Education and Poverty in Special Province of Yogyakarta: The

Approach of Solow Growth Technology Model in Production Theory

Suripto Suripto

1,2

, Firmansyah Firmansyah

and FX. Sugiyanto

Faculty of Economics and Business, Diponegoro University

Faculty of Economics, Ahmad Dahlan University

suriptobantul@gmail.com

Keywords: Solow Growth Model, Educational Investment, Poverty, Poverty line.

Abstract: From the economic aspect, the level of education is believed to reduce poverty by improving skills that can

influence the household income. Meantime, the poor with skills produced from formal and non-formal

education will be rescued from market price shocks. By using the perspective of the production function with

adopts Solow's growth model technology, this study analyses how the formal and non-formal educations

affect income levels, and subsequently consumption. With certain lines of consumption, a household is

classified as poor or not poor so that it can be examined the probability of household being either poor or non-

poor influenced by formal and non-formal education. This research is applied on Special Province of

Yogyakarta and is expected to explain one aspect of poverty behaviour in Special Province of Yogyakarta.

1 INTRODUCTION

Poverty is a development effort to create prosperity

through the fulfilment of human needs. Failure to

meet basic needs can occur due to a market and re-

quires the government's side to overcome it.

According to Word Bank (2001), poverty is the

understanding, or inability to achieve, a generally

accepted standard of living.

In 2012 the Special Province of Yogyakarta

experienced the worst level of poverty in the bottom

25 of 33 provinces) but has a very good Human

Development Index (HDI). An interesting finding in

D.I.Yogyakarta Province shows that high HDI is not

followed by low poverty rates.

Good HDI will impact productive communities

and subsequently depends on economic growth and

declining unemployment. The improvement of HDI

will be followed by economic growth and declining

unemployment rate. HDI can encourage the

improvement of human resources and in turn, will

result in economic growth and decline in

unemployment.

Improving the quality of human resources can

occur with cheap investment educators. The impact of

education on poverty is examined by (Grimm, 2005),

found to be a direct effect of education and income,

depending on the choice of employment and house-

hold composition. Education is an efficient way to

reduce poverty and fairer inequality

The cause of someone being poor is an interesting

study to observe. According to Barnes (2005), the

globalisation resulted in industrialisation shifting

from manufacturing industry to service industry, and

there was a reduction of manpower with low human

resources replaced by high human resource work-

force. Barnes (2005) sees that the main factor causing

poverty is the depletion of human resources of the

poor.

The solution to poverty reduction is done by

increasing the human resources of the poor.

Investment in education will affect the ability of the

poor to earn income. Rising incomes will reduce the

number of poor families. Bhaumik and Banik (2009)

found that human capital improvements are strongly

related to the resilience of the poor to obtain

permanent income. Increasing formal education to the

poor will improve skills and sensitivity to external

changes. This sensitivity will avoid the loss of their

income. Poor people with more intensive formal

724

Suripto, S., Firmansyah, F. and Sugiyanto, F.

Education and Poverty in Special Province of Yogyakarta: The Approach of Solow Growth Technology Model in Production Theory.

In Proceedings of the 2nd International Conference on Economic Education and Entrepreneurship (ICEEE 2017), pages 724-731

ISBN: 978-989-758-308-7

skills will be spared from the failure of price-level

shocks in the output market.

Theoretically, poverty is influenced by low

productivity. A person's productivity level can be

influenced by the level of education, real knowledge

and skills and the level of health. The higher

education that is graduated and the longer they go to

education will have better skills and will have an

impact on higher incomes and have a lower chance of

becoming poor.

1.1 Solow Growth Model

It is assumed that the family is the smallest unit of

production of goods and services by using its

production factor in the form of capital and labour.

Capital consists of human capital and physical

capital.

The main assumptions of Solow's growth model

are; (I) the economy is closed for international

transactions, (ii) all stored output is invested, (iv)

perfect price flexibility and monetary neutrality (i) the

economy consists of one sector producing one type of

commodity that can be used for either investment or

consumption purposes; Apply and the economy al-

ways generates its potential output; (V) the rate of

technological progress, population growth, and the

rate of capital depreciation are all exogenously

determined.

Solow growth model is built based on two big

ideas namely production function and the equation of

model accumulation function. The production

function is assumed to follow the Cobb-Douglas

production function as follows (C. Jones, 1998),

(Romer, 2000), and the production function is based

on physical capital (K), Productivity Augmented

Labor (AL) and human capital (Jones) 1986):







),,(

tttt

LAHKALHKFY

(1)

α is worth between 0 and 1

0)(),(



ttt

eheh

(2)

1.2 The Impact of Education on Labor

Productivity

Education is one of the most important inputs to

produce human resources. Education produces a

stock of accumulated skills and experiences that make

workers more productive, (Bassetti, 2012). Trostel

(2004) suggests that the production function of

human capital increases at a low level of education

and declines at a high level of education. Trostel

(2004) concluded that the educational relationship

with labour productivity is non-linear and directly

related to the accumulation of human capital. In other

words, the production function of human capital has

a cubic form, which is a typical production function

used in the function of microeconomic production.

(Bassetti, 2008) States that education is the only

input that increases human capital. Education deals

with one's technological development capabilities.

Education will enable one to capture new

technologies and develop technology that will

ultimately increase production through increased

productivity (B. F. Jones, 2014). The process of the

occurrence of human capital depends on the time in

which the individual provides time for education. If

Lt is the population at time t in an economy, μ is the

time the individual chooses to work; it is the

willingness of the individual at time t who is willing

to invest his or her opinion for education. So the

model of individuals willing to invest in education is:

Solow's growth model emphasises the importance

of individual technology development from self-

development because of the stock of knowledge.

Knowledge stocks can occur from a person's

education. The advent of technology will result in the

depreciation of human capital stocks, because the

new technology will require new knowledge to

master the technology and will replace the old

knowledge possessed by someone. High technology

requires new knowledge and will leave the old

knowledge known as the effects of vice (vintage

effect). Technological advances affect the

improvement of knowledge and will increase the

demand for experts resulting in obsolete experts; the

ultimate impact will increase the demand for

individual education, known as the technical

depreciation effect (Bassetti, 2008).

If Eht is the effect that an individual obtains

because of the education obtained at time t, and t is

the depreciation of human capital due to the effects of

obsolescence at time t, then the model of human

capital accumulation through education is:

0)('

)(





hEh



(3)

The Meaning of Equation (3) is the effect of

individual educational investments on individual

stocks of capital determined by individual

productivity be-cause of education reduced by

depreciation due to the effects of knowledge

obsolescence.

Education and Poverty in Special Province of Yogyakarta: The Approach of Solow Growth Technology Model in Production Theory

725

By combining two equations (2) and (3) then it is

assumed that the stock of human capital is linearly

correlated with the depreciation of knowledge then

obtained:

)(

ehEhe





(4)

It is assumed that the productivity gained from the

educational investment will outweigh the effects of

obsolescence (E> σ) so that educational investment

affects the accumulation of individual knowledge.

The process of knowledge accumulation can be writ-

ten as follows:

)exp(

EeE







(5)

Equation (5) means that the stock of knowledge

accumulation will depend on the individual choice of

the school and the knowledge stock is not

proportional to the time of the education.

His process of obtaining knowledge stock is the

aggregate sum of the individual activities in

conducting educational activities, so the equation of

accumulated knowledge stock is:





hLdihiA

(6)

Hi is the level of human capital owned by

individuals in period t, and is the average human

capital that all workers do. From equation (6) it is

known that the average stock of knowledge is

determined by the level of education, then based on

equations (5) and (6) can be obtained:

)exp(

eEE







(7)

Where is the average level of education pursued

in a given region, and by the combination of

equations (6), equations (5), and equation (1) and

considering the size per effective labour obtained:























)exp(

)(

eEE

eEEp

(8)

is the output per unit of effective labour and is

capital per effective labour, equation (8) shows that

education is the input resulting from the existence of

human capital education. Findings (C. I. Jones, 2001)

found that there is a positive relationship between

GDP growth and the level of education affecting the

growth of a country's output.

The per capita output is obtained by combining

equation (7), equation (8), and equation (5). If the

educational investment is, which means educational

investment per capita depends on the amount of time

to pursue education, then the equation is obtained:







)(Aheky

(9)

Total production will be influenced by the total

acquisition of knowledge A and the average length of

time for education. In the output growth equation

becomes:

kefAhyg ln)(ln)1(ln)(ln





(10)

The output growth is influenced by the growth of

knowledge due to education investment (

) and

the average growth of the school year and the growth

of physical investment per capita. The growth of

knowledge measured by Ah can be seen as the

residual variable (Bassetti, 2008), so output depends

on the level of education. The growth of output is

writ-ten:





Xeyg

(11)

The total productivity of a production function is

influenced by the average school year

of βi and the

control variable influencing the acquisition of

knowledge determined by external factors (

1.3 Research Model

Equation model 10 is used to explain the state of

poverty in the Special Province of Yogyakarta.

Assuming that the output produced by the family

follows equation 11, and all outputs obtained are used

to consume goods and services. The poverty rate in

this study was calculated using the head count index

method. Household poverty rate based on the poverty

line of Central Bureau of Statistics (BPS), the line of

papers is Rp 303,843.

The dependent variable is dummy variable that is

poor household and not poor so this research use

Cumulative Logistic Distribution Function (logit

model) that is:

P(Yi = 0/Xj) =





(12)

Logit model (LYi) for empirical estimation

purposes, as follows:

iij



















(13)

ICEEE 2017 - 2nd International Conference on Economic Education and Entrepreneurship

726

1

is an odds ratio that is defined as the ratio

of house-hold probability belonging to the poor

category of household probability belonging to the

non-poor category. The independent variable (Xi)

consists of the year of school variable and the control

variable.

Table 1: Independent variables.

Year of School Variable

MSEKO

Average length of school for all

household members in a year

IJAH1

The highest diploma owned by the

head of household, 1 if less than Senior

High School, 0 if the high school and

above.

Control variables

Household size in person

UMUR

Age of head of household in the year.

PKR

Work of the head of household, 1 if

agriculture, 0 if non-agricultural.

SKR

Status of Occupation of the head of

household, 1 if informal, 0 if formal.

GEO3

Domestic area of residence, 1 if the

residence in the land area, 0 if the

residence in the other part.

MPKR

On average all household members

work in year



: Variable pester, β0: constant, βj: parameter coefficient

2 METHODS

Estimation of logit model using Maximum

Likelihood Estimator (MLE) because of logit model

is the nonlinear model in parameter and in variable

and data used is individual data, so probability value

is unknown (Gujarati, 2004). The logit model is then

tested individually (partially) by testing the Z test

statistic, testing the model as a whole (simultaneous)

with likelihood ratio test statistic (LR), and testing the

goodness of fit Goodness with McFadden R2

(R2McF). Interpretation of logit model will be

distinguished by variable type that is category

variable and numeric / continuous variable by looking

at odds ratio and Marginal effect.

The data used in this study is secondary data with

the main data derived from raw data Susenas D.I.

Yogyakarta in 2013, supplemented with and

supporting data including PDRB data, poverty data,

public welfare indicator data (inkesra), and economic

indicators. The sample numbered 3606 households.

2.1 Variable Operational Definition

Dependent variable (LYi) is household poverty status

in Special Province of Yogyakarta in the form of a

dummy variable, 1 if household falls into the poor

category and 0 if not poor. Definition of the

dependent variable and independent variable used in

this re-search are:

 Household poverty status is absolute poverty,

households are said to be poor if their income is

not able to meet their minimum requirements. In

this study, it is said to be poor if household per

capita expenditure is below the poverty line of

Rp303,843 per capita per month.

 Household size is the number of people living in

households six months or more, or who will be

living in households six months or more.

 The age of the head of the household is the age

of a person of the household member who is

responsible for the daily needs of the household.

 The work of the head of the household is the

type of household head's work which is

differentiated in the agricultural and non-

agricultural sectors.

 Occupation status of head of household is the

status of employment of head of household

which is differentiated into non-formal (in-

formal) and formal status.

 The territory of residence shall be the area of

residence of the household based on the

topography of the territory which is divided in-

to land and non-land areas.

 The average length of school for all household

members is the number of years that all

household members take in formal education

which is calculated to the highest level of

education or the highest grade ever occupied.

 The highest diploma of household head is the

highest certificate owned by the head of the

household based on the highest education that is

completed.

 The average member of the working house-hold

is the average member of the working household

and will affect the household in-come level.

3 RESULTS AND DISCUSSION

The determinant model of Special Province of

Yogyakarta in 2013 provides information that the size

of household heads, household heads, employment

status of head of households have a positive and

significant impact on household poverty status.

Variable area of residence, the average length of the

school of household members, the highest Owned by

Education and Poverty in Special Province of Yogyakarta: The Approach of Solow Growth Technology Model in Production Theory

727

the head of household, the average member of the

working household and the age of the household head

had a negative and significant effect on the household

poverty status (Table 2).

Table 2: Estimation result of determinant model household

poverty in special province of Yogyakarta Year 2013 (n =

3606).

Variable

Estimate

Odds

Ratio

Marginal

Effect

-0.9526

-2.697

0.3857

-0.0722

IJAH*

-0.0489

-2.451

0.9523

-0.0037

MSEKO*

-0.2938

-12.17

0.7454

-0.0223

UR*

0.4420

12.749

1.5558

0.0335

UMUR**

-0.0069

-1.6986

0.9931

-0.0005

PKR*

0.7538

6.3125

2.1250

0.0571

SKR*

0.5323

3.6613

1.7028

0.0403

MPKR**

-0.3711

-1.766

0.6900

-0.0281

GEO3*

-0.4048

-3.3552

0.6671

-0.0307

R2McF

0,223584

LR statistic (10 df)

3,35228

Probability(LR stat)

0.000000

*, **, significant at the 5% significance level and 10%

Test Model individually in Table 2 by comparing

the Z value of statistics with Z table with the

significance level () of 0.05 or 0.10. The estimation

results indicate that the variables of household

members (UR), occupation of head of household

(PKR), employment status of head of household

(SKR), residence area (GEO3), average length of

member school of household (MSEKO) and diploma

(IJAH) has a significant and statistically significant

effect on the 5 per-cent significance level of

household poverty status in Special Province of

Yogyakarta. The average member of the working

household (MPKR) and the age of the household head

(UMUR) affect the household poverty status in D.I

Yogyakarta province with a significance level of 10

percent.

From the regression result, the estimated logit

model shows the LR statistic value of 718.5542. The

comparison of the statistical LR value with the table

value indicates that the LR value is considerably

larger than the value of the table at the 0.05

significance level. This means that statistically

independent variables together affect the probability

of household poverty in Special Province of

Yogyakarta.

Test the goodness of fit by looking at the value of

R2McF of 0.223584, which means that 22.36 percent

variation of household poverty status in Special

Province of Yogyakarta can be explained by the

variables in the model. This R2McF value is good for

cross-data (Kabananukye, et.all, 2004).

The household education variable in this study is

represented by the highest certificate owned by the

head of household (IJAH). The 2013 logit model

obtained that the highest certificate owned by the

head of household has a negative and significant

effect on the poor status of the household. Estimated

value of 0.048922 and odds ratio of 0.9523. This

means that every increase of one level of highest

education certificate owned by the head of household

head then the probability of the household into the

poor category will be 0.9523 times the house-hold

with lower education level. In other words, the higher

the diploma held by the head of household, the lower

the probability of the poor category of the household.

The marginal effect of the highest diploma variable

owned by the head of household is -0,0037, meaning

the chances of household entering into the poor

category will be reduced by 0.37 percent if the highest

certificate owned by the head of house-hold is

increased one level higher. This shows that education

plays an important role in the family to get out of

poverty. The higher the diploma held by the head of

the household will have a large stock of knowledge

and the productivity of the head of the household will

increase. The head of household responsible for the

fulfilment of the economic needs provided with

higher formal education will have an impact on

increasing the productivity, and the quality of output

produced so that the wages received will increase.

Households included in the poor category will be

smaller. The same statement that the education of the

head of the household negatively affects poverty by

the re-search of Ueda, et.al (2005: 11), (Guillaumont,

Guillaumont Jeanneney, & Wagner, 2017).

The variable of human resources (HR) in the

research was obtained by the average variable of

school length of the household member (SEKO). The

result of coefficient estimate shows that the average

length of the school of a member of the household has

significant influence with household risk to be poor.

The coefficients of the MSEKO variable are -

0.293816 with the odd ratio of 0.7454. This means

that every in-crease in the average length of school

for one-year household members, the chances of poor

households being 0.293816 households with the

average length of school for smaller household

members. The marginal effect of this variable

indicates that the probability of households falling

into the poor category in the year is reduced by 2.23

ICEEE 2017 - 2nd International Conference on Economic Education and Entrepreneurship

728

percent if there is an additional one-year-old school

member household. From the interpretation of this

logit model proves that education as an effort to

improve human re-sources has a strong relationship

with the risk of households entering the poor

category. Poverty has a strong relationship with

education and economic growth. Education is a

multidimensional process that will impact on

economic growth and, on the other hand, reduce

poverty by increasing labour productivity (Brück,

n.d.) et.al. (2013). A more pro-active individual with

higher quality output results can earn higher wages.

Education plays a very important role in building

human capabilities and promoting economic growth

through skills and knowledge. The results of the study

(Brück, nd, et.al (2007: 26) also state that education

of members of households is important in improving

welfare.Babatunde & Adefabi (2005) argue that

education triggers economic growth through many

factors such as increased employment, Reducing

fertility and poverty levels, promoting technological

development, and the source of political stability

Education is the first step in the path of the

development process and providing the basis for

improving the socio-economic conditions of a

country education is considered an important

instrument for reducing poverty (Jung & Thorbecke,

2003).

The number of household members has a positive

and significant effect on the poverty status of the

household. Each additional one household member,

the chances of a household going into the poor

category would be 15558 households with fewer

household members. The greater the number of

household members the more likely the households

will be in the poor category. The marginal effect of

0.0335 means that if the mean sample of household

member’s increased one person, then the chances of

households entering the poor category will increase

by 3.35 percent. The results of this study indicate that

the number of household members has a positive and

significant effect on poverty, so that by the re-search

hypothesis and theory. Geda, et.al (2005) in the study

of the determinants of poverty in Kenya al-so stated

that household size has a positive influence and an

important determinant of poverty. A large number of

household members will reduce the ability of

households to meet the need to obtain knowledge

stock through educational investment.

The coefficient of age variable of the head of

household is equal to -0,006894 with odds ratio equal

to 0.9931. Artiga every increase of 1-year-old head of

household then the probability of the household into

the poor category will be 0.99 times household with

age of head of household is younger. The

interpretation of this result is that the older the head

of household, the lower the household risk of the poor

category. The marginal effect of -0.0005, means that

the increase of the sample means the age of head of

household by one year, then the probability of house-

holds entering the poor category will decrease by 0,05

percent. The older age of household head of

household income and household wealth is higher so

that it can support sufficiently expenditure to fulfil

education investment requirement. This result is no

different from the research conducted by Christiaen-

sen and Todo, 2014 in a study of the determinants of

poverty in developing countries found that the age of

household heads has a negative and significant effect

on poverty.

The work has a high correlation to household

poverty in Yogyakarta Special Province in 2013. The

estimated coefficient of the household head variable

is 0.753755 with an odds ratio of 2.1250. This means

that households with heads of households working in

agriculture have a probability of falling into the poor

category of 2.1250 times households with heads of

households working in non-agricultural sectors. In

other words, households with heads of households

working in the agricultural sector are more at risk of

poverty than households with heads of households

working in non-agricultural sectors. The marginal

effect of household head's job variable in the

agricultural sector in 2013 is 0,0571. This means that

if the opportunity to enter into the poor category will

in-crease by 5.71 percent if the head of households

works in the agricultural sector. Households working

in the agricultural sector have low productivity aver-

ages so that households with heads of households

working in the agricultural sector have a greater

likelihood of being poor. These results are consistent

with the results of the research from Kabananukye,

et.al (2004: 36) and (Geda, de Jong, Kimenyi, &

Mwabu, 2005) which suggest that the agricultural

sector positively affects poverty and is a strong

determinant of poverty reduction.

In addition to the head of the household business

field, in this study also included the variable status of

the work of the head of the household. The estimation

result of 2013 logit model obtained the estimated

value of the coefficient of the employment status of

head of household (SKR) equal to 0,532260 with ratio

odd ratio 1,7028. This means that house-holds with

heads of households working in the in-formal sector

have a probability of falling into the poor category

1.7028 times households with heads of households

working in the informal sector. Marginal effect

variable occupation status of head of house-hold in

the informal sector in 2013 is equal to 0.0403. This

means the opportunity to enter into the poor category

will increase by 4.03 percent if the head of household

works in the informal sector. Based on the data of

Susenas 2013, the characteristics of poor households

with informal employment are most of the heads of

Education and Poverty in Special Province of Yogyakarta: The Approach of Solow Growth Technology Model in Production Theory

729

households with the highest degrees of primary

school (71.56 percent), working in agriculture (64.65

percent) with unpaid employment assisted workers

(53.65 percent), 72 percent) and those with free

workers (24.88 percent). This suggests that poor

households working in the informal sector are more

than 70 percent educated with a low formal education

so that they will have limited skills and skills. They

mostly work on agricultural sectors that do not

require certain skills.

Other employment variables that can describe

the characteristics of poverty in D.I. Yogyakarta is the

average member of the working household (MPKR).

Based on the results of logit estimation, obtained the

estimated value of MPKR coefficient of -0.371064

with an odd ratio of 0.6900. This means that the

average number of household members working

increased 1, the probability that households will fall

into the poor category will be 0.6900 house-holds

with fewer household members working. This means

that the more stout the members of the house-hold are

working, the less likely the households will be poor.

The marginal effect of the MPKR variable is -0.0281,

which means that households will fall into the poor

category reduced by 2.81 percent if the number of

working households increases by one per-son.

Increasing the average number of working household

members will lower the likelihood of households

being categorised as poor.

The estimated value of the dummy of residence

(GEO3) is significant at the 5 percent significance

level with an estimated value of 0.404787, while the

odds ratio of 0.6671. This means that the probability

of households falling into the category of poor living

in the mainland area is 0.6671 times than in non-

mainland areas. These results indicate that non-land

areas have a higher poverty risk than inland areas.

The marginal effect of -0.0307. This means that

households in the poor category for households in the

mainland area will be reduced by 3.07 percent com-

pared with households living in non-mainland areas.

Characteristics of residence based on the location of

topography turned out to affect poverty. This is be-

cause the topography of the non-mainland area is

made up of slopes and valleys. This region is a

mountainous region so that transportation facilities

are still difficult, facilities and infrastructure that

support the fulfilment of household needs such as

education, health, economy or entertainment is still

very mini-mal. This result is not much different from

the results of the study of the determinants of poverty

in Kenya showing that poverty rates differ in different

regions (Kabananukye, et al., 2004).

4 CONCLUSIONS

The results of estimation and analysis, obtained some

conclusions as follows. Household size, age of head

of household, occupation of head of household,

employment status of head of household, occupation

of head of household, average of working member of

household, highest certificate owned by head of

household, average length of school of household

member And residential areas are the variables that

are able to explain the characteristics of poor

households in Special Province of Yogyakarta in

2013. Variables that can increase poverty by 2013

from the order of magnitude of marginal effect are:

employment in the agricultural sector, informal

employment status, and household size. Variables

that can reduce poverty by 2013 are the area of

mainland residence, the average member of the

working household, the average length of the

schooling of household members, the highest

certificate held by the head of the household and the

age of the head of the household. Increased

investment of human resources through formal

education can reduce the chances of poor households.

In contrast, agricultural employment, informal

employment status will increase the likelihood of

poor households.

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