Demand Model for Adult Continuing Education using the Tobit model and the Heckman Selection Model

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1 , pp Demand Model for Adult Continuing Education using the Tobit model and the Heckman Selection Model Seung-gil, Lee 1, Sun Young, Chang 2 1 Department of Tourism Management, 2 General Education, Namseoul University, 91 Daehakro, Seonghwan-eup, Seobuk-gu, Cheonan City, Choongnam, Korea { dongbang0120@hanmail.net} {sychang@nsu.ac.kr} Abstract. The purpose of this study is to provide the most compatible model for estimating the determinants of demand for continuing adult through analytical comparison of the Tobit Model and the Heckman Selection Model. Tobit Model and the Heckman Selection models were used to conduct the analysis of raw data from 2013 National Statistics Office(NSO) in which vocational, foreign language, and sports and liberal were selected as the dependent variables. The results of the likelihood ration test used to evaluate the compatibility of the models indicated variances between the two models; the results of the comparison of the models based on the value of the log-likelihood function showed variance of each dependent variable between the two models. Keywords: adult, demand models, Tobit model, Heckman model 1 Introduction At the national level, provides the basis for economic development and serves the function of reproducing citizens instilled with the prevalent values of a civil society. Thus, in consideration of all these aspects, further research in continuing adult needs to be conducted meticulously; for myriad opportunities provided by continuing adult have significant implication for the future-in engendering increases in future income, human resource investment, economic development. Moreover, research relevant to adult need to be conducted thoroughly not only for its impact on policy-decisions but also for its scholarly contributions to the field of. Thus, a methodology which identifies the amount of expenditure spent on and the extent of positive impact wielded by a particular group on al expenditure is tremendously important in the establishment of progressive academic discussions and effective policy-making. Based on this context, the present study aims to establish the most compatible demand model for the estimation of demand for adult through the comparison of the Tobit model and the Heckman Selection model. ISSN: ASTL Copyright 2015 SERSC

2 1.1 Previous Research Tobit model have been used in studies on the estimation of expenditure on private in Egypt[2], and on the estimation of the determinants of demand for expenditure on private have been carried out in Vietnam[3]. Furthermore, for the estimation of the determinants of demand for expenditure on adult in Korean society, studies using the Tobit model for the estimation of the determinants of demand for expenditure on adult can be found in recent years[5]. According to the results of the study, determinant factors which had positive influence on expenditure for vocational were al background, occupation, income per household. Statistically significant determinant factors for expenditure on foreign language were found to be al background, occupation, number of elderly, age, income, and residence. For expenditure on sports and liberal, al background, age, income, and home ownership were found to be statistically significant variables. However, this study on the selection of the most compatible model through analysis and comparison of the two models is very limited: while one study [6], which uses both the Tobit model and the Heckman Selection model to estimate the factors for expenditure on private secondary suggests the determinant factors through analysis carried out using each model, it does not give any indication as to which model is the more compatible through analysis and comparison. Instead of the Heckman selection model, Doublehurdle model which is one of the sample selection models was compared with the Tobit model to determines the suitability of the models [7, 8]. In study [7], Doublehurdle model was found to be a more compatible model than the Tobit model for explaining the key demand variables in rural tourism. In study [8], it was concluded that the Double-hurdle model was more superior than the Tobit model for analyzing purchasing decisions and determinants of urban household expenditure on alcohol. Furthermore, the Tobit model and Heckman selection model were compared and analyzed in study [9] to determine the demand variables and the determinant factors for expenditure on urban household dining. 2 Research Model The Tobit model is a truncated regression model [10] which can be applied when the range of values taken by the dependent variable is deleted or truncated so that it can not be observed above or below a particular value; it s a model that allows for effective verification of the influence of the independent variable on the dependent variable with a predetermined range possessing a non-negative integer number of 0 or more[11]. In the Heckman model, it is assumed that participation decisions influence consumer decisions. That is, consumption of 0 signifies the result of participation, not consumer decision-thus the observed values include consumption equation of positive consumption levels[13]. The Heckman model is made up of two steps: in the first step, the Probit model is used to estimate the parameter using maximum likelihood estimation. Then, in step 2, in order to adjust the sample selection bias, IMR(inverse mill s ratio) that was derived in step one is included in the variable; in order to resolve 126 Copyright 2015 SERSC

3 heteroscedasticity, the parameter is estimated using generalized least-square estimation method. 3 Empirical Analysis The result of the analysis using the Tobit and Heckman models are shown in diagram 1. The bold sections indicate statistically significant variables for each model. The method used to interpret the influence of independent variables through the selection of the either two models was likelihood ratio test. The likelihood ratio test is a statistical technique used to verify the significance or non-significance of the correlational relationships of stochastic variables or the degree of correlation[14]. Table 1. Estimated Tobit model and Heckman model(n=9433) Dependent Variables Independent Variables MALE MARRIED HIGHSC Vocational Coef (t-value) (-3.774)*** (0.818) (2.428)** Tobit Model Foreign language Coef (t-value) (-1.505) (0.314) (1.198) Sport and liberal Coef (t-value) (-2.527)** (1.759)* (1.764)* Vocational Heckman Model Foreign language Sport and liberal Coef(t-value) Coef(t-value) Coef(t-value) Probit Truncated Probit Truncated Probit Truncated (-4.818)*** (0.591) (2.629)*** (0.198) (-0.135) (-0.167) (-1.545) (0.087) (1.92) (0.124) (0.015) (-0.129) (-2.06) (2.120)** (3.314)*** (0.208) (-0.237) (-0.260) COLLE (1.544) (1.171) (0.952) (2.062)** (-0.175) (1.613) (-0.121) (2.822)*** (-0.269) UNIVE (2.443)** (2.239)** (3.355)*** (2.581)*** (-0.160) (2.577)*** (-0.123) (4.311)*** (-0.254) GRADU (3.445)*** (0.682) (2.977)*** (3.035)*** (-0.157) (0.739) (-0.082) (3.783)*** (-0.250) WHITEJOB (1.955)* (0.585) (1.208) (1.248) (-0.110) (-0.371) (0.135) (0.192) (-0.029) BLUEJOB (-0.032) (-0.965) (-0.880) (-0.101) (0.380) (-1.697)* (0.134) (-0.796) (0.227) MULTIHOU (1.758) (1.391) (1.116) (1.972)** (-0.188) (1.754)* (-0.127) (1.354) (-0.236) OLDHOUSE (-0.828) (0.080) (-0.145) (-2.315)** (0.149) (-1.587) (0.108) (0.176) (-0.203) FAMAHOU (2.189)** (2.845)*** (-0.092) (3.816)** (-0.225) (2.356)** (-0.112) (-0.473) (0.273) Copyright 2015 SERSC 127

4 THIRTY FORTY FIFTY SIXTY SEVENTY THREEHUN FOURHUN FIVEHUN SIXHUN SEVENHUN OWNER CITY Constant IMR( ) Log likelihood function (-1.348) (-0.810) (0.287) (0.123) (-0.209) (2.054)** (4.087)*** (2.903)*** (0.507) (5.337) (0.889) (-1.599) (0.780) (-1.110) (-0.456) (1.004) (-0.435) (-0.297) (1.183) (1.678)* (3.464)*** (1.649)* (4.377)*** (-0.477) (0.500) (0.253) (-1.325) (0.177) (-0.343) (0.256) (-0.098) (3.267)*** (5.484)*** (2.239)** (4.152)*** (7.914)*** (3.614)*** (0.483) (-0.200) (-1.250) (-1.249) (0.168) (0.161) (-0.927) (4.206)*** (5.232)*** (4.642)*** (1.595) (6.597)*** (1.132) (-2.270)** (-9.712) (0.180) (0.227) (-0.018) (0.051) (0.175) (-0.218) (-0.199) (-0.209) (-0.228) (-0.210) (-0.211) (0.198) (0.201) (-0.192) (-1.189) (-0.735) (0.701) (-0.810) (-0.151) (2.247)** (2.342)** (3.932)*** (2.176)** (5.129)*** (0.046) (1.194) (-9.304) (0.125) (0.142) (-0.104) (0.128) (0.119) (-0.131) (-0.131) (-0.125) (-0.120) (-0.131) (-0.185) (-0.134) (0.128) (-0.124) (-1.697)* (-0.537) (-0.661) (0.393) (-0.409) (4.474)*** (6.072)*** (4.540)*** (6.690)*** (9.711)*** (3.415)*** (-0.144) ( ) (0.241) (0.214) (0.203) (-0.230) (0.182) (-0.250) (-0.248) (-0.265) (-0.261) (-0.259) (-0.232) (0.232) (0.263) (-0.256) The method used to interpret the influence of independent variables through the selection of the either two models was likelihood ratio test. The likelihood ratio test is a statistical technique used to verify the significance or non-significance of the correlational relationships of stochastic variables or the degree of correlation[14]. The likelihood ration test used to assess the goodness-of-fit of the two models is LR=2*(LLFprobit+LLFtruncation LLFtobit). LLFprobit and LLFtruncation indicate the likelihood function value derived from the Heckman model; LLFtobit indicate the likelikhood function value derived form the Tobit model. The likelihood ration test statistics take on the value of X2. If the variance between the two models are nonexistent the value of the X2 will be smaller than the peril point; inversely, if the variance between the two models are exist, the value of the X2 will be greater than the peril point.thus the results of the likelihood ration analysis indicate that the value of X2 for the three types of dependent variables Vocational ( , df: 23), Foreign language ( , df:23), Sport and liberal ( , 128 Copyright 2015 SERSC

5 df: 23) are greater than the peril point(35.17); this signifies that there are variances between the two models. Another statistical method is to select a model based on the Log-likelihood function to test the compatibility of the two models[15]. The comparison of the likelihood ratio of the two models show , , for the Tobit model and , , for the Heckman selection model; the compatibility regarding each dependent variable could not be selected without variance. Accordingly, upon the examination of the influence of the independent variables, the Tobit model would provide the most desirable assessment of the dependent and independent variables regarding expenditure on Vocational, Foreign language, Sport and Liberal. The reason for this is that there were no statistically significant variables in expenditure to be found regarding truncation using the Heckman selection model. The analysis of the raw data(the data before the elimination of outlier) showed that the distribution of male and female participants of the raw data to be greatly uneven with much of the survey distributed in 0: regarding expenditure for Vocational, the number of participants with actual expenditure were 471 (4.7%), those with no expenditure were 9575(97.1%); number of participants with expenditure for foreign language, with actual expenditure were 290(2.9%), those with no expenditure were 9576(97.1%); regarding expenditure for sports and liberal, the number of participants with expenditure were 708(7%), those with no expenditure were 9338(93%). The number of participants from the selective sampling implemented in the Heckman selection model were 221, 118, and 423 each with excessive distribution of 0 leading to the conclusion that this model was incompatible. 3 Discussion The Heckman selection model can provide a comprehensive understanding of consumer behavior in that it differentiates the consumer behavior into two steps; determinant factors of the participant demand and determinant factors of demand on expenditure. Thus the Heckman model can not be assumed to be superior to the Tobit model since the mechanisms of consumer behavior and determinant factors of participation can be configured differently. In other words, Tobit model assumes that the demand or expenditure of consumer spending on goods and services constitute a group within the range of a limited value. All consumers are potential users of the goods; based on the assumption that market participation and consumption levels are affected by the same variables, the Heckman model participation equation and consumption equation are correlated in terms of range of error, the participation decision influences consumer behavior. Consequently, the analysis of the two models would rely on the characteristics of the implemented data in assessing their compatibility. Thus, further studies which facilitate the comparison and analysis of the three models-the double-hurdle, Tobit, and the Heckman selection models are expected for future discussion. Copyright 2015 SERSC 129

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