Models Evaluated: 16 Dependent Variable: <em>Ln_PER_RGDP</em> S|N Model AIC Specification 1 16 -4.0889 ARDL(1, 0, 0, 0, 0) 2 15 -4.0552 ARDL(1, 0, 0, 0, 1) 3 12 -4.0477 ARDL(1, 0, 1, 0, 0) 4 14 -4.0448 ARDL(1, 0, 0, 1, 0) 5 8 -4.0445 ARDL(1, 1, 0, 0, 0) 6 11 -4.0212 ARDL(1, 0, 1, 0, 1) 7 13 -4.0121 ARDL(1, 0, 0, 1, 1) 8 10 -4.0118 ARDL(1, 0, 1, 1, 0) 9 7 -4.0066 ARDL(1, 1, 0, 0, 1) 10 6 -3.9994 ARDL(1, 1, 0, 1, 0) 11 4 -3.9970 ARDL(1, 1, 1, 0, 0) 12 9 -3.9894 ARDL(1, 0, 1, 1, 1) 13 3 -3.9672 ARDL(1, 1, 1, 0, 1) 14 5 -3.9626 ARDL(1, 1, 0, 1, 1) 15 2 -3.9589 ARDL(1, 1, 1, 1, 0) 16 1 -3.9357 ARDL(1, 1, 1, 1, 1) Note(s): * indicates chosen optimal lag specification based on the Akaike Information Criterion The Akaike criterion shows that ARDL(1, 0, 0, 0, 0) is the best lag specification for the ARDL model, thereby indicating that it is best to include only a single lag of the endogenous variable (<em>Ln_PER_RGDP</em>), and 0 lags of the other exogenous variables (<em>Ln_PER_PEE, Ln_PENR, Ln_SENR, </em>and <em>Ln_TENR</em>). On this basis, an ARDL model was estimated and the bounds cointegration method was applied to test for cointegration as seen in the following tables. Table 4.4: Auto Regressive Distributed Lag (ARDL) Model Estimates Dependent Variable: <em>Ln_PER_RGDP</em><em>_t</em> Regressors Coefficient Standard Error t-statistic Prob. <em>Ln_PER_RGDP _t-1</em> 0.723844 0.063884 11.33053 0.0000 <em>Ln_PER_PEE</em><em>_t</em> 0.006558 0.014438 0.454194 0.6529 <em>Ln_PENR</em><em>_t</em> 0.166945 0.048731 3.425881 0.0017 <em>Ln_SENR_t</em> 0.105751 0.044395 2.382033 0.0235 <em>Ln_TENR</em><em>_t</em> 0.033421 0.036354 0.919326 0.3650 <em>C</em> 2.80666 0.598588 4.688802 0.0001 &nbsp; Table 4.5: Bounds Cointegration Test &nbsp; Computed Wald (F-Statistic): 8.5420 10% level 5% level 2.5% level 1% level <em>k </em>= 4 I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) <em>F</em>* 2.45 3.52 2.86 4.01 3.25 4.49 3.74 5.06 Source: Pesaran et al. <em>k</em> signifies the number of regressors <em>F</em>* corresponds to the model with unrestricted intercept and trend In the above table, the bounds test statistic (8.5420) surpasses the upper-bound (4.01) at the 5% level of significance and therefore leads to the rejection of the null hypothesis of &ldquo;no cointegration&rdquo;. Based on this result, a &ldquo;restricted&rdquo; error correction model was estimated as well as a long-run &lsquo;equilibrium&rsquo; model as seen in the subsequent tables and equations. Table 4.6a: Error Correction Model Dependent Variable: &Delta;<em> Ln_PER_RGDP</em><em>_t</em> Regressors Coefficient Standard Error t-statistic Prob. <em>∆Ln_PER_PEE</em><em>_t</em> 0.0065 0.0144 0.4541 0.6529 <em>∆Ln_PENR</em><em>_t</em> 0.1669 0.0487 3.4258 0.0017 <em>∆Ln_SENR</em><em>_t</em> 0.1057 0.0443 2.3820 0.0235 <em>∆Ln_TENR</em><em>_t</em> 0.0334 0.0363 0.9193 0.3650 <em>ECT _t-1</em> -0.2761 0.0638 -4.3227 0.0001 &nbsp; Table 4.6b: Long-Run Model Dependent Variable: <em>Ln_PER_RGDP</em><em>_t</em> Regressors Coefficient Standard Error t-statistic Prob. <em>Ln_PER_PEE</em><em>_t</em> 0.0237 0.0489 0.4850 0.6310 <em>Ln_PENR</em><em>_t</em> 0.6045 0.1253 4.8213 0.0000 <em>Ln_SENR</em><em>_t</em> 0.3829 0.1106 3.4602 0.0016 <em>Ln_TENR</em><em>_t</em> 0.1210 0.1500 0.8064 0.4261 <em>C</em> 10.1633 0.5757 17.6524 0.0000 &nbsp; In the error correction model, the error correction term (<em>ECT_t-1</em>) is expectedly negative and statistically significant at the 5% level (based on its <em>p</em>-value (0.0001)). Its magnitude (-0.2761) indicates a low but significant rate of adjustment to long-run equilibrium and specifically implies that approximately 27.61% of all discrepancies in long-run equilibrium will be corrected in each period. On the other hand, in the long-run model, the first long-run coefficient (<em>Ln_PER_PEE</em><em>_t</em>) is expectedly positive but its <em>p</em>-value (0.6310) indicates that it is statistically insignificant at the 5% level of significance, thereby implying that increment in <em>Ln_PER_PEE</em> will not cause <em>Ln_PER_RGDP</em> to increase. . Similarly, the fourth long-run coefficient (<em>Ln_TENR</em>) is expectedly positive but its <em>p</em>-value (0.4261) indicates that it is statistically insignificant at the 5% level of significance, thereby implying that increment in <em>Ln_TENR</em> will not cause <em>Ln_PER_RGDP</em> to increase. On the other hand, the second long-run coefficient (<em>Ln_PENR</em>) is expectedly positive and its <em>p</em>-value (0.0000) indicates that it is statistically significant at the 5% level of significance, thereby implying that increment in <em>Ln_PENR</em> will cause <em>Ln_PER_RGDP</em> to increase by 0.6045. Similarly, the third long-run coefficient (<em>Ln_SENR</em>) is expectedly positive and its <em>p</em>-value (0.0016) indicates that it is statistically significant at the 5% level of significance, thereby implying that increment in <em>Ln_SENR</em> will cause <em>Ln_PER_RGDP</em> to increase by 0.3829. The intercept also appears to be positive and statistically significant thereby indicating that the long-run model has a positive autonomous component measuring up to 10.1633 units. <strong>4.4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Model Evaluation Results</strong> <strong>4.4.1&nbsp;&nbsp;&nbsp; Test of Goodness-of-Fit</strong> Table 4.7: Test of Goodness-of-Fit Summary Model R² Adj. R² ARDL Model 0.9875 0.9854 ECM 0.6948 0.6567 &nbsp; The adjusted R² of the ARDL model has a magnitude of 0.9854 and therefore implies that the ARDL model explains as much as 98.54% of the variation in its endogenous variable. Further, the adjusted R² of the ECM has a magnitude of 0.6567 and therefore implies that the error correction model (ECM) explains as much as 65.67% of the variation in its endogenous variable. <strong>4.4.2&nbsp;&nbsp;&nbsp; T-Test and F-Test</strong> Table 4.8: F-Test Summary Model F-Statistic 5% Critical Value Prob. Remarks ARDL Model 490.1238 F(5,31) = 2.52 0.0000 Jointly Significant @ 5% ECM 15.2700 F(4,32) = 2.67 0.0000 Jointly Significant @ 5% &nbsp; The F-statistic (490.1238) for the ARDL model exceeds its 5% critical value (2.66), thereby implying that the parameters of the ARDL model are jointly significant at the 5% level of significance. Further, the F-statistic (15.2700) of the ECM also exceeds its 5% critical value (2.84), thereby implying that the parameters of the error correction model (ECM) are jointly significant at the 5% level of significance. Table 4.9: T-Test Summary T-Test for the Long-Run Estimates Regressors t-statistic 5% Critical Value Remarks <em>Ln_PER_PEE</em><em>_t</em> 0.4850 1.9600 Insignificant <em>Ln_PENR</em><em>_t</em> 4.8213 1.9600 Significant <em>Ln_SENR</em><em>_t</em> 3.4602 1.9600 Significant <em>Ln_TENR</em><em>_t</em> 0.8064 1.9600 Insignificant <em>C</em> 17.6524 1.9600 Significant &nbsp; T-Test for the Error Correction Model (ECM) Estimates &nbsp; Regressors t-statistic 5% Critical Value Remarks &nbsp; <em>∆Ln_PER_PEE</em><em>_t</em> 0.4541 1.9600 Insignificant &nbsp; <em>∆Ln_PENR</em><em>_t</em> 3.4258 1.9600 Significant &nbsp; <em>∆Ln_SENR</em><em>_t</em> 2.3820 1.9600 Significant &nbsp; <em>∆Ln_TENR</em><em>_t</em> 0.9193 1.9600 Insignificant &nbsp; <em>ECT _t-1</em> -4.3227 1.9600 Significant &nbsp; &nbsp; In the long-run model, the t-statistics for the first and fourth parameters are less than the 5% critical value (1.96), thereby indicating that the first and fourth parameters are statistically insignificant at the 5% level of significance, while the t-statistic for the second, third, and fifth parameters are greater than the 5% critical value (1.96), thereby indicating that they are statistically significant at the 5% level of significance. Similarly, in the ECM, the t-statistics for the first and fourth parameters are less than the 5% critical value (1.96), thereby indicating that the first and fourth parameters are statistically insignificant at the 5% level of significance, while the t-statistic for the second, third, and fifth parameters are greater than the 5% critical value (1.96), thereby indicating that they are statistically significant at the 5% level of significance. <strong>Normality Test</strong> Table 4.10: Jarque-Bera Normality Test Summary Model Skewness Kurtosis JB Statistic Prob. ARDL Model -0.5558 2.8731 1.9297 0.3810 ECM -0.7369 2.9430 3.3544 0.1868 &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; In the ARDL model, the <em>p</em>-value (0.3810) of the J-B test exceeds the 0.05 benchmark, and therefore indicates that the residuals of the ARDL model are normally distributed. Further, in the ECM, the <em>p</em>-value (0.1868) of the J-B test also exceeds the 0.05 benchmark, and therefore indicates that the residuals of the error correction model (ECM) are normally distributed. <strong>4.4.4&nbsp;&nbsp;&nbsp; Heteroskedasticity Test</strong> Table 4.11: Breusch-Pagan-Godfrey Heteroskedasticity Test Summary Model BPG Statistic (Obs*R-sq) Prob. ARDL Model 4.3085 0.5059 ECM 7.2979 0.1209 &nbsp; In the ARDL model, the <em>p</em>-value (0.5059) of the BPG test exceeds the 0.05 benchmark, and therefore indicates that the residuals of the ARDL model are homoskedastic. Similarly, in ECM, the <em>p</em>-value (0.1209) of the BPG test also exceeds the 0.05 benchmark, and therefore indicates that the residuals of the error correction model (ECM) are homoskedastic. <strong>4.4.5&nbsp;&nbsp;&nbsp; Autocorrelation Test</strong> Table 4.12: Breusch-Godfrey Serial Correlation Test Summary Model BG Statistic (Obs*R-sq) Prob. ARDL Model 0.1021 0.7493 ECM 0.8776 0.3488 &nbsp; In the ARDL model, the <em>p</em>-value (0.7493) of the BG test exceeds the 0.05 benchmark, and therefore indicates that the residuals of the ARDL model are not serially correlated. Similarly, in ECM, the <em>p</em>-value (0.3488) of the BG test also exceeds the 0.05 benchmark, and therefore indicates that the residuals of the error correction model (ECM) are not serially correlated. <strong>4.4.6&nbsp;&nbsp;&nbsp; Functional Specification Test</strong> Table 4.13: RESET Model Specification Test Summary Model Test Statistics Value Degrees of Freedom Prob. ARDL Model t-statistic 0.805722 30 0.4267 F-statistic 0.649189 (1, 30) 0.4267 ECM t-statistic 0.533837 31 0.5973 F-statistic 0.284982 (1, 31) 0.5973 &nbsp; In the ARDL model, the F-statistic <em>p</em>-value (0.4267) of the RESET test exceeds the 0.05 benchmark, and therefore indicates that the ARDL model was adequately specified. Further, in the ECM, the F-statistic <em>p</em>-value (0.5973) of the RESET test exceeds the 0.05 benchmark, and therefore indicates that the error correction model (ECM) was adequately specified. <strong>4.4.7&nbsp;&nbsp;&nbsp; CUSUMSQ Stability Test</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The Cumulative Sum of Residuals (CUSUM) Squares test was used to examine the stability of the ARDL model. The result is captured in the following figure. Figure 4.6: CUSUMSQ Plot &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; In interpreting the CUSUMSQ test, we may conclude that there is instability only if the CUSUMSQ plot falls outside the boundaries of the upper and lower dotted lines which signify the &ldquo;5% level of significance&rdquo;. In this regard, the plot of the CUSUMSQ test in the above figure shows that the ARDL model becomes momentarily unstable in year 2002. However, apart from 2002, the ARDL model appears to be stable in every other year as indicated by the confinement of the CUSUMSQ plot between the upper and lower dotted lines. Overall, considering the fact that this momentary period of instability does not coincide with any major event in Nigeria&rsquo;s education sector, we can conclude that instability is due to chance, and that the estimates of the model are reliable because apart from year 2002 the ARDL model appears to be stable.