Returns to Investment in Higher Education: Is There a Difference between Distance Learning and Traditional Universities in the Fields of Physics, Mathematics, Social Studies, Computer Science and Economics?

In this paper, we extend the literature on the rate of returns to Investment in Higher Education towards studies in distance learning Universities. In particular, we explore the difference in returns between, on one hand, graduates of a distance learning university (the Hellenic Open University, HOU) and on the other hand, graduates from two traditional universities, in Greece. The data used in the analysis is collected with field research from graduates of Physics, Mathematics, Social Studies, Computer Science and Economics. Our findings show that the rate of return to investment in education for HOU graduates is about four times higher than that of the graduates of the two traditional Universities, for the first degree graduates and about double the rate for the Master’s degree graduates. From policy perspective, our results suggest that a distance learning University may not only be considered as a sec-ond chance to education for mature students, often facing time and budget restrictions, but, it may also be seen as a worthwhile investment enabling much higher private returns compared to the alternative route, i.e. following studies in traditional universities. Therefore, distance learning universities may be used by policy authorities as a vehicle to reduce income inequalities and increase social mobility.


Introduction
The theory of human capital was introduced in the general economic theory by the work of three scholars: Mincer (1958), Schultz (1961) and Becker (1964).
Since then the human capital theory and empirical studies have experienced a phenomenal growth. Human capital is now a major element of analysis in studies relating to the remuneration of workers, distribution of income, the likelihood of unemployment for various groups of people, migration between regions and between countries, social mobility between generations, technology and economic development. In the literature section below, we present and discuss the results from several empirical studies examining the returns to investment in higher education worldwide and in Greece.
The purpose of this paper is first, to provide an estimation of the returns to investment in education, i.e. the effects of a university degree on wages in Greece and second, to provide an estimation of the difference (if any) between the education returns of the Hellenic Open University (HOU) graduates and the traditional universities graduates. The data used was extracted from 2112 questionnaires that were collected with field research in 2014 1 from graduates of Physics, Mathematics, Social Studies, Computer Science and Economics.
The remainder of the paper is organized as follows. Section 2 presents a brief review of the literature regarding previous findings on returns to investment in education, with emphasis in Greece. Section 3 presents our model of a modified Mincer equation for measuring education returns, the specification of variables used, and we provide a description of the data and present the estimating methodology. Section 4 discusses the estimation results from our Mincer type model and presents the returns to investment in education in Greece for the distance learning University and traditional universities, as well as, the test of the difference between them. Finally, Section 5 contains concluding remarks and states the policy implications of our findings.

Literature Review
There have been several studies estimating the rate of return to higher education (see e.g. D 'Aguiar, & Harrison (2016), Naylor et al. (2015); Oreopoulos et al. (2013); Psacharopoulos (2012), Harmon (2011) and Heinrich & Hildebrand (2005) for some excellent surveys in different time periods). For Greece there have been several studies beginning as early as 1965. The first study was done by Leibestein in 1965 and found a "low" rate of return. Psacharopoulos (1982), and 1 Please see the "Data description" section below for details.  Lambropoulos and Psacharopoulos (1992) using the same data as Leibenstein (1967) and a specially designed questionnaire of the Statistical Service of Greece (NSSG) have found a rate of return of 15% for 1960, 14% for 1964, 15.1% for 1975, 10.5% for 1977, 13.6% for 1981 and 10.2% for 1985.
Ten years later, Patrinos (1995) using data from the Wage Survey of the National Statistical Service (NSSG) for the year 1977 and Kanellopoulos (1997) with data from the Household Survey of NSSG for year 1987-8, have found very similar rates of return, namely 5.6% and 5.4%, respectively.
Using more recent data of the 1993 Household Survey of NSSG, Magoula and Psacharopoulos (1999) estimated the rate of return for 1993 to be 6.3%. Two years later Tsakloglou and Cholezas (2001) estimated the rate of return for men and women using the Household Surveys for the years 1974, 1988 and 1995 and found them to be 9.3%, 6.2% and 8.7% for men for the respective years and 11.9%, 8.0% and 10.4% for women. Tsakloglou and Cholezas re-estimated the rate of return adjusting for the periods of unemployment of each individual but the differences are negligible. In a more recent work Prodromidis and Prodromidis (2008) using the same source of data have found estimates of rate of return for men and women for the years 1988, 1994 and 1998 as follows 3.9%, 6.3% and 7.6% for men for the respective years and 8.1%, 6.2% and 14.1% for women.
Four recent studies by Mitrakos et al. (2010), by Livanos and Pouliakas (2011), by Kanellopoulos et al. (2013) and by Kanellopoulos and Cholezas (2014) have used the Labor Survey of the NSSG and have estimated rates of return to higher education for more recent years. Mitrakos et al. (2010) have used the Labor Surveys of 2004-2007 to estimate the rate of return of twenty years after graduation for several professions. Their estimates range between 4% and 10.5%, while it is 9.3% for a post graduate degree and 7.8% for a doctorate. Livanos and Pouliakas (2011) have found that the rates of return for 2003 for men and women were 5.9% and 5.0% respectively for the first degree, 7.6% and 19.2% for a Master's and surprisingly negative for a Ph.D., −2.0% for men and −6.6% for women. Mitrakos et al., and Kanellopoulos and Cholezas have estimated and compared rates of return for men and women, for various professions for the periods 2004-2007 and 2010-2012, namely before and after the Greek debt crisis. Their results appear in Table 1.
Several comments can be made regarding the results of the above studies. First, the differences of the rates or return estimated for the same or near years are substantial. For example, the rates of return for 1974 and 1977 are 10.6% and 10.2%, respectively, and for 1975 it is 15.1%. For 1994 the rate of return is estimated by different authors to be 9.6%, 8.7% and 6.3%. One year later, 1995, the estimates are 5.6% and 5.4%. For the period 2004-7 the estimates are 5.3%, 7.0% and 7.4%.
growth of the economy and rather limited supply of university graduates in the first period and the reversal of these conditions in the second.
Third, the returns to education for post graduate studies are significantly higher than the rates of return of the first degree.
Fourth, the rates of return for higher education remain high even after the 2008 sovereign debt crisis, but the recession has brought about some changes in the ranking of the various professions.
Much of the literature on the rate of returns is often focused on the differences between men and women or on the differences between sections of employments, or even between time periods. However, no attention has be given so far, to the best of our knowledge, on the private rates of return obtained by graduates of distance learning universities This is a shortcoming of the existing li-

The Basic Mincer Equation
Along the lines suggested by Psacharopoulos and Patrinos (2004), we use the Mincer (1958)  The Mincer equation in its basic form is: lnW a a S a X a X = + + + (1) where lnW is the logarithm of wages, S the years of education and X the years of working experience, α 1 is the rate of return for an additional year of education and equal to the discount interest rate.
This equation, though half a century has passed, is still used in several variations as it describes quite well the data in the real world. The dependent variable, wages, is in logarithm, as opposed to independent variables that are the years of education and working experience. Taking the logarithm of the variables is a technique commonly used in econometric models for convenience or for a better fitting to the data. But in the case of the Mincer equation there is also a theoretical justification, see e.g. Bunzel et al. (2008) for the use of the dependent variable in logarithm within a regression that tries to explain the returns to human capital. As noted by Mincer op.cit., education has a multiplier effect on human capital which is described by the nonlinear increase in earnings compared with the increase of years of education (since α 1 > 0). Thus, the percentage change in W (wages) after a change of one unit in the years of education is constant (i.e. Following Psacharopoulos and Patrinos (2004) in using questionnaire data, schooling years are replaced by dummy variables for each level of education i.e. in order to find the different rate of return for the different education levels a dummy variable is used for each level of education in the Mincer equation.
Thus, the equation takes the form: where the variables D 1 , D 2 , D 3 and D 4 represent the four levels of education: no education, primary, secondary, and university education, respectively.
From (2) the private rates of return between levels of education are calculated by: where R b is the rate of return to basic education, R s the rate of return to secondary education, R Uf the rate of return to first degree graduates of University where i is individual i, t = 1, •••, 8 (4 year before graduation and 4 years after), D 2 = 1 for secondary school graduates, D 3 = 1 for first degree holders, and D 4 = 1 for Master's holders, W is the annual income from main work in constant 2010 prices, Χ are the years of working experience, S is a dummy variable for sex, DOM denotes family status, SLM the current state of the respondent in the labour market, M the degree mark (secondary level or Bachelor's or Master's), MATCH the relevance of the job to the degree (mismatching), OQ is a dummy to account for overqualification, SEC is the sector of employment, TRUN accounts for an active participation in trade unions, LANG is the knowledge of a foreign language (xx = 1 for English, 2 for French, 3 for German and 4 for any other foreign language), COMP is computer skills (Word, Excel, PowerPoint, database management, use of Internet, accounting packages and other specialised software) and u t,i is the disturbance term or error term that is assumed to be a random variable representing all the variables that affect the logarithm of wages and were not taken into account in (4).

Data Description
The data for the variables in (4)  The questionnaire was stratified into five different categories of individuals: 1) HOU first degree graduates; 712 questionnaires were completed from this category.
2) First degree graduates of traditional Universities; 120 questionnaires were completed from this category.
3) Applied for a HOU degree but not selected, secondary education graduates; 734 were completed from this category. The selection of students, both undergraduate and graduate is done at HOU by lottery. 4) Master's degree HOU graduates; 345 were completed from this category. 5) Traditional Universities Master's graduates; 201 were completed from this category.
The total number of questionnaires collected by the survey was 2112. Each individual was asked to report remuneration and employment data for a total of eight years, of which four years were before graduation and four years after. Therefore, the original sample size consisted of 16,896 observations.

Methodology for Estimating the Returns to Investment for HOU and Traditional University Graduates
For the estimation of the returns to investment for the HOU first degree and Master's graduates and the graduates from traditional universities Equation (4) was estimated separately using the sample data for HOU graduates and the traditional universities graduates. Category C "Applied for a HOU degree but not selected secondary education graduates" was included in both samples for control purposes.
The objective was to find estimates for the coefficients of D 2 , D 3 and D 4 and then calculate the rates of return between levels of education for HOU graduates and traditional university graduates using (3). A problem arises with the estimation of the coefficient of the D 2 variable. The variable cannot be included in the estimated equation because it will cause perfect multicollinearity. In fact the same applies for each of the dummy variables categories included in (4) and one variable from each category has to be excluded. When estimating (4) the coefficients of the excluded dummies are included in the intercept. If the Mincer equitation was to be estimated in its simple form, as in (2), the coefficient of the D 1 variable, α 1 , could had been calculated as 1 0 2 3 4ˆˆα β α α α = − − − . However, the same technique cannot be used when estimating (4) because the coefficients of all the excluded dummies would be included into the intercept.
To circumvent this problem (4) was estimated in two stages: first it was estimated without the D 2 , D 3 and D 4 dummies. Therefore, the effects of education on wages were left in the residuals. Then the latter were saved and they were used as a regressant in the following regression, with regressors the dummy variables representing the levels of education. Again, to avoid multicollinearity one After the estimation of (4) and (5) using the two samples i.e. the sample for the HOU graduates and the sample for the traditional university graduates, (7) can be calculated for each of these two categories 3 and the difference in the returns between the two categories of graduates can be tested using a Wald type test as follows: By substituting (6) and (7) into (8) and (9) where the superscripts H and T indicate that the coefficient is from the regression with the HOU and traditional universities sample, respectively.
If the null hypothesis in (10) is rejected at least 0.05 level of statistical significance then it will be concluded that the difference in the rates of return for the first degree studies between HOU and traditional universities is different. Further, if the null hypothesis in (11) is rejected at least 0.05 level of statistical significance then it will be concluded that the difference in the rates of return for the master's between HOU and traditional universities is different.

Estimation Method
It is obvious that (4) has to be estimated with panel data because it concerns with 3 Due to missing questionnaire data, the actual sample size used for HOU graduates (categories A, C and D) was 8351 observations and for the traditional universities graduates (categories B, C and E) was 4713 observations. graduates (subscript i) and for each graduate we have 8 observations for different consecutive years -four before graduation and four after (subscript t).
There are different methods for estimating panel data models: 1) with fixed effects (FE), 2) with random effects (RΕ) and 3) with neither fixed nor random effects.
The FE method is used when the interest is only for the analysis of the effects of variables that change over time. FE are investigating the relationship between the dependent and independent variables in an entity (country, person, company, etc.). Each entity has its own unique style that may or may not affect the va- In the case of FE, (4) is modified as in (12) 4 , where Φ i are n − 1 dummy variables and n is the total number of questionnaires. Each of these dummies absorbs the effects on the dependent variable that are specific to each individual. So, the heterogeneity among persons that has not been modelled into (4) is taken into account.
Unlike the fixed effects models (FE) the random effects models (RE) assume that the variation between individuals is random and uncorrelated with the independent variables included in the model. Thus, the distinction between FE and RE model is whether or not the non-observed effects on the dependent variable for each person contain and effects that are correlated across individuals. 4 Note that the D 2 , D 3 and D 4 variables were removed from (4) and included in (5)  Therefore, if we consider that there are differences among individuals that affect the dependent variable then RA models have to be used.
In the case of RE (4) is modified as in (13): where e t,i is the disturbance term within each individual (i is each cross-section) and u t,i is the disturbance term across individuals.
To determine which estimation method has to be used (Equation (12) or (13)) the Hausman test has been used where the null hypothesis is that the model has RE while the alternative is that it has FE. If the Hausman test shows that the RE model has to be used (Equation (13) zero. If we could not reject the null hypothesis then we would conclude that the use of the RE estimation method is not appropriate and OLS should be used.
The chi-square statistic from the Hausman test when (4) is estimated using the sample for HOU graduates was 79.41 and it was statistically significant at 0.00 level of significance while when it was estimated using the traditional universities sample it had a value of 10,939 and it was also statistically significant at 0.00 level of significance. Therefore, it is concluded that the null hypothesis should be rejected and (4) should be estimated using the FE model (described by (12), above) for both datasets (HOU/traditional Universities).

Results
The estimation results from the estimation of (12) using the HOU and the tradi- that the coefficients of computer skills are not statistically significant.
As explained in Section 3 ("Methodology"), in order to estimate the coefficients of the dummy variables for each level of education, after the estimation of the modified Mincer equation the residuals were saved and they have been used as a regressant with the regressors being the dummy variables for each level of education (Equation (5)). The results from these regressions are presented in Table 2 below.
Then the returns to education for HOU and traditional universities can be calculated using (7), above. These are presented in columns four and five in Table 3 below. Columns four and five present the returns to education investment for undergraduate and master's studies, respectively, in HOU and in traditional universities. The results shown are from the estimation of (5) using the sample for HOU graduates and the sample from traditional universities graduates; the dependent variable is the residuals from the estimation of (12). Two stars indicate statistical significance at less than 1% level of significance.  Table 2 and (6), (7). Notes: The first column was calculated from (6) while four and five were calculated from (7). Column four shows the returns for each year of study in HOU and in traditional universities while column five shows the total returns for the master's degree awarded by HOU and by traditional universities. Table 3 shows that the returns of university education are higher in case of graduates holding Bachelor's degree than those with Master's degree, a result verified by literature see e.g. Liwinski (2016).
Our results are in line with previous studies in Greece, see among others e.g. Kanellopoulos and Cholezas (2014), showing that returns to education for postgraduate studies are significantly higher than the rates of return of the first degree and, also, that the he rates of return for higher education are high even after the 2008 sovereign debt crisis. We observe that the returns to investment for studies in HOU are significantly higher than that of traditional universities graduates (approximately four times higher). The same applies to the returns for studies in the HOU master's degree relative to those from traditional universities. The return to investment in HOU is about twice that of the traditional universities.
To draw conclusions from these results a final test should be made: the statistical significance in the difference of returns for undergraduate and postgraduate studies between HOU graduates and the graduates from traditional university should be tested. Therefore, to test hypotheses (8) and (9), presented in subsection 3.4 above, the Wald test has been used, as described by (10) and (11).
The F-statistic for (10) had a value of 284.52 and it was statistically significant at 0.000 level of statistical significance while the F-statistic for (11) had a value of 6.25 and it was statistically significant at 0.012 level of statistical significance. Therefore, for both (10) and (11) the null hypothesis is rejected and the alternative is adopted 5 . Consequently, for both first and master's degree holders there is a difference in the returns to investment (in schooling years) between the Distance Learning and Traditional Universities in Greece.

Conclusions and Policy Implications
In this paper, we extend the literature on the rate of returns to Investment in Higher Education towards studies in distance learning Universities. To this aim, we first, develop a methodology for measuring the return to investment in education for both undergraduate and graduate studies. Second, we explore the difference in returns between, on one hand, graduates of the distance learning university (the Hellenic Open University, HOU) and on the other hand, graduates from two traditional universities, in Greece. The returns to investment in education were estimated using a modified form of the Mincer equation. The data used was extracted from questionnaires collected with field research performed within the framework of a HOU research project. A methodology was also developed for testing the statistical significance of the difference in the returns to education for HOU and traditional universities graduates using a Wald test.
We proceed our analysis by first estimating a modified Mincer equation and our findings show, first, that women are paid lower wages than men in the la-5 That is, the alternative hypothesis is adopted with zero margin of error in the case of undergraduate studies while the error possibility for postgraduate studies is 1.2% which is far below the acceptable statistical error of 5% (significance level) that is normally used. bour market, a result confirmed by some previous studies though some other studies support quite the opposite. Second, the relevance of the job to the degree of studies is statistically significant. This is a rather innovative result not explored by other studies.
Next, we turn our analysis into finding the rate of return to investment in education. We found that the rate of return to investment in education for HOU graduates is four time higher than that of the traditional Universities for the first degree graduates and about double for the Master's degree graduates. This result can be explained because HOU graduates are at a more mature stage in their carriers when they are getting their degree while most of the traditional University graduates are at a very early stage as they are just entering the labour market.
Finally, we test for the statistical significance in the difference of returns for undergraduate and postgraduate studies between HOU graduates and the graduates from traditional university by using the Wald test. This test shows that the difference of returns between HOU graduates and the other graduates is indeed statistically significant.
From policy perspective, our results are interesting for the Ministry of education that is responsible for the educational policy of higher education in Greece and also for the HOU administration authorities. This is so, because our findings suggest that a distance learning University may not only be considered as a second chance to education for mature students often facing time and budget restrictions, but, it may also be seen as a worthwhile investment enabling much higher private returns compared to the alternative route, i.e. following studies in traditional universities. Therefore, distance learning universities may be used by policy authorities as a vehicle to reduce income inequalities and increasing social mobility.