research article the long-term impact of human capital...

Research ArticleThe Long-Term Impact of Human Capital Investment on GDPA Panel Cointegrated Regression Analysis

Ahmet Goumlkccedile Akpolat

Department of Economics Faculty of Economic and Administrative Sciences Sakarya University Esentepe Campus54187 Sakarya Turkey

Correspondence should be addressed to Ahmet Gokce Akpolat aakpolatsakaryaedutr

Received 30 April 2014 Revised 10 July 2014 Accepted 10 July 2014 Published 5 August 2014

Academic Editor Thanasis Stengos

Copyright copy 2014 Ahmet Gokce Akpolat This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This study aims to determine the long-run impact of physical and human capital on GDP by using the panel data set of 13developed and 11 developing countries over the period 1970ndash2010 Gross fixed capital formation is used as physical capital indicatorwhile education expenditures and life expectancy at birth are used as human capital indicators Panel DOLS and FMOLS panelcointegrated regression models are exploited to detect the magnitude and sign of the cointegration relationship and comparethe effect of these physical and human capital variables according to these two different country groups As a consequence ofpanels DOLS and FMOLS models the impact of physical capital and education expenditures on GDP in the developed countriesis determined as higher than the impact in the developing countries On the other hand the impact of life expectancy at birth onGDP is determined as higher in the developing countries

1 IntroductionThe concept of human capital has begun to be evaluated asa component and determinant of economic growth partic-ularly after the Second World War Before the war the maintarget of theoretical discussions about human capital was notto define or to measure its contribution to economies [1]Kiker [2] notes six reasons about the concept of human capitalwhich are unrelated to economic growth that the evaluationshad been mostly centered around until the WWII Howeverthe studies made after the war have begun to associate theconcept of human capital with the concept of economicgrowth Schultz [3] attributes the major explanation ofnational output differences among countries to investmentin human capital He emphasizes that the main reason ofwage differentials between workers is the human capital dif-ferentials which are gained bymeans of education and healthInvestment in human capital is profitable like a physicalcapital investment according to him Becker [4] states that theinvestments aiming to improve physical and mental health oflabor force are significant human capital investments and theroot cause of welfare differences between nations is the dif-ferences of human capital formation among countries rather

than physical capital ones Alongside these studies there existmany studies explaining the determinants of human capitaland its effects on growth up to the 1980s (some of which are[5ndash10]) Even though these and other different studies men-tion the importance of human capital on economic growthbeginning of its articulation to the growth theory is after themid-1980s Romer [11] develops a model assuming knowl-edge as a production input which has increasing marginalproductivity According to Romer technological change isa consequence of accumulation of knowledge acquired byforward-looking and profit-maximizing firmsrsquo productionand research activities Romer also uses the concept ofldquolearning by doingrdquo developed by Arrow [12] in order toexplain the technological development process According tohim technology is a product acquired by these types of firmsby means of ldquolearning by doingrdquo process Lucas [13] statesthat unskilled labor may be transformed into a skilled formby schooling Schooling is the key to development of humancapital One of the determinants of steady state per capita out-put level is human capital developed by means of schoolingaccording to him ([13] [14 pages 220ndash222]) Mankiw et al[15] include the human capital in the neoclassical growth

Hindawi Publishing CorporationEconomics Research InternationalVolume 2014 Article ID 646518 10 pageshttpdxdoiorg1011552014646518

2 Economics Research International

theory and state that the explanatory power of the model isincreased as compared with the neoclassical model owing tothis inclusion Benhabib and Spiegel [16] use cross-countryestimates of physical and human capital stocks as indicatorsand run the growth accounting regressions implied by aCobb-Douglas production function They find that humancapital is insignificant at explaining per capita growth ratesThey also develop a model in which the growth rate oftotal factor productivity depends on a nationrsquos human capitalstock level According to this alternative model they findthe result that human capital positively affects the growthrate of total factor productivity Besides these studies lots ofempirical studies are made to determine the human capitaland growth relationship [17ndash28] While education expendi-tures and schooling are exploited as education indicatorshealth expenditures and life expectancy at birth stand outas health indicators in most of these studies The majorityof these studies indicate that both improvements in healthand education indicators lead to a positive effect on growthand GDP due to the developments of human capital level ofcountries

Because economic growth is a long-run phenomenonit is so important to determine the long-run effects ofphysical and human capital variables Due to this fact themain purpose of this study is to test the effect of humanand physical capital on GDP The study aims to realizethis by means of using gross fixed capital formation asphysical capital indicator and education expenditures andlife expectancy at birth as human capital indicators byanalyzing the data of the 13 developed and the 11 developingcountries The remarkable feature of the study is that it usesthe cointegrated panel regression models which are panelsDynamic Ordinary Least Squares (DOLS) [29] and FullyModified Ordinary Least Squares (FMOLS) [30] methodsBecause the precondition of these models is the existenceof cointegration between variables there is no need to takedifferences of variables to overcome nonstationarity By thisway any loss of information concerning variables does notoccur Another objective of the study is to measure themagnitude of the effect of these explanatory variables onGDP according to these two different groups of countriesHereby we can understand which variable is more effectiveto increase GDP in which country group

The rest of the study is as follows Section 2 presentsa brief summary about the relationship between educa-tion health and economic growth The empirical resultsin Section 3 introduce the consequences of the cointegratedpanel analysis which are panels DOLS and FMOLS Section 4presents an overall assessment about the consequences of theeconometric analysis Section 5 presents a conclusion

2 A Brief Summary about Education Healthand Economic Growth Relationship

The studies that associate education with economic growthsuggest some reasons to clarify the issue Ozturk [31] statesfour reasons about this relationship (i) Education advancesthe efficiency of labor and thus production through scientific

and technological developments which it causes (ii) Educa-tion provides developing the potential skills of individuals(iii) Education enhances the ability to adapt to emergingbusiness opportunities (iv) Educational institutions provideknowledge to be transferred to future generations by edu-cating teaching staff [31] Moreover the impact of educationcontinues over generations owing to the fact that educatedindividuals cultivate healthier andmore educated generationsso they maintain the high human capital level of theirsociety Because the fertility rates of educated families arelow population growth will be balanced and savings percapita remain high High level of saving rates positivelycontributes to economy [32] In addition to these increasein educational level of society leads to an improvementon income distribution and prevents poverty because ofits providing of advancement of individualsrsquo high-earningcapacity [33]

As for health and growth relationship several reasonsand channels are stated by economists on how health affectseconomic growth First of all healthier people reveal a moreeffective performance throughout their professional livesrather than people having low level of health Furthermoreadvances in health level of society increase the educationalinvestments which increase the long-life expected returns ofeducation Besides these improvements in health level ofstudents bring about their having a better cognitive abilitythat helps to receive a better education [34] Bloom et al[35] convey that a significant cause of studentsrsquo learningdisabilities is diseases Ram and Schultz [36] and Sachsand Malaney [37] state that taking malaria under controlimproves labor force and student efficiency Improvementsin both labor force and student efficiency positively affecteconomic growth as it is known As noted by Behrman[38] malnutrition in childhood is detected to relate withthe low economic efficiency Jack and Lewis [39] state thatthe increase in life expectancy of adults leads to increase intheir investments on their own children and so improves thehuman capital of next generations Weil [34] declares thatdecreasing mortality rates leads to increase in retirement ageand so saving rates of society thus provide a high level ofinvestments

3 Econometric AnalysisThis paper examines the relationship between educationexpenditures and life expectancy at birth (which are bothevaluated within the concept of human capital) and GDP Inthe study the relationship between human capital and GDPis analyzed for 13 developed and 11 developing countries overthe period 1970ndash2010The data were obtained from theWorldBank databaseThedeveloped countries that we use their dataare Australia Austria Belgium Canada Denmark FinlandFrance Japan Netherlands Norway Spain United Kingdomand United StatesThe developing countries are Brazil ChileEgypt Ireland Israel Malaysia Mexico Pakistan SingaporeTurkey and Uruguay Even though Ireland Israel and Sin-gapore are counted as developed countries recently they hadbeen counted as developing countries in most of this 41-yearperiod They gained the status of developed country towards

Economics Research International 3

Table 1 The panel unit root test results for the series

Variables Developing countries Developed countriesConstant Constant and trend Constant Constant and trend

LGDP Level 1st diff Level 1st diff Level 1st diff Level 1st diffLLC minus314593lowastlowastlowast minus88058lowastlowastlowast minus20277lowastlowast minus73363lowastlowastlowast minus76703lowastlowastlowast minus1063lowastlowastlowast minus3885lowastlowastlowast minus111682lowastlowastlowast

IPS 127455 minus95454lowastlowastlowast minus33668lowastlowastlowast minus79070lowastlowastlowast minus26551lowastlowastlowast minus8326lowastlowastlowast minus3647lowastlowastlowast minus777488lowastlowastlowast

ADF-Fisher Chi-Square 122047 1320300lowastlowastlowast 44819lowastlowastlowast 1010400lowastlowastlowast 45138lowastlowast 12094lowastlowastlowast 56221lowastlowastlowast 104909lowastlowastlowast

PP-Fisher Chi-Square 173827 1784180lowastlowastlowast 211644 1439000lowastlowastlowast 78426lowastlowastlowast 13594lowastlowastlowast 279579 122823lowastlowastlowast

LCAP Level 1st diff Level 1st diff Level 1st diff Level 1st diffLLC minus32774lowastlowastlowast minus164715lowastlowastlowast minus059623 minus158420lowastlowastlowast minus5328lowastlowastlowast minus15214lowastlowastlowast minus31742lowastlowastlowast minus149583lowastlowastlowast

IPS 004853 minus156084lowastlowastlowast minus209876lowastlowast minus143212lowastlowastlowast minus130231lowast minus12585lowastlowastlowast minus43880lowastlowastlowast minus115838lowastlowastlowast

ADF-Fisher Chi-Square 166501 227626lowastlowastlowast 322634lowast 201078lowastlowastlowast 303298 192078lowastlowastlowast 65966lowastlowastlowast 160226lowastlowastlowast

PP-Fisher Chi-Square 233207 226310lowastlowastlowast 353005lowastlowast 199022lowastlowastlowast 386300lowast 182448lowastlowastlowast 25946 153410lowastlowastlowast

LED Level 1st diff Level 1st diff Level 1st diff Level 1st diffLLC minus298467lowastlowastlowast minus144884lowastlowastlowast 011309 minus114927lowastlowastlowast minus74089lowastlowastlowast minus101269lowastlowastlowast minus32115lowastlowastlowast minus874055lowastlowastlowast

IPS 116821 minus133925lowastlowastlowast minus171766lowastlowast minus111555lowastlowastlowast minus30173lowastlowastlowast minus104757lowastlowastlowast minus31114lowastlowastlowast minus939929lowastlowastlowast

ADF-Fisher Chi-Square 127975 192206lowastlowastlowast 317368lowast 146698lowastlowastlowast 505854lowastlowastlowast 160616lowastlowastlowast 468568lowastlowastlowast 13703200lowastlowastlowast

PP-Fisher Chi-Square 173836 189475lowastlowastlowast 196087 153423lowastlowastlowast 774953lowastlowastlowast 205261lowastlowastlowast 453554lowastlowast 40534900lowastlowastlowast

LLIF Level 1st diff Level 1st diff Level 1st diff Level 1st diffLLC minus144411lowast minus82187lowastlowastlowast 307602 minus12077lowastlowastlowast minus3627lowastlowastlowast minus271061lowastlowastlowast minus157953lowast minus27531lowastlowastlowast

IPS 138782 minus31948lowastlowastlowast 383115 minus29379lowastlowastlowast 255006 minus258662lowastlowastlowast minus101970 minus26971lowastlowastlowast

ADF-Fisher Chi-Square 326369lowast 878737lowastlowastlowast 544389lowastlowastlowast 910401lowastlowastlowast 228534 404455lowastlowastlowast 450026lowastlowast 557048lowastlowastlowast

PP-Fisher Chi-Square 191742lowastlowastlowast 1126150lowastlowastlowast 244556 331132lowastlowastlowast 272810 400190lowastlowastlowast 409731lowastlowast 586349lowastlowastlowast

The null hypotheses of all unit root tests state that the series include unit root while the alternative hypotheses state the absence of unit rootlowastlowastlowast lowastlowast and lowast indicate stationarity at 1 5 and 10 significance levels respectively

the end of this period The exploited model is indicated asfollows

LGDP119894119905= 120572

1119894LCAP

119894119905+ 120572

2119894LED119894119905+ 120572

3119894LLIF119894119905

(119894 = 1 2 3 119873) (119905 = 1 2 3 119879)

(1)

The variables in the equation are natural logarithmsof GDP (LGDP) gross fixed capital formation (LCAP)education expenditures (LED) and life expectancy at birth(LLIF) respectively

Because our study is a long-term analysis the cointegra-tion relationship between the variables has great importanceIn this context we initially apply unit root tests to examine thedegree of stationarity of the variables If we are able to detectthat the variables have the same order of stationarity PedroniFisher and Kao panel cointegration tests can be applied todetermine the existence of cointegration After determinationof this relationship magnitude and sign of this relationshipbetween the variables are analyzed by means of the methodsof panels DOLS and FMOLS

31 Panel Unit Root Tests We utilize 4 different panel unitroot tests in our analysis These are Levin et al [40] Im et al[41] ADF Fisher Chi-square [42] and PP Fisher Chi-square[42] tests While the null hypothesis of all these tests statesthe existence of unit root the alternative hypotheses state theabsence of it Table 1 shows the unit root test results of ourserieslowastlowastlowastlowastlowast andlowast indicate stationarity at 1 5 and 10significance level respectively When we examine Table 1

we may easily observe the stationarity of all the series atfirst difference The constant and constant and trend modelsindicate the stationarity at first difference Due to this reasonwe can apply panel cointegration tests to detect the existenceof long-run relationship

32 Panel Cointegration Tests We make panel cointegrationanalysis by applying three panel cointegration tests Theseare Pedroni [43] Kao [44] and Johansen Fisher panelcointegration tests Pedroni [43] developed 7 different teststo determine the existence of panel cointegration All of thesecan be divided and applied as constant and constant and trendtests The results are illustrated in Table 2

Five of these 7 Pedroni tests for the developing countriesdemonstrate cointegration in constant and constant andtrend models respectively In the trendless (constant) model4 test statistics show significance at 10 and 1 test statisticshows significance at 5 level In the model having trend(constant and trend) 2 test statistics are significant at 12 test statistics are significant at 5 and 1 test statisticis significant at 10 level For the developed countries 2test statistics show cointegration at 5 and 2 test statisticsshow cointegration at 10 level in the trendless model Inthe constant and trend model cointegration is determinedaccording to 3 test statistics at 5 level 1 test statistic alsoindicates cointegration at 10 significance level

We can apply Kao [44] cointegration test in additionto Pedroni tests Table 3 illustrates the results of Kao panelcointegration test


Table 2 The results of Pedroni cointegration tests

Pedroni cointegration tests Developing countries Developed countriesConstant Constant and trend Constant Constant and trend

Panel v-stat 215391lowastlowast 145106lowast 227641lowastlowast 085554Panel rho-stat minus084610 minus069233 minus104253 minus025242Panel pp-stat minus147257lowast minus224762lowastlowast minus218951lowastlowast minus215791lowastlowast

Panel adf-stat minus154850lowast minus276468lowastlowastlowast minus151014lowast minus186789lowastlowast

Group rho-stat 000147 027134 minus015512 066472Group pp-stat minus126503lowast minus175129lowastlowast minus203574lowastlowast minus169854lowastlowast

Group adf-stat minus134975lowast minus245622lowastlowastlowast minus123116 minus138851lowast


Table 3 Kao panel cointegration test results

Country group ADF test stat ProbDeveloping countries minus3860268 00001Developed countries minus4135364 00000The optimal lag length is determined as 9 for developing countries and 5 fordeveloped countries according to Schwarz information criterion

The null hypothesis states the absence of cointegrationaccording to Kao test As illustrated in Table 3 the nullhypothesis is rejected and the alternative hypothesis isaccepted for both developing and developed countries Wecan easily conclude the existence of cointegration accordingto Kao test

The results of Johansen Fisher cointegration test areindicated in Table 4 When we take a glance at the resultsfor developing countries the null hypothesis stating thenonexistence of cointegrated vector is rejected The nullhypothesis suggesting that there is at most one cointegratedvector is also rejected Nevertheless the null hypothesissuggesting the existence of at most 2 cointegrated vectors isaccepted Thus we can conclude that there is cointegrationrelationship for the developing countries

When we examine the table for developed countriesrejection of the first null hypothesis suggesting the absenceof cointegrated vector and acceptance of the second nullhypothesis suggesting the existence of at most 1 cointegratedvector are easily observed As it is determined for thedeveloping countries we can conclude that there is cointe-gration relationship between the variables for the developedcountries

After the determination of the cointegration we can applypanel DOLS [29] and panel FMOLS [30] methods Thesetests are applicable under the condition that existence ofcointegration is determined By this means the magnitudeand direction of the relationship between our dependentvariable LGDP and our explanatory variables LCAP LEDand LLIF can be detected

33 Panel DOLS and Panel FMOLS Models Under theexistence of cointegration relationship the use of standardpooled least squares method may lead to biased estimationsdue to problems of serial correlation and endogeneity Panels

DOLS and FMOLS methods are efficient techniques to elim-inate these problems Panel DOLS is a parametric methodwhich is used to obtain long-run coefficients by takinginto account the lead and lagged values of variables PanelFMOLS is a method eliminating serial correlation effect byapplying a nonparametric transformation to residuals whichare obtained from cointegration regression Panels DOLSand FMOLS techniques facilitate establishing a regressionwithout the need to take differences of the cointegratedvariablesThus it becomes possible to analyze without loss ofany information about dependent and explanatory variables

331 Panel DOLS Model Pedroni [29] constructed abetween-dimension group-mean panel DOLS estimator byaugmenting the cointegrating regressionwith lead and laggeddifferences of the regressor to control for the endogenousfeedback effect Panel DOLS estimator is constructed asfollows

119884

119894119905= 120572

119894+ 120573

119894119883

119894119905+

119901119894

sum

119896=minus119901119894

120574

119894119896Δ119883

119894119905minus119896+ 120576

119894119905 (2)

Here 119901119894and minus119901

119894are lagged and lead values It is assumed that

there is no dependence relationship between cross-sectionsaccording to this model120573

119894is DOLS estimator obtained from 119894th unit in panel and

can be expressed as follows

120573

lowast

119894= 119873

minus1

119873

sum

119894=1

(

119879

sum

119905=1

119885

119894119905119885

1015840

119894119905)

minus1

(

119879

sum

119905=1

119885

119894119905119884

lowast

119894119905)

(3)

Here 119885119894119905= (119883

119894119905minus 119883

119894 Δ119883

119894119905minus119901 Δ119883

119894119905+119901) is the vector of

regressors in 2(119901 + 1) times 1 dimension The group-mean panelDOLS estimator is estimated by obtaining arithmeticmean ofcointegration coefficients and is shown as

120573 = 119873

minus1

119873

sum

119894=1

120573

119894 (4)

120573

119894is the estimated coefficient obtained from DOLS for

each cross-section Group-mean panel DOLS t-statistic isestimated as follows

119905 120573= 119873

minus12

119873

sum

119894=1

119905 120573119894

(5)


Table 4 Johansen Fisher panel cointegration test results

Hypothesis

Developing countries Developed countries

Fisher stat(from trace test) Prob

Fisher stat(from maximumeigenvalue test)

Prob Fisher stat(from trace test) Prob


Prob

None 2441 00000 4606 00000 7755 00000 6170 00001At most 1 6132 00000 4974 00006 3336 01518 1792 08786At most 2 2777 01835 2332 03838 2685 04171 2355 06017At most 3 1860 06697 1860 06697 1841 08605 1841 08605

119905 120573119894

is t-statistic of each coefficient obtained from DOLS foreach cross-section [29 45]

332 Panel FMOLS Model The group-mean panel FMOLSmethod [30] is based on the following panel regressionmodel

119884

119894119905= 120572

119894+ 120573119883

119894119905+ 119890

119894119905

119883

119894119905= 119883

119894119905minus1+ 120576

119894119905

(6)

Here 119890 and 120576 are error terms and are accepted as stationaryThe panel FMOLS estimator for 120573 estimator can be estimatedas follows

120573

lowast

119873119879= 119873

minus1

119873

sum

119905=1

(

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

)

minus1

times (

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

119884

lowast

119894119905minus 119879120591

119894)

119884

lowast

119894119905= (119884

119894119905minus 119884

119894) minus

119871

21119894

119871

22119894

Δ119883

119894119905

(7)

where

120591

119894=

Γ

21119894+ Ω

0

21119894minus

119871

21119894

119871

22119894

(

Γ

22119894minus Ω

0

22119894) (8)

Here Ω119894= Ω

0

119894+ Γ

119894+ Γ

1015840

119894shows long-run covariance matrix

where Ω0119894is the contemporaneous covariance and Γ

119894is a

weighted sum of covariances 119871119894is the lower triangular in the

decomposition ofΩ119894

333 Results of Panels DOLS and FMOLS Models After thepresentation of panels DOLS and FMOLS models we canexamine the consequences Table 5 indicates panels DOLSand FMOLS results for the developing countries

Table 5 represents the results of panels DOLS and FMOLSregressions According to the panel DOLS results LCAP issignificant at 1 level in 11 developing countries All of thecoefficients have positive signs which are compatible with thetheory Accordingly FMOLS results demonstrate that LCAPseries for all the developing countries have positive and sta-tistically significant signs at 1 levelWhenwe examine panelgroup statistics the coefficient of LCAP series is 0451805 in

DOLS model and 038 in FMOLS model That means 1increase in gross fixed capital formation leads to a 045increase inGDPaccording to theDOLSmodel consequenceswhile 1 increase in gross fixed capital formation leads to a038 increase in the GDP according to the FMOLS

When we examine LED series we observe that LEDseries of 10 of these 11 developing countries have positiveand statistically significant signs at 1 significance level OnlySingaporersquos LED series is determined to have negative andstatistically insignificant signs When we look at FMOLSmodel results we see that LED series of 8 developingcountries are detected as significant at 1 significance levelandLED series of 2 countries are detected as significant at 10significance level Only LED series of Pakistan is determinedto have a negative and insignificant sign The panel groupstatistic of the LED series in the panel DOLS model showsthat the coefficient of the LED series is 0365050 in theFMOLS model it is 041 That means 1 increase in theeducation expenditures leads to a 0365050 increase inGDPaccording to the DOLS model and 041 increase accordingto the FMOLS model

When we examine the LLIF series we observe that theLLIF series are statistically significant and have positive signsfor 7 developing countries at 1 level and they are statisticallysignificant and have negative signs for 2 developing countriesat 10 level The series are detected to be insignificant for2 developing countries According to the FMOLS modelresults the LLIF series of 10 countries have positive signswhich are statistically significant at 1 level When weexamine the panel group statistics the coefficient of the LLIFseries is 4765741 in the DOLS model and 458 in the FMOLSmodelThat means 1 increase in the life expectancy at birthleads to a 476 increase in the GDP according to the DOLSmodel and 458 increase according to the FMOLS model

Table 6 represents the panels DOLS and FMOLS regres-sion results for the developed countriesTheLCAP series of 12of these 13 developed countries are determined as statisticallysignificant at 1 significance level according to the panelDOLS model Only the LCAP series of Denmark is detectedas insignificant When we examine the FMOLS results weobserve that LCAP series are determined as significant at1 significance level for 12 developed countries Only one ofthem is detected as significant at 5 significance level Whenwe examine the panel group statistics we can observe thatthe LCAP series is determined as 0475 and 042 accordingto the DOLS and FMOLSmodel respectively Based on these


Table 5 Panel DOLS and panel FMOLS results for the developing countries

Country Panel DOLS estimation FMOLS estimationVariable Coefficient 119905-stat Variable Coefficient 119905-stat

BrazilLCAP 0315483 1399346lowast LCAP 031 171lowastlowast

LED 0689395 2655973lowastlowastlowast LED 048 272lowastlowastlowast

LLIF minus1931459 minus0945024 LLIF 255 272lowastlowastlowast

ChileLCAP 0572649 8572678lowastlowastlowast LCAP 036 667lowastlowastlowast


LLIF minus3169962 minus3848773lowastlowastlowast LLIF 110 186lowastlowast

EgyptLCAP 0199314 5932171lowastlowastlowast LCAP 020 621lowastlowastlowast


LLIF 0453760 0792565 LLIF 120 270lowastlowastlowast

IrelandLCAP 0175749 3418237lowastlowastlowast LCAP 023 422lowastlowastlowast


LLIF 10764085 5551465lowastlowastlowast LLIF 1013 499lowastlowastlowast

IsraelLCAP 0213562 2852816lowastlowastlowast LCAP 026 3 12lowastlowastlowast



MalaysiaLCAP 0290281 6866725lowastlowastlowast LCAP 021 343lowastlowastlowast



MexicoLCAP 0683498 14058544lowastlowastlowast LCAP 070 1137lowastlowastlowast

LED 0107866 2604453lowastlowastlowast LED 008 160lowast


PakistanLCAP 0889916 12539836lowastlowastlowast LCAP 073 651lowastlowastlowast

LED minus0335293 minus3170375lowastlowastlowast LED minus009 minus063LLIF 7545253 7359024lowastlowastlowast LLIF 507 351lowastlowastlowast

SingaporeLCAP 0631917 4311902lowastlowastlowast LCAP 044 368lowastlowastlowast

LED minus0075487 minus0411517 LED 022 136lowast


TurkeyLCAP 0759918 13484764lowastlowastlowast LCAP 049 470lowastlowastlowast


LLIF minus2497145 minus7432869lowastlowastlowast LLIF 081 103

UruguayLCAP 0237569 4274276lowastlowastlowast LCAP 020 291lowastlowastlowast



Panel group DOLS results Panel group FMOLS resultsLCAP 0451805 23430837lowastlowastlowast LCAP 038 16 44lowastlowastlowast




results 1 increase in the gross fixed capital formation leadsto a 0475 and 042 increase in the GDP according to thepanels DOLS and FMOLS models respectively

The outcomes of the LED series indicate that the coef-ficients of the LED series of the 12 developed countries aresignificant at 1 level while the series of USA is significant at10 level according to the DOLS model The FMOLS resultsdemonstrate that the series of 11 countries are significant at1 and the series of 2 countries are significant at 10 levelWhen we examine the panel group statistics we see that

the coefficient of the LED series is determined as 045 and047 according to the panels DOLS and the FMOLS modelsrespectively

The consequences of the LLIF series illustrate theseresults the coefficients of the 6 countries are determined assignificant at 1 and the coefficients of the 2 countries aredetermined as significant at 5 significance level while thecoefficients of the 5 countries are determined as insignificantaccording to the panel DOLS model FMOLS model resultsshow that the coefficients of the 8 countries are significant


Table 6 Panel DOLS and panel FMOLS results for the developed countries

Country Panel DOLS estimation FMOLS estimationVariable Country Variable Country Variable Country

AustraliaLCAP 0296102 5534409lowastlowastlowast LCAP 031 7 22lowastlowastlowast



AustriaLCAP 0414813 6106861lowastlowastlowast LCAP 042 608lowastlowastlowast

LED 0567336 9086922lowastlowastlowast LED 055 8 75lowastlowastlowast

LLIF minus0030922 0052822 LLIF 009 013

BelgiumLCAP 0631432 9574863lowastlowastlowast LCAP 064 5 65lowastlowastlowast


LLIF 4100562 4117858lowastlowastlowast LLIF 494 3 09lowastlowastlowast

CanadaLCAP 0457853 17146689lowastlowastlowast LCAP 042 1545lowastlowastlowast



DenmarkLCAP 0150649 1014066 LCAP 021 167lowastlowast


LLIF minus0652479 minus0487875 LLIF minus053 minus035

FinlandLCAP 0423049 10468373lowastlowastlowast LCAP 036 11 77lowastlowastlowast



FranceLCAP 0352652 6595592lowastlowastlowast LCAP 036 881lowastlowastlowast


LLIF 1114062 1825239lowastlowast LLIF 129 2 45lowastlowastlowast

JapanLCAP 0755467 13154394lowastlowastlowast LCAP 063 1101lowastlowastlowast



NetherlandsLCAP 0612448 9977939lowastlowastlowast LCAP 051 660lowastlowastlowast



NorwayLCAP 0451903 7206008lowastlowastlowast LCAP 030 5 11lowastlowastlowast


LLIF 2311630 1847358lowastlowast LLIF 265 169lowastlowast

SpainLCAP 0247169 2842918lowastlowastlowast LCAP 042 4 37lowastlowastlowast


LLIF 6585542 minus0760928 LLIF 463 282lowastlowastlowast

United KingdomLCAP 0635106 6874095lowastlowastlowast LCAP 039 3 79lowastlowastlowast


LLIF minus1144236 minus0760928 LLIF 115 070

United StatesLCAP 0748623 5240288lowastlowastlowast LCAP 052 3 74lowastlowastlowast

LED 0269667 1316384lowast LED 032 151lowast

LLIF 0982308 0188860 LLIF 660 134lowast

Panel group DOLS results Panel group FMOLS resultsLCAP 0475174 28216627lowastlowastlowast LCAP 042 2528lowastlowastlowast





Table 7 The comparison of the panels DOLS and FMOLS results

VariablesDeveloping countries Developed countries

Panel DOLS FMOLS Panel DOLS FMOLSCoefficient 119905-stat Coefficient 119905-stat Coefficient 119905-stat Coefficient 119905-stat

LCAP 0451805 2343083 038 1644 0475174 28216627 042 2528LED 0365050 1774895 041 1595 0449935 30208345 047 3034LLIF 4765641 805644 458 1102 2533908 13013286 340 1392

at 1 while the coefficient of the 1 country is significantat 5 and the coefficient of the 1 country is significant at10 significance level When the panel group statistics areexamined the results indicate that the coefficient is about253 and 340 according to the panels DOLS and the FMOLSmodels respectively By these results 1 increase in the lifeexpectancy at birth is accompanied with a 253 increase inGDP according to the DOLS and 340 increase according tothe FMOLS

4 An Overall Assessment of the Panels DOLSand FMOLS Modelsrsquo Outcomes

Table 7 compares the results of the panels DOLS and FMOLSmodels of developing and the developed countries It isobserved that the coefficients of LCAP and LED series of thedeveloped countries are higher than the developing countriesrsquocoefficients of LCAP and LED series The coefficient ofLCAP series of the developing countries is 0451805 and 038according to the panels DOLS and FMOLS models whilethe coefficient of LCAP series for the developed countriesis 0475174 and 042 according to the panels DOLS andFMOLS model results respectively The coefficient of LEDseries of the developing countries is 0365050 and 041 asa result of the panels DOLS and FMOLS models whilethe coefficient of LED series for the developed countries is0449935 and 047 according to the results of panels DOLSand FMOLS models respectively As a result of these modeloutcomes we can conclude that both of the physical capitaland education investments of the developed countries ledto a higher increase in output as compared with the outputincrease of the developing countries In other words bothof the physical capital and education expenditures of thedeveloped countries had been more efficient than these typesof investments of the developing countries for this specifiedtime period 1970ndash2010

When we want to evaluate the effect of life expectancyat birth on the aggregate output we see that the effect ofthis series is higher in the developing countries rather thanthe effect in the developed countries While the coefficient ofLLIF series is 4765641 and 458 according to the panelsDOLSand FMOLS model outcomes for the developing countriesthe coefficient of LLIF series of the developed countries isdetected as 2533908 and 340 as a result of these modelsrsquooutcomes One possible explanation for this consequence isthat retirement period of older people gradually increasesdue to the increase in life expectancy at birth as timepasses Therefore financial burden of retirement over theemployed population gradually increases and the share of

health expenditures (especially remedial healthcare) in GDPalso increases which restricts the economic growth rateowing to the reduction in investments made to other areasOn the other hand the contribution of the employees inthe developing countries to their economies gradually risesbecause increase in the life expectancy in those developingcountries leads to labor force being employed a longer timerather than increasing financial burden of retirement Owingto this fact the coefficient of LLIF series of the developingcountries turns out to be higher than the developed countriesrsquocoefficient of LLIF series according to both of the panelsDOLS and FMOLS model consequences

5 ConclusionIn this paper we employ the panel data of 13 developed and11 developing countries to determine the panel cointegrationand cointegrated regression relationship between physicalcapital human capital and GDP series over the period 1970ndash2010 We use gross fixed capital formation as physical capitalinvestment indicator As human capital indicators we useeducation expenditures and life expectancy at birth As aresult of panel unit root and cointegration tests all of thesefour variables are detected as nonstationary but cointegratedBecause the sufficiency condition of cointegration is providedin order to implement panel cointegrated regression testswe apply panels DOLS and FMOLS models It is found thatphysical capital investments and education expenditures aremore efficient to increase GDP in the developed countries incomparison to the developing countries according to bothof the panels DOLS and the FMOLS model consequencesOn the other hand life expectancy at birth is detected asmore efficient to increase GDP in the developing countriescompared to the developed countries Based on these resultswe can conclude that the developed countries which weexploit their data had made more efficient physical capitaland education investments as compared with the developingcountries in the analyzed period of time However weinterpret the main reason of life expectancy at birth tobecome more efficient in respect of increasing the GDP inthe developing countries as compared with the developedcountries as follows increase in the life expectancy of thesecountries causes a positive contribution to the economy dueto a longer time employment of the labor force rather thanan increase in the financial burden of retirement and healthexpenditures made for older people in contrast with thedeveloped countries That means that while the increasein the life expectancy of the developed countries leads toa positive contribution to economy it also restricts the


economic growth owing to it increasing the financial burdenof retirement and medical expenses for elders

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Savvides A and T Stengos Human Capital and EconomicGrowth Stanford University Press 2009

[2] B F Kiker ldquoThe historical roots of the concept of humancapitalrdquoThe Journal of Political Economy vol 74 no 5 pp 481ndash499 1966

[3] T W Schultz ldquoInvestment in human capitalrdquo The AmericanEconomic Review vol 51 no 1 pp 1ndash17 1961

[4] G S Becker ldquoInvestment in human capital a theoreticalanalysisrdquo Journal of Political Economy vol 70 pp 9ndash49 1962

[5] E F Denison ldquoUnited States economic growthrdquo Journal ofBusiness vol 35 no 2 pp 109ndash121 1962

[6] W L Hansen ldquoTotal and private rates of return to investmentin schoolingrdquo Journal of Political Economy vol 71 no 2 1963

[7] S G Becker Human Capital A Theoretical and EmpiricalAnalysis with Special Reference to Education NBER New YorkNY USA 1964

[8] M J Bowman ldquoPrinciples in the valuation of human capitalrdquoReview of Income and Wealth vol 14 no 3 pp 217ndash246 1968

[9] J Mincer ldquoThe distribution of labor incomes a survey withspecial reference to the human capital approachrdquo Journal ofEconomic Literature vol 8 no 1 p 26 1970

[10] G Psacharopoulos and M Woodhall Education for Devel-opment An Analysis of Investment Choices Johns HopkinsUniversity Press 1985

[11] P M Romer ldquoIncreasing returns and long-run growthrdquo TheJournal of Political Economy vol 94 no 5 pp 1002ndash1037 1986

[12] K Arrow ldquoEconomic welfare and the alloca tion of resourcesfor inventionrdquo in The Rate and Direction of Inventive ActivityEconomic and Social Factors pp 609ndash626 NBER 1962

[13] R E Lucas Jr ldquoOn the mechanics of economic developmentrdquoJournal of Monetary Economics vol 22 no 1 pp 3ndash42 1988

[14] E Unsal Iktisadi Buyume 1 Baskı Imaj Yayınevi AnkaraTurkey 2007

[15] G Mankiw D Romer and D Weil ldquoA contribution to theempirics of economic growthrdquo Quarterly Journal of Economicsvol 152 pp 407ndash437 1992

[16] J Benhabib and M M Spiegel ldquoThe role of human capital ineconomic development evidence from aggregate cross-countrydatardquo Journal of Monetary Economics vol 34 no 2 pp 143ndash1731994

[17] R J Barro ldquoEconomic growth in a cross section of countriesrdquoQuarterly Journal of Economics vol 106 no 2 pp 407ndash443 1991

[18] D Asteriou and G M Agiomirgianakis ldquoHuman capital andeconomic growth time series evidence fromGreecerdquo Journal ofPolicy Modeling vol 23 no 5 pp 481ndash489 2001

[19] M A Babatunde and R A Adefabi ldquoLong run relationshipbetween education and economic growth in Nigeria evidencefrom the Jo hansenrsquos cointegration approachrdquo in RegionalConference on Education inWest Africa Constraints and Oppor-tunities pp 1ndash21 Dakar Senegal November 2005

[20] K Gyimah-Brempong and M Wilson ldquoHealth human capitaland economic growth in Sub-Saharan African and OECDcountriesrdquo Quarterly Review of Economics and Finance vol 44no 2 pp 296ndash320 2004

[21] K Gyimah-Brempong O Paddison and W Mitiku ldquoHighereducation and economic growth in Africardquo Journal of Develop-ment Studies vol 42 no 3 pp 509ndash529 2006

[22] S Kalemli-Ozcan H E Ryder and D N Weil ldquoMortalitydecline human capital investment and economic growthrdquoJournal of Development Economics vol 62 no 1 pp 1ndash23 2000

[23] A Bhargava D T Jamison L J Lau and C J L MurrayldquoModeling the effects of health on economic growthrdquo Journalof Health Economics vol 20 no 3 pp 423ndash440 2001

[24] D Mayer ldquoThe longminusterm impact of health on economicgrowth in Mexico 1950ndash1995rdquo Journal of International Devel-opment vol 13 no 1 pp 123ndash126 2001

[25] D E Bloom D Canning and J Sevilla ldquoThe effect of healthon economic growth a production function approachrdquo WorldDevelopment vol 32 no 1 pp 1ndash13 2004

[26] C Dreger and H E Reimers ldquoHealth care expenditures inOECD countries a panel unit root and cointegration analysisrdquoIZA Discussion Paper No 1469 2005

[27] A G Akpolat and N Altintas ldquoThe long-term impact of healthon GDP in 19 OECD countriesrdquo International Journal of SocialEcology and Sustainable Development vol 3 no 1 pp 53ndash602012

[28] M S de Baldini Rocha and V Ponczek ldquoThe effects of adultliteracy on earnings and employmentrdquo Economics of EducationReview vol 30 no 4 pp 755ndash764 2011

[29] P Pedroni ldquoPurchasing power parity tests in cointegratedpanelsrdquo Review of Economics and Statistics vol 83 no 4 pp727ndash731 2001

[30] P Pedroni ldquoFully modified OLS for heterogeneous cointe-grated panelsrdquo in Nonstationary Panels Panel Cointegrationand Dynamic Panels H B Baltagi Ed vol 15 of Advances inEconometrics pp 93ndash130 2000

[31] N Ozturk ldquoIktisadi kalkınmada egitimin rolurdquo Sosyo EkonomiDergisi vol 1 no 1 pp 27ndash44 2005

[32] H Inac U Guner and S Sarısoy ldquoEgitimin EkonomikBuyume ve Kalkınma Uzerindeki Etkilerirdquo Eskisehir OsmangaziUniversitesi IIBF Dergisi pp 59ndash70 2006

[33] R Sari ldquoKazanclar ve egitim iliskisi Il baz ında yeni veri tabanıile kanıtrdquoODTUGelistirmeDergisi vol 29 no 3-4 pp 367ndash3802002

[34] D N Weil ldquoAccounting for the effect of health on economicgrowthrdquo NBER Working Paper Series Working Paper 114552005

[35] D E BloomD Canning andG FinkDisease andDevelopmentRevisited (No w15137) National Bureau of Economic ResearchCambridge Mass USA 2009

[36] R Ram and T W Schultz ldquoLife span health savings andproductivityrdquo Economic Development and Cultural Change vol27 no 3 pp 399ndash421 1979

[37] J Sachs and P Malaney ldquoThe economic and social burden ofmalariardquo Nature vol 415 no 6872 pp 680ndash685 2002

[38] J R Behrman ldquoEarly life nutrition and subsequent educationhealth wage and intergenerational effectsrdquoHealth and Growthvol 6 pp 167ndash183 2009

[39] W Jack and M Lewis ldquoHealth investments and economicgrowth macroeconomic evidence and microeconomic foun-dationsrdquo in Health and Growth M Spence and M Laureen


Eds The International Bank for Reconstruction and Develop-mentWorld Bank Washington DC USA 2009

[40] A Levin C Lin and C J Chu ldquoUnit root tests in panel dataasymptotic and finite-sample propertiesrdquo Journal of Economet-rics vol 108 no 1 pp 1ndash24 2002

[41] K S Im M H Pesaran and Y Shin ldquoTesting for unit roots inheterogeneous panelsrdquo Journal of Econometrics vol 115 no 1pp 53ndash74 2003

[42] G S Maddala and S Wu ldquoA comparative study of unit roottests with panel data and a new simple testrdquo Oxford Bulletin ofEconomics and Statistics vol 61 no S1 pp 631ndash652 2001

[43] P Pedroni ldquoCritical values for cointegration tests in hetero-geneous panels with multiple regressorsrdquo Oxford Bulletin ofEconomics and Statistics vol 61 no 1 pp 653ndash670 2001

[44] C Kao ldquoSpurious regression and residual-based tests for coin-tegration in panel datardquo Journal of Econometrics vol 90 no 1pp 1ndash44 1999

[45] S Nazlıoglu Makro Iktisat Politikalarının Tarım SektoruUzerindeki Etkileri Gelismis Ve Gelismekte Olan Ulkeler IcinBir Karsılastırma [Yayınlanmamıs Doktora Tezi] TC ErciyesUniversitesi Sosyal Bilimler Enstitusu Kayseri Turkey 2010

Submit your manuscripts athttpwwwhindawicom

Child Development Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Education Research International


Biomedical EducationJournal of



Psychiatry Journal

ArchaeologyJournal of



AnthropologyJournal of


Research and TreatmentSchizophrenia


Urban Studies Research

Population ResearchInternational Journal of


CriminologyJournal of


Aging ResearchJournal of



NursingResearch and Practice

Current Gerontologyamp Geriatrics Research

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AddictionJournal of


Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geography Journal


Research and TreatmentAutism


Economics Research International


theory and state that the explanatory power of the model isincreased as compared with the neoclassical model owing tothis inclusion Benhabib and Spiegel [16] use cross-countryestimates of physical and human capital stocks as indicatorsand run the growth accounting regressions implied by aCobb-Douglas production function They find that humancapital is insignificant at explaining per capita growth ratesThey also develop a model in which the growth rate oftotal factor productivity depends on a nationrsquos human capitalstock level According to this alternative model they findthe result that human capital positively affects the growthrate of total factor productivity Besides these studies lots ofempirical studies are made to determine the human capitaland growth relationship [17ndash28] While education expendi-tures and schooling are exploited as education indicatorshealth expenditures and life expectancy at birth stand outas health indicators in most of these studies The majorityof these studies indicate that both improvements in healthand education indicators lead to a positive effect on growthand GDP due to the developments of human capital level ofcountries

Because economic growth is a long-run phenomenonit is so important to determine the long-run effects ofphysical and human capital variables Due to this fact themain purpose of this study is to test the effect of humanand physical capital on GDP The study aims to realizethis by means of using gross fixed capital formation asphysical capital indicator and education expenditures andlife expectancy at birth as human capital indicators byanalyzing the data of the 13 developed and the 11 developingcountries The remarkable feature of the study is that it usesthe cointegrated panel regression models which are panelsDynamic Ordinary Least Squares (DOLS) [29] and FullyModified Ordinary Least Squares (FMOLS) [30] methodsBecause the precondition of these models is the existenceof cointegration between variables there is no need to takedifferences of variables to overcome nonstationarity By thisway any loss of information concerning variables does notoccur Another objective of the study is to measure themagnitude of the effect of these explanatory variables onGDP according to these two different groups of countriesHereby we can understand which variable is more effectiveto increase GDP in which country group

The rest of the study is as follows Section 2 presentsa brief summary about the relationship between educa-tion health and economic growth The empirical resultsin Section 3 introduce the consequences of the cointegratedpanel analysis which are panels DOLS and FMOLS Section 4presents an overall assessment about the consequences of theeconometric analysis Section 5 presents a conclusion

2 A Brief Summary about Education Healthand Economic Growth Relationship

The studies that associate education with economic growthsuggest some reasons to clarify the issue Ozturk [31] statesfour reasons about this relationship (i) Education advancesthe efficiency of labor and thus production through scientific

and technological developments which it causes (ii) Educa-tion provides developing the potential skills of individuals(iii) Education enhances the ability to adapt to emergingbusiness opportunities (iv) Educational institutions provideknowledge to be transferred to future generations by edu-cating teaching staff [31] Moreover the impact of educationcontinues over generations owing to the fact that educatedindividuals cultivate healthier andmore educated generationsso they maintain the high human capital level of theirsociety Because the fertility rates of educated families arelow population growth will be balanced and savings percapita remain high High level of saving rates positivelycontributes to economy [32] In addition to these increasein educational level of society leads to an improvementon income distribution and prevents poverty because ofits providing of advancement of individualsrsquo high-earningcapacity [33]

As for health and growth relationship several reasonsand channels are stated by economists on how health affectseconomic growth First of all healthier people reveal a moreeffective performance throughout their professional livesrather than people having low level of health Furthermoreadvances in health level of society increase the educationalinvestments which increase the long-life expected returns ofeducation Besides these improvements in health level ofstudents bring about their having a better cognitive abilitythat helps to receive a better education [34] Bloom et al[35] convey that a significant cause of studentsrsquo learningdisabilities is diseases Ram and Schultz [36] and Sachsand Malaney [37] state that taking malaria under controlimproves labor force and student efficiency Improvementsin both labor force and student efficiency positively affecteconomic growth as it is known As noted by Behrman[38] malnutrition in childhood is detected to relate withthe low economic efficiency Jack and Lewis [39] state thatthe increase in life expectancy of adults leads to increase intheir investments on their own children and so improves thehuman capital of next generations Weil [34] declares thatdecreasing mortality rates leads to increase in retirement ageand so saving rates of society thus provide a high level ofinvestments

3 Econometric AnalysisThis paper examines the relationship between educationexpenditures and life expectancy at birth (which are bothevaluated within the concept of human capital) and GDP Inthe study the relationship between human capital and GDPis analyzed for 13 developed and 11 developing countries overthe period 1970ndash2010The data were obtained from theWorldBank databaseThedeveloped countries that we use their dataare Australia Austria Belgium Canada Denmark FinlandFrance Japan Netherlands Norway Spain United Kingdomand United StatesThe developing countries are Brazil ChileEgypt Ireland Israel Malaysia Mexico Pakistan SingaporeTurkey and Uruguay Even though Ireland Israel and Sin-gapore are counted as developed countries recently they hadbeen counted as developing countries in most of this 41-yearperiod They gained the status of developed country towards






















LGDP119894119905= 120572

1119894LCAP

119894119905+ 120572

2119894LED119894119905+ 120572

3119894LLIF119894119905

(119894 = 1 2 3 119873) (119905 = 1 2 3 119879)

(1)

























119884

119894119905= 120572

119894+ 120573

119894119883

119894119905+

119901119894

sum

119896=minus119901119894

120574

119894119896Δ119883

119894119905minus119896+ 120576

119894119905 (2)

Here 119901119894and minus119901





120573

lowast

119894= 119873

minus1

119873

sum

119894=1

(

119879

sum

119905=1

119885

119894119905119885

1015840

119894119905)

minus1

(

119879

sum

119905=1

119885

119894119905119884

lowast

119894119905)

(3)

Here 119885119894119905= (119883

119894119905minus 119883

119894 Δ119883

119894119905minus119901 Δ119883

119894119905+119901) is the vector of


120573 = 119873

minus1

119873

sum

119894=1

120573

119894 (4)

120573



119905 120573= 119873

minus12

119873

sum

119894=1

119905 120573119894

(5)



Hypothesis






Prob


119905 120573119894



119884

119894119905= 120572

119894+ 120573119883

119894119905+ 119890

119894119905

119883

119894119905= 119883

119894119905minus1+ 120576

119894119905

(6)


120573

lowast

119873119879= 119873

minus1

119873

sum

119905=1

(

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

)

minus1

times (

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

119884

lowast

119894119905minus 119879120591

119894)

119884

lowast

119894119905= (119884

119894119905minus 119884

119894) minus

119871

21119894

119871

22119894

Δ119883

119894119905

(7)

where

120591

119894=

Γ

21119894+ Ω

0

21119894minus

119871

21119894

119871

22119894

(

Γ

22119894minus Ω

0

22119894) (8)

Here Ω119894= Ω

0

119894+ Γ

119894+ Γ

1015840



119894is a




























































LLIF minus0030922 0052822 LLIF 009 013

































LLIF 0982308 0188860 LLIF 660 134lowast









LCAP 0451805 2343083 038 1644 0475174 28216627 042 2528LED 0365050 1774895 041 1595 0449935 30208345 047 3034LLIF 4765641 805644 458 1102 2533908 13013286 340 1392











References
























































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal


























LGDP119894119905= 120572

1119894LCAP

119894119905+ 120572

2119894LED119894119905+ 120572

3119894LLIF119894119905

(119894 = 1 2 3 119873) (119905 = 1 2 3 119879)

(1)

























119884

119894119905= 120572

119894+ 120573

119894119883

119894119905+

119901119894

sum

119896=minus119901119894

120574

119894119896Δ119883

119894119905minus119896+ 120576

119894119905 (2)

Here 119901119894and minus119901





120573

lowast

119894= 119873

minus1

119873

sum

119894=1

(

119879

sum

119905=1

119885

119894119905119885

1015840

119894119905)

minus1

(

119879

sum

119905=1

119885

119894119905119884

lowast

119894119905)

(3)

Here 119885119894119905= (119883

119894119905minus 119883

119894 Δ119883

119894119905minus119901 Δ119883

119894119905+119901) is the vector of


120573 = 119873

minus1

119873

sum

119894=1

120573

119894 (4)

120573



119905 120573= 119873

minus12

119873

sum

119894=1

119905 120573119894

(5)



Hypothesis






Prob


119905 120573119894



119884

119894119905= 120572

119894+ 120573119883

119894119905+ 119890

119894119905

119883

119894119905= 119883

119894119905minus1+ 120576

119894119905

(6)


120573

lowast

119873119879= 119873

minus1

119873

sum

119905=1

(

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

)

minus1

times (

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

119884

lowast

119894119905minus 119879120591

119894)

119884

lowast

119894119905= (119884

119894119905minus 119884

119894) minus

119871

21119894

119871

22119894

Δ119883

119894119905

(7)

where

120591

119894=

Γ

21119894+ Ω

0

21119894minus

119871

21119894

119871

22119894

(

Γ

22119894minus Ω

0

22119894) (8)

Here Ω119894= Ω

0

119894+ Γ

119894+ Γ

1015840



119894is a




























































LLIF minus0030922 0052822 LLIF 009 013

































LLIF 0982308 0188860 LLIF 660 134lowast









LCAP 0451805 2343083 038 1644 0475174 28216627 042 2528LED 0365050 1774895 041 1595 0449935 30208345 047 3034LLIF 4765641 805644 458 1102 2533908 13013286 340 1392











References
























































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal






















119884

119894119905= 120572

119894+ 120573

119894119883

119894119905+

119901119894

sum

119896=minus119901119894

120574

119894119896Δ119883

119894119905minus119896+ 120576

119894119905 (2)

Here 119901119894and minus119901





120573

lowast

119894= 119873

minus1

119873

sum

119894=1

(

119879

sum

119905=1

119885

119894119905119885

1015840

119894119905)

minus1

(

119879

sum

119905=1

119885

119894119905119884

lowast

119894119905)

(3)

Here 119885119894119905= (119883

119894119905minus 119883

119894 Δ119883

119894119905minus119901 Δ119883

119894119905+119901) is the vector of


120573 = 119873

minus1

119873

sum

119894=1

120573

119894 (4)

120573



119905 120573= 119873

minus12

119873

sum

119894=1

119905 120573119894

(5)



Hypothesis






Prob


119905 120573119894



119884

119894119905= 120572

119894+ 120573119883

119894119905+ 119890

119894119905

119883

119894119905= 119883

119894119905minus1+ 120576

119894119905

(6)


120573

lowast

119873119879= 119873

minus1

119873

sum

119905=1

(

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

)

minus1

times (

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

119884

lowast

119894119905minus 119879120591

119894)

119884

lowast

119894119905= (119884

119894119905minus 119884

119894) minus

119871

21119894

119871

22119894

Δ119883

119894119905

(7)

where

120591

119894=

Γ

21119894+ Ω

0

21119894minus

119871

21119894

119871

22119894

(

Γ

22119894minus Ω

0

22119894) (8)

Here Ω119894= Ω

0

119894+ Γ

119894+ Γ

1015840



119894is a




























































LLIF minus0030922 0052822 LLIF 009 013

































LLIF 0982308 0188860 LLIF 660 134lowast









LCAP 0451805 2343083 038 1644 0475174 28216627 042 2528LED 0365050 1774895 041 1595 0449935 30208345 047 3034LLIF 4765641 805644 458 1102 2533908 13013286 340 1392











References
























































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal







Hypothesis






Prob


119905 120573119894



119884

119894119905= 120572

119894+ 120573119883

119894119905+ 119890

119894119905

119883

119894119905= 119883

119894119905minus1+ 120576

119894119905

(6)


120573

lowast

119873119879= 119873

minus1

119873

sum

119905=1

(

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

)

minus1

times (

119879

sum

119905=1

(119883

119894119905minus 119883

119894)

2

119884

lowast

119894119905minus 119879120591

119894)

119884

lowast

119894119905= (119884

119894119905minus 119884

119894) minus

119871

21119894

119871

22119894

Δ119883

119894119905

(7)

where

120591

119894=

Γ

21119894+ Ω

0

21119894minus

119871

21119894

119871

22119894

(

Γ

22119894minus Ω

0

22119894) (8)

Here Ω119894= Ω

0

119894+ Γ

119894+ Γ

1015840



119894is a




























































LLIF minus0030922 0052822 LLIF 009 013

































LLIF 0982308 0188860 LLIF 660 134lowast









LCAP 0451805 2343083 038 1644 0475174 28216627 042 2528LED 0365050 1774895 041 1595 0449935 30208345 047 3034LLIF 4765641 805644 458 1102 2533908 13013286 340 1392











References
























































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal
























































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LLIF 0982308 0188860 LLIF 660 134lowast









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References
























































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal









LCAP 0451805 2343083 038 1644 0475174 28216627 042 2528LED 0365050 1774895 041 1595 0449935 30208345 047 3034LLIF 4765641 805644 458 1102 2533908 13013286 340 1392











References
























































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal









References
























































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal





















Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal





research article the long-term impact of human capital...

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