On The Modeling of District Policy Effects to Household Expenditure: A Hierarchical Bayesian Approach Nur Iriawan (Joint work with Pudji Ismartini) Institut Teknologi Sepuluh Nopember (ITS), Indonesia.
[email protected]
Joint Meeting of the 2011 Taipei International Statistical Symposium and 7th Conference of the Asian Regional Section of the IASC December 16 – 19, 2011
Outline • • • • • • •
Introduction: Overview of household welfare Hierarchical data structure Hierarchical models Bayesian methods Household expenditure data of DI Yogyakarta Two level hierarchical Bayesian models Results 2
Introduction • Some factors that affect the welfare problems can be broadly categorized into two main things: – behavior paradigms: the effort of responsibilities of each individual or household in achieving their welfare levels. – policy paradigms: associated with economic conditions, politics and government policy
• Since 2001, Indonesia imposed a financial balance system between central and local governments. • This system has been changed the Indonesian governance systems from centralized into decentralized system. • 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.
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Why is Hierarchical Bayesian Needed? •
Household data is often view as hierarchical data structure, with household nested in its residence area (districts)
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Nesting creates dependencies in the data
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Hierarchical models are formulated for analyzing data with complex sources of variation which refer to hierarchical structure of data.
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For complex hierarchical models, parameter estimation using classical approach becomes very difficult to be done.
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Classical hierarchical model using a maximum likelihood approach works well when the number of higher level unit is large This condition might not be hold in real condition.
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There are some advantages in using Bayesian approach.
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Model for individual data
Model for agregated data
Model for each group of data separately (Stevens, 2007)
Taking the hierarchical structure of the data into account
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Household Expenditure Analysis • Household expenditure analysis in Indonesia is continuously conducted by Indonesian government for several objectives, i.e: – the implementation of direct cash transfer (DCT) programs from Indonesian government to the poor as compensation for fuel price increased in 2005 and 2008. – Formulation of pro-poor government policy such as determination of targets for the provision of health insurance, and rice aids to the poor – Government policy framework for social and infrastructure development; such as rural roads, irrigation, schools, clean water, sanitation, housing, health centers, which are the catalyst for raising the level of public welfare.
• The analysis is conducted by constructing a model by using non monetary variables as predictors in order to predict the household expenditure 7
Objectives This paper proposes to model how policies affect the wellbeing of each household by using a hierarchical Bayesian approach.
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Hyperparameter vs Hierarchycal data structure Model
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Konferensi Nasional Sains dan Aplikasinya, UNISBA 2011
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y[i] p
Hyperparameter on Beta-Binomial-Poisson
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up per bou nd
alpa.alpha
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alpa
beta.alpha
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Konferensi Nasional Sains dan
f or(i IN 1 : N) UNISBA 2011 Aplikasinya,
beta
beta.beta
model; { for( i in 1 : N ) { y[i] ~ dbin(n,p) } n ~ dpois(lambda) p ~ dbeta(alpa,beta) alpa ~ dgamma(alpa.alpha,alpa.beta) alpa.alpha ~ dgamma(0.001,0.001) alpa.beta ~ dgamma(0.001,0.001) lambda ~ dgamma(alpha,betha) alpha ~ dgamma(0.001,0.001) betha ~ dgamma(0.001,0.001) beta ~ dgamma(beta.alpha,beta.beta) beta.alpha ~ dgamma(0.001,0.001) beta.beta ~ dgamma(0.001,0.001) 5/21/2011
}
Konferensi Nasional Sains dan Aplikasinya, UNISBA 2011
Hyperparameter on Simple Linear Regresi na me:
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mean.a.mu
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y [i] f or(i IN 1 : N)
Konferensi Nasional Sains dan Aplikasinya, UNISBA 2011
beta.beta
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model; { for( i in 1 : N ) { y[i] ~ dnorm(mu[i],tau) } a ~ dnorm(mean.a,var.a) for( i in 1 : N ) { mu[i]
