On The Modeling of District Policy Effects to Household Expenditure: A Hierarchical Bayesian Approach

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1 On The Modeling of District Policy Effects to Household Expenditure: A Hierarchical Bayesian Approach Nur Iriawan Statistics Department, Institut Teknologi Sepuluh Nopember, Indonesia. nur_i@statistika.its.ac.id Pudi Ismartini Ph.D. student at Statistics Department, Institut Teknologi Sepuluh Nopember ismartini@mhs.statistika.its.ac.id Abstract. Household data such as household expenditure data are widely used as a basis for policy decision making. Since Household data is often view as hierarchical structured data, with household nested in its district of residence area, both the district condition and its households influence each other. In this case, it is important to have contextual analysis to model the significance of district policy impacts to household expenditure. This paper proposes to develop a model for analyzing district policy effects to household expenditure by using a hierarchical Bayesian approach. The model is developed by taking into account household and district characteristics as a reflection of government policy at district level. The result shows that district policy in the economic, health, education and housing facilities do affect to household expenditure through its household characteristics. Keywords: A Hierarchical Bayesian Models, Hierarchical Structured Data, District Policy, Household Expenditure 1 Introduction Household expenditure patterns approach is widely used to analyze the pattern of household income for the following reasons. First, household income is generally very difficult to be measured accurately, especially in developing countries. Second, consumption expenditure is more reliable than income as an indicator of a household s permanent income because it does not vary as much as income in the short term [1]. Basically the factors that affect the welfare problems can be broadly categorized into two main things. Those are behavior paradigms and policy paradigms []. Behavioral paradigms related to the effort of responsibilities of each individual or household in achieving their welfare levels. In each household, there are specific factors that potentially contribute to the paradigm of such behavior. hile the policy paradigms associated with economic conditions, politics and government policy. In addition, nonhousehold factors may also affect the difference in the level of welfare. An example is 1

2 community-level factors such as geography and availability of public facilities (economic, education, and health facilities). Since 001, Indonesia imposed a financial balance system between central and local governments [0]. This system has been changed the Indonesian governance systems from centralized into decentralized system. Consequently, the achievement of local government will be largely determined by the active and innovative role of local government in determining its local policy in order to achieve prosperity and welfare of its residents. Determination of the local government's policy is generally influenced by the availability of natural resources, human resources, infrastructure and geography. Since the inter-regional conditions vary from one another, the policy taken by each local government can also vary. This may lead to differences in development levels among regions that could cause any difference in its people welfare levels. Bista [] states that a condition in some countries in the last period shows the more good economic growth the more increase income its residents. This suggests that there is influence of region s conditions in affecting the household conditions. The diversity of levels of household expenditure between regions can be indicated by the diversity of levels of poverty across regions. DI Yogyakarta (DIY) Province which is the smallest province in Indonesia, i.e % of Indonesian total area, has poverty rate about 16.8% of the total DIY provincial population in 010 [3]. That number is higher than average percentage of poor people of Indonesia (13.3 %)[3]. Table 1 illustrates the level of poverty by district in the DIY Province which varies between its five districts. It is shown that Yogyakarta district which is the smallest district with the smallest population in DIY, has the smallest percentage of poor people compare to other district in DIY. This might indicate the presence of district-level factors that affect the welfare of its people. Table 1. Percentage of Total Area, Household, Population and Poor Population by Districts in DI Yogyakarta Province [4] No Districts Percentage of Total Area Percentage of Household Percentage of Population Percentage of Poor people (1) () (3) (4) (5) (6) 1 Kulon Progo Bantul Gunung Kidul Sleman Kota Yogyakarta DI Yogyakarta Province Since, household data is nested in its regional residence; it is classified as hierarchical case. In this case, household expenditure can be influenced by factors from several different levels, i.e. factors at the household level and factors at the regional level. Hierarchical models are formulated for analyzing data with complex sources of variation [5]. In many cases, complex sources of variation refer to hierarchical structure of data [6] and [7]. In hierarchical data structure, data can be classified in different levels.

3 Standard unilevel models are not appropriate for analysis of such hierarchical system [8]. The consequences of using unilevel analysis on hierarchical data are the parameter estimates are inefficient and standard error are negatively biased Hox [7] and [8]. Goldstein [4], Hox [5], and Raudenbush and Bryk [7] stated that there are several advantages of using hierarchical models to hierarchical data. It can be used to analyze information from several different levels into a single statistical analysis. Hierarchical analysis is taking into account the influence of variation at each level of data on variations in the response. This allows researchers to determine the contribution of variation at each level of response variation. Several studies on hierarchical models have been done in a wide variety of areas. Hierarchical models are commonly used to analyze student achievement from different schools by taken into account the student s characteristics and schools characteristics [9], [10], and [11]. In the area of health, hierarchical models are usually used for analyzing the effectiveness of therapy on patients [1] and for survival analysis [13]and[14]. It is noted that hierarchical models, mostly use classical approach in estimation process. However, for the case of the complex hierarchical models, the solution of parameter estimates with the classical approach becomes very difficult to obtain [5]. Raudenbush and Bryk [5] state that a hierarchical models using a classical approach works well when the number of higher level unit is large. In some applications, however, this condition will not hold. In this case, there are distinct advantages in using Bayesian approach ([3]). This paper proposes to model how policies affect the well-being of each household by using a hierarchical Bayesian Models. 1.1 Hierarchical Models A hierarchical model is formed by two types of sub-models, i.e. micro models (the models at a lower level) and macro models (models at higher levels) ([6]). For two level hierarchical models, there is a first level model as micro models and second level models as macro models. The first level models investigate association between household expenditure with various household characteristics. And the second level express association between coefficients in the first level models with district characteristic. If there is N household from m districts, and n is number of households in districts, so m 1 n N. To set notation, let i = 1,, n household index, and = 1,,..m represent a district index. is n 3 x p matrix of a household characteristics where p = k+1 and k represent number of predictors of micro models. is px q matrix of district characteristics where q=l+1and l represent number of predictors of macro models. The micro models is specified as follows : y β r (1.1) where r is residual vector of micro models with assumption n x1vector of considered observation of samples and β is coefficients. Then, the macro models are specified as follows: r 0 I. y is N(, n ) p x1 vector of first level

4 β γ u (1.) where γ is coefficient vector of macro models, u is residual vector of macro models with assumptions u N( 0, T). Thus single equation models for equation (1.1) and (1.) are specified as follows: y γ u r (1.3) where r 0 I, u N( 0, T) and Cov( u, r ) 0. N(, n ) s i 1. Bayesian Methods Consider Bayes Theorem [18] and [19]: p( y θ) p( θ) p( θ y) p( y ) (1.4) where θ and y are both random, θ is parameter vector and y denotes vector of observations from the sample. p( y ) is defined as normalized constant with respect to θ. Then, the posterior can be represented as a proportional form as follows: p( θ y) p( θ y) p( θ) (1.5) Refer to equation (1.5), the posterior distribution of hierarchical Bayesian models are specified as followed [5]: p( β, γ, Ω, T y) p( y β, Ω) p1( β γ, T) p( γ, Ω, T) (1.6) where Ω Var( y ) I. p ( β γ, T ) and N 1 p (,, ) γ Ω T denote first stage prior and second stage prior, respectively. Figure 3 shows flow chart for the hierarchical Bayesian models. Data and Methods 4 Household expenditure can be identified through various characteristics. Houghton and Nguyen [15] state that there are several household characteristics that affect household expenditure. Those characteristics are marital status of household head, age of household head, gender of household head, ethnicity of household head, household size, urban, number of years of education of household head, leadership ob of household head, and skill ob of household head. Grosh and Baker [16] develop model for household expenditure by using several predictors, i.e. education level of household head, house area, types of wall, type of floor, source of drinking water, kitchen, toilet facilities, and electricity. Mukaramah, et.all [14] states that foreign direct investment affects household income distribution. This paper will use predictors based on those previous studies and other predictors of macro models that might influence household expenditure. Since public service facilities and how local government determines the allocation of its local budgets illustrates concrete steps of the government in determining its local policies, then these characteristics will also be used in this paper

5 Household income model will be developed by using two levels hierarchical Bayesian models with the first level unit is household and the second level unit is district. Predictors used in the model are characteristics of household and characteristics of districts. The sample coverage area of data used in this paper is DI. Yogyakarta Province (DIY). Since DIY is consisted of five districts, thus the number of second level unit is five. Those five districts are Kulon Progo, Bantul, Gunung Kidul, Sleman, Yogyakarta. The differences regarding the household expenditure level in the DIY inter-district can be seen in figure 1 and figure. Figure 1 shows that district of Yogyakarta averagely has the highest level of household expenditure followed by Sleman. However, household expenditure in Sleman is more vary compare to other districts, while variation of household expenditure in Yogyakarta is much lower than Sleman and Bantul (figure ). Figure 1. Map of DIY by Mean of Household Expenditure Figure. Map of DIY by Coefficients of Variation of Household Expenditure 5

6 .1 Data Descriptions The model used in this paper basically relies on the Socio-Economic Survey 009 which is conducted by Statistics Indonesia and publication of DI. Yogyakarta Province. The dependent variable used in the model is ln of household expenditure per capita (y ), while the predictors used are household characteristics as the first level predictors and district characteristics as the second levels predictors. Table 1 shows list of the first level predictors ( ) and the second level predictor ( ). Table 1. List of Predictors Predictors Descriptions Level of education of household head Household size Type of sources of drinking water Type of cooking fuel Type of house wall Type of house floor Number of foreign company Number of high school Percentage of district budget spending for economics facilities Percentage of district budget spending for education facilities Percentage of district budget spending for health facilities Percentage of district budget spending for housing and public facilities. Hierarchical Bayesian Models The two level hierarchical Bayesian models for household expenditure is specified as follows: 6 y β β r i 0 k ki i k 1 β u ; p 0 and 4 p p0 p1 3 p β u β u β u β u ; p 5 and 6 p p0 p1 3 p 6 p 6

7 The estimation of parameters of interest is supported by the computational powerful of recent software, such as inbugs 1.4. This software is an interactive windows version of the BUGS program for Bayesian analysis of complex statistical models by implementing MCMC techniques and Gibbs sampling. The estimation process yields coefficients model of a hierarchical Bayesian models for household expenditure in DIY. Figure 3. Flow chart for two levels hierarchical Bayesian models 3 Discussions The estimated coefficients of two levels hierarchical Bayesian models for household expenditure are displayed with 95% confidence intervals in Table. It is shown that most 7

8 of the predictors of micro models are significant except for types of cooking fuels in Yogyakarta district and types of wall in Bantul district. Since Yogyakarta is an urban area, type of cooking fuels used in Yogyakarta does not vary compare to other districts. The data shows that almost 84 % of household in Yogyakarta use electricity/gas/kerosene for their cooking fuels. hile in Bantul, there is almost 95% of its household has a stone wall house. The result shows that district characteristics do effects household expenditure through the specific types of household characteristics. For example, percentage of district budget spending for education facilities affects household expenditure through level of education of household head. It points out that district policy in education field influences to its household welfare. The two levels hierarchical Bayesian models for household expenditure in DI Yogyakarta Province is specified as follows. y Parameters of micro models Table. Two Level Hierarchical Bayesian Models : Estimated Coefficients estimated Values Confidence Interval (95%) Parameters of macro Lower upper models bounds bounds 8 estimated Values Confidence Interval (95%) Lower bounds upper bounds β γ β γ β γ β γ E β γ β γ E β γ β γ β γ β γ β γ β γ β γ β γ β γ β γ E

9 Table. (Continued) Parameters of micro models estimated Values Confidence Interval (95%) Parameters of macro Lower upper models bounds bounds estimated Values Confidence Interval (95%) Lower bounds upper bounds β γ β γ E β γ β β β β β β β β β β β β β β Conclusions and Future Perspectives This paper has proposed to model district policy effects to household expenditure by using a hierarchical Bayesian models. This model shows that there are several district characteristic that affect household expenditure through household characteristics. Those district characteristics reflect its district policy. Another interesting future perspective is to investigate other specific district characteristics that might affect household expenditure. 4 Acknowledgments The authors would like to express a gratitude to both Statistics Indonesia and Statistics Department of Institut Teknologi Sepuluh Nopember (ITS), Surabaya, which sponsors this research. The authors wish to thank the anonymous referees for their valuable comments which led to considerable improvement in this article. 9

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