How Much do Socioeconomic Conditions Influence People s Schooling Duration?

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1 How Much do Socoeconomc Condtons Influence People s Schoolng Duraton? CARMEN GARCÍA PRIETO JULIO LÓPEZ DÍAZ Unversdad de Valladold (December, 2005) Abstract: A wde sample of countres has been used to contrast the effectve nfluence on the populaton s schoolng duraton of some varables usually consdered n theoretcal models. But we have also found that socoeconomc condtons have a specal nfluence because they reduce the chance that people have to access the educatonal system. Key Words: Schoolng, Human Captal, Stochastc fronters JEL Codes: H52, I20, J24 We are grateful to the comments suggested by Zenón Jménez-Rdruejo and Patrca Gómez Costlla. Any error s solely due to us. Correspondng author: Carmen García Preto. Dpto. de Fundamentos del Análss Económco. Avda. Valle Esgueva, Valladold. Tf Fax e-mal: cgp@eco.uva.es. 1

2 1. Introducton Human captal theory gves educaton an nvestment nature, n such a way that ndvduals take a decson about extendng the educatonal perod beyond compulsory schoolng after a cost-beneft analyss. Overlappng generatons models take nto account the nfluence on ths knd of decson of such noneconomc elements as educatonal, demographc and nsttutonal factors. In any case, soco-economc determnants nfluence the educatonal decsons of the ndvduals, sometmes playng a decsve role: Wth adverse socoeconomc condtons, the populaton of a country could be expected not to acheve an educatonal level as hgh as t could wth other condtons. Nevertheless, ths factor s usually not consdered by theoretcal models when assessng determnants of human captal. In ths paper an emprcal analyss wth data from a wde range of countres s carred out, n order to fnd evdence of the effectve nfluence of the factors mentoned by theoretcal models n the educatonal level attaned by ther populaton, whle also takng nto account socoeconomc determnants. The study s undertaken usng stochastc fronter technques n order to fnd an educatonal producton functon, consderng socoeconomc condtons as determnants of educatonal neffcency. 2. Model, sample and varables The educatonal producton functon s formulated as follows: p log( ed ) = log( ed ) u wth u 0 [1] 2

3 ed beng the educatonal attanment n each of the N countres analysed, p ed the potental schoolng tme,.e. the hghest attanable wth the best condtons and u a non-negatve random varable that measures educatonal neffcency. The potental schoolng tme s derved from a set of varables X that all come from human captal theoretcal models, plus a random dsturbance v : p log( ed ) = β ' X + v [2] where β s a vector of parameters to be estmated and v s supposed to be normally dstrbuted wth zero mean and varance σ 2 v. By substtutng [2] n the expresson [1], a composed error term ω = v obtaned, and the result s: u s log( ed ) = β ' X + v u wth u 0 [3] The neffcency term u s determned by a set of country-specfc varables Z = ( z,... z ) reflectng socoeconomc condtons, n a specfcaton that follows ' 1 k Battese and Coell (1995): u = δ ' Z + ξ [4] where δ s a vector of parameters, and ξ s a new dsturbance term that follows a zero mean normal dstrbuton wth varance σ 2 u and truncated at δ ' Z. In such a way ξ δ ' Z and thus, u s dstrbuted as a normal wth a mean that depends + ' 2 on the socoeconomc varables, truncated at zero, u N ( δ Z, σ ). 3. Sample and varables u The study has been carred out wth data from a heterogeneous set of countres. The crteron to select the sample has been orented by the dsposal of a suffcently wde database wth adequate nformaton about the educatonal level of each country. The Cohen and Soto (2001) database was chosen because of 3

4 some advantages presented: It s a recent study wth relable nformaton from OECD, natonal or UNESCO censuses, and the data set conssts of a wde number of countres (a total of 95, although we only employed 75 n the estmaton, due to the lack of nformaton about some varables). As a consequence, the dependent varable n the estmaton s the average years of schoolng of people between 25 and 64 years old n 2000, taken drectly from the later nternatonal database. Ths varable has been named Ed and table 2 presents a lst of the countres used n the estmaton, ordered by ths varable. Unted Kngdom s the most educated country wth average years of study, whle the last place s for Burkna Faso wth only In the fronter, we have taken nto account lfe expectancy at brth, Lfexpect, and the age of retrement, Retrement, as varables that nfluence the expected length of the ncome generatng perod. In ths way, a hgher lfe expectancy and a hgher age of retrement should be expected to cause a longer schoolng perod. Lfexpect s the average of the natonal values from twenty years ago, offered by The World Bank, and retrement was provded by the U.S. Socal Securty Admnstraton, va the web. On the other hand, when nterest rates rse, the opportunty cost of the schoolng perod wll be hgher, so a negatve sgn s expected for nterest. Ths varable s the average real nterest rate n the last ffteen years, taken from the Internatonal Monetary Fund. The length of compulsory educaton, Compulsory, has also been consdered, because a longer compulsory duraton rases the average schoolng of the whole populaton. In ths case, the UNESCO s web page was the orgn of the nformaton. Fnally, a hgher publc expendture n educaton, Pubexp, could make access to the school system easer by means of grants for people wth lower economc resources, a publcly fnanced transport system, etc. Total publc expendture n educaton as percentage of GDP was consdered, and t was calculated as the average of data from the last ffteen years provded by the World Bank. Wth respect to the neffcency, some varables were selected to reflect the socoeconomc condtons of the populaton n each country and the dfferences between them when accessng the general educatonal system and specally, 4

5 unversty educaton. Frst, pupteach s the pupl-teacher rato n prmary, and t s a general ndcator of the qualty level of the educatonal system. Exppupun s the expendture per pupl on unversty as percentage of GDP per capta. Ths varable reveals the general socoeconomc condton of each country, because t compares the cost of a place at unversty to the general ncome level of an average ctzen,. Fnally, Malnut s a dummmy that takes a value of 1 n the case of prevalence of chld malnutrton. All these varables have been obtaned from the World Bank database and t could be thought that all of them could present a postve nfluence n the educatonal neffcency, makng the level of educaton of each country lower. Other possble nfluences, not explctly consdered, would be ncluded n the random dsturbance ξ from expresson [4]. The fnal model estmated has been the followng: log( Ed ) = β + β Pubexp + β Lfexp + β Compulsory + β Retrement + β5interest + v u u = δ + δ Expupun + δ Pupteach + δ Malnut + ξ u and v beng ndependent, the lkelhood functon s maxmzed usng the estmaton program Fronter 4.1 (see, Coell,1996 for a detaled descrpton of ths program). Then, an ndex of effcency s calculated for each country as follows: From expresson [1] we have that: ed ed e [5] p u = An ndex of the educatonal neffcency for each ndvdual the followng way: = u p = EE can be defned n EE e ed ed [6] and, from estmaton results, t wll be estmated 1 u as EE E( e ω ) =. 4. Estmaton Results The estmaton results are presented n table 1. The nterest rate has been excluded because t was not sgnfcant n any estmaton realsed. The rest of the varables, as can be seen, are sgnfcant. All of them have the expected nfluence and have a 1 See Battese and Coell (1988) for more detals. 5

6 postve effect on the average level of educaton. The parameters can be nterpreted as quas-elastctes, and so, from these results, the mportance of publc expendture n educaton can be hghlghted as a key varable n the human captal accumulaton process. As for the neffcency, the sgn of the estmated parameters are also adequate, and t s worth pontng out that the dsappearance of nfant malnutrton wll rase the schoolng of the populaton by 9 per cent. 2 2 The estmaton s valdated by the sgnfcance of the parameter γ = σ u σ, that ndcates the relatve contrbuton of u to total varance of the error term σ = σu + σ. If there s no neffcency, the varance of v u wll be zero, and γ wll be zero as well. On the other hand, the lkelhood rato test presented at the end of table 1 contrasts the hypothess that H 0 : γ = δ 0 = δ 1 = δ 2 = δ 3 = 0. The 2 statstc s asymptotcally dstrbuted as a mx of χ and the crtcal value can be found n Kodde and Palm (1986). The hypothess s rejected. Table 2 shows average years of schoolng for each country analysed, next to ther effcency ndex. Mean educatonal effcency for the whole sample s 77 per cent; that s to say, countres acheve, on average, 77 per cent of the attanable level, although the dsperson s hgh among countres. The most effcent country s Korea wth 98 per cent and Burkna Faso s the last one, wth just 16 per cent. 4. Conclusons The analyss has revealed that the socoeconomc stuaton s an mportant determnant of the average schoolng duraton n many countres, especally where people often do not fnsh compulsory educaton, and t should be taken nto account by emprcal studes n order to quantfy the effect of classc demographc or nsttutonal varables. On the other hand, publc expendture on educaton has a hgher nfluence on schoolng duraton than other classcal varables such as lfe expectancy or age of retrement. References 6

7 Battese, G.E. and T. Coell, 1988, Predcton of Frm-Level Techncal Effcences wth a Generalzed Fronter Producton Functon and Panel Data, Journal of Econometrcs 38, Battese, G.E. y T. Coell, 1993, A stochastc fronter producton functon ncorporatng a model for techncal neffcency effects, Workng papers n Econometrcs and Appled Statstcs nº 69, Department of Econometrcs, Unversty of New England, Armdale, Australa. Battese, G.E. and T. Coell, 1995, A Model for Techncal Ineffcency Effects n a Stochastc Fronter Producton Functon for Panel Data, Emprcal Economcs, 20, pp Coell, T., 1996, A Gude to FRONTIER Verson 4.1: A Computer Program for Stochastc Fronter Producton and Cost Functon Estmaton, CEPA workng paper 96/07, Department of Econometrcs, Unversty of New England, Armdale, Australa. Cohen, D. and M. Soto, 2001, Growth and human captal: good data, good results, OCDE techncal papers, nº 179. Kodde, D.A. and F.C. Palm, 1986, Wald crtera for jontly testng equalty and nequalty restrctons, Econometrca, 54,

8 Table 1. Estmaton Results Coeffcent St. Devaton. t-statstc FRONTIER Intercept Pubexp Lfexp Compulsory Retrement INEFFICIENCY Intercept Exppupun Pupteach Malnut σ γ Log-lkelhood LR-test of one-sded error Table 2: Years of schoolng and effcency ndexes. Unted Kngdom (0.96) Span 9.50 (0.79) Venezuela 6.26 (0.59) Australa (0.95) Malaysa 9.31 (0.91) Turkey 6.25 (0.77) Canada (0.94) Cyprus 8.87 (0.77) Iraq 6.11 (0.79) Germany (0.95) Jamaca 8.66 (0.83) Zamba 6.10 (0.94) Swtzerland (0.96) Panama 8.56 (0.86) Kenya 6.06 (0.75) Unted States (0.95) Guyana 8.51 (0.91) Chna 5.96 (0.63) Japan (0.96) Uruguay 8.36 (0.91) Domncan Rep (0.67) Korea (0.98) Peru 8.32 (0.92) Iran 5.34 (0.67) Denmark (0.92) Argentna 8.30 (0.84) Honduras 5.32 (0.61) New Zealand (0.91) Zmbabwe 8.29 (0.93) Ghana 5.26 (0.65) Sweden (0.89) Ecuador 8.22 (0.90) El Salvador 5.10 (0.58) Fnland (0.93) Bolva 8.09 (0.92) Guatemala 4.84 (0.66) Austra (0.93) Fj 8.00 (0.86) Cameroon 4.65 (0.68) Netherlands (0.80) Mexco 7.95 (0.82) Tunsa 4.44 (0.40) Hungary (0.94) Phlppnes 7.94 (0.94) Inda 4.34 (0.57) Belgum (0.84) Maurtus 7.59 (0.82) Madagascar 3.71 (0.55) France (0.89) Thaland 7.51 (0.90) Hat 3.60 (0.59) Bulgara (0.96) South Afrca 7.35 (0.78) Morocco 3.58 (0.42) Italy (0.91) Portugal 7.28 (0.65) Cote divore 3.18 (0.47) Jordan (0.87) Indonesa 7.25 (0.92) Central Af. Rep (0.49) Ireland (0.86) Colomba 7.13 (0.86) Senegal 2.56 (0.40) Romana (0.95) Syra 7.09 (0.81) Burund 2.04 (0.35) Chle 9.94 (0.92) Egypt 6.76 (0.76) Ethopa 1.93 (0.34) Greece 9.90 (0.89) Costa Rca 6.72 (0.59) Mal 1.14 (0.18) Trndad & Tobago 9.60 (0.94) Paraguay 6.59 (0.79) Burkna Faso 0.93 (0.16) 8