Higher Education: Demand and Supply

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Introduction

The provision of higher education in a country is affected by a number of factors including population, rural and urban population distribution, enrollment trends, gender, and ethnic background, etc. It is the responsibility of the Federal and State governments to ensure that there is sufficient number of colleges and universities to fulfill the educational needs of the population. There are various datasets published by National Center for Education Statistics, US Census Bureau, and US Department of Education, which can be analyzed to identify the key trends and relationships between different variables to understand the education status of the country. In this study, the demand and supply of higher education in the US is analyzed by conducting a parametric test.

The model considers the supply of higher education as the dependent variable and the demand for higher education as the independent variable. The supply of higher education (S) is determined by the number of higher education institutes in the US (National Center for Education Statistics (NCES), 2018a), and its data is collected from Statista. The demand for higher education (D) is determined by the number of undergraduate enrollment in the US (National Center for Education Statistics (NCES), 2018b). The relationship between demand and supply of higher education is based on the basic economic principle which states that the supply of a product or service is derived from the demand for it. A control variable is also added to the model is Cost (C), which represents the “average cost for tuition and other fees* at universities in the United States” (Institute for College Access & Success, 2018). The reason for adding the cost variable is that both demand and supply of higher education like any other service is affected by the tuition fee and other expenses incurred by students. Therefore, it could help in improving the model’s results.

The current research is a longitudinal study of the relationship between dependent and independent variables. In total, 15 values of each variable are collected from 1980 to 2016. The reason for this limited sample size is the inability of the researcher to find comparative data for all variables in the same period. The impact of the limited size sample on research outcomes would be assessed in the conclusion part of this report.

(I) The estimation of the relationship between dependent and independent/control variables is made by implementing a multivariate regression model that generates a linear equation in the following manner.

Where

S_it =Number of Higher Education Institutes

D_it =Total Enrollment

C_it =Average Cost for Tuition Fees

The multivariate regression model assists in determining the changes in the values of the dependent variable caused by the changes in the values of explanatory/independent variables (Keith, 2015). The strength and direction of the coefficient of the slope, βn is assessed for predicting the relationship between the selected variables. In the equation (I), ε_itrepresents the error or residual of the model, which is the value of the dependent variable not entirely predicted by the regression analysis.

Regression Analysis

The results of the multivariate regression model are given in Table 1.1-1.2.

Multiple R	0.955515365
R Square	0.913009612
Adjusted R Square	0.898511214
Standard Error	135.6287559
Observations	15

Table 1.1. Regression Statistics

ANOVA	df	SS	MS	F	Significance F
Regression	2	2316801.82	1158400.91	62.97313782	4.33339E-07
Residual	12	220741.9132	18395.15943
Total	14	2537543.733

Table 1.2. Regression Output

	Coefficients	Standard Error	t Stat	P-value
Intercept	1817.780965	449.1381714	4.047264474	0.001618254
Average Cost for Tuition and Fees	0.016935473	0.031288687	0.541265047	0.598230068
Total Enrollment	0.127903236	0.038741418	3.301459872	0.006323626

Table 1.3. Regression Analysis

Adjusted R²

The adjusted R² is 0.8985. It indicates that approximately 89.85% of the variation in the number of higher education institutions (S) is explained by two independent variables— Total Enrollment (D) and Average Cost for Tuition and Fees (C).

Evaluation of Independent Variables Using a t-test

Table 2 provides the results of the t-tests for each of the independent variables.

	Coefficients	Standard Error	T-Stat	P-Value
Intercept	1817.780965	449.1381714	4.047264474	0.001618254
Average Cost for Tuition and Fees	0.016935473	0.031288687	0.541265047	0.598230068
Total Enrollment	0.127903236	0.038741418	3.301459872	0.006323626

Table 2. T-Test Analysis.

Analysis of t statistics

Total Enrollment:

H₀: βTotal Enrollment = 0; H_A; β Total Enrollment β0

Reject H₀ at the 5% level (P-value < 0.05)

Average cost for tuition and fees

H₀: β Average Cost for Tuition and Fees = 0; H_A; β Average Cost for Tuition and Fees β0

Do not reject H₀ at the 5% level (P-value > 0.05)

Analysis of F

H₀: βTotal Enrollment = βAverage Cost for Tuition and Fees = 0;

H_A: at least one β is not equal to zero

ANOVA	df	SS	MS	F	Significance F
Regression	2	2316801.82	1158400.91	62.97313782	4.33339E-07
Residual	12	220741.9132	18395.15943
Total	14	2537543.733

Table 3. F-Test Analysis.

F = 62.973

Critical value of F:

F(2,12) = 3.89

Since 59.5515 > 3.89, reject the null hypothesis. At least one of the β’s is not equal to zero.

Conclusion and General Comments

It could be concluded that the regression model implemented in this report has a high goodness of fit based on the value of adjusted R². It is crucial for a model to have a high value of adjusted R² as it implies that the relationship based on its results can be used for predicting changes in the value of the dependent variable. Although the current model used only two independent variables and 15 data observations, the higher value of adjusted R² means the model is robust, and it can be used in the real-life setting.

(II) The following regression equation is obtained from the values of coefficients given in Table 2.

The coefficient of the slope of Total Enrollment (D_it) has a higher value than that of Average Cost for Tuition and Fees (C_it). The research outcomes also indicate that there is a positive influence of Total Enrollment and Average Cost for Tuition and Fees. It implies that when the population grows and the number of individuals seeking higher education increases, the number of colleges and universities also increase. Furthermore, the positive relationship between cost (price) and supply implies that when the cost (price) goes up, the supply of higher education also increases. Since the level of confidence assumed for testing the results of the regression model is 95%, therefore the p-value is compared with the standard error term of 5%. The relationship between Supply and Total Enrollment is found to be significant since its p-value is less than 0.05. On the other hand, the relationship between Supply and Average Cost is found to be insignificant since its p-value is more than 0.05.

Although the current analysis is performed by using real-life data, there are many other instances in my personal life in which regression analysis can help to predict the relationship between different variables. Every decision, which can be measured in numerical terms, can be assessed by using the regression analysis. However, it must be understood that not every situation or model is linear, and there are other types of regression techniques that can be used to predict relationships. One real-life example is the determination of my month saving, which is affected by various factors including income and expenses. My monthly income includes work related pay that I receive from my employer and the money sent to me by my parents. My expenses include food, travel, leisure, and others. The regression model can be implemented in which my monthly saving is the dependent variable, and my income and expenses are independent variables. Furthermore, my monthly saving is affected when I am staying at my parents’ house. Therefore, a dummy variable could be added to the model representing the time when I am at the college residence (0) or when I am at my parents’ house (1).

a dummy variable could be added to the model

It is just one example, and there can be many decisions that could be analyzed by using the regression analysis. The model implemented in this report can be changed in the future given the assumptions made for the study are changed. It means that if the confidence level for testing the results is adjusted, then it could affect the significance of each variable. Furthermore, it is suggested that the value of adjusted R² can be improved by increasing the sample size or by adding more explanatory variables in the model.

References

Institute for College Access & Success. (2018). Average cost for tuition and other fees* at universities in the United States from 2000/01 to 2013/14 (in U.S. dollars). Web.

Keith, T. Z. (2015). Multiple regression and beyond: An introduction to multiple regression and structural equation modelling (2nd ed.). New York, NY: Routledge.

National Center for Education Statistics (NCES). (2018a). Number of higher education institutions in the United States from 1980 to 2015. Web.

National Center for Education Statistics (NCES). (2018b). Undergraduate enrollment numbers in the United States from 1970 to 2027, by full/part-time attendance (in 1,000). Web.