Selection of a system of simultaneous equations model

dc.contributor.advisorJirawan Jitthavech, advisorth
dc.contributor.authorWarangkhana Keerativiboolth
dc.descriptionThesis (Ph.D. (Statistics))--National Institute of Development Administration, 2009th
dc.description.abstractOne of the most important problems in statistical modeling is to choose an appropriate model from a class of candidate models. In real life, we may not know what the true model is, but we hope to find a model that is a reasonably accurate representation. A model selection criterion represents a useful tool to judge the propriety of a fitted model, by assessing whether it offers an optimal balance between goodness of fit and parsimony, the attributes of the best model. In this dissertation, the Akaike information criterion for a system of simultaneous equations model (SAIC) where errors are both serially and contemporaneously correlated was proposed to select the most appropriate system of the model. Our approach consists of two stages. Firstly, the Prais-Winsten transformation was extended to correct the second-order autocorrelation problem and to recover the two lost observations in a simultaneous equations model. Secondly, the log-likelihood function of the multivariate model was able to be applied directly to construct the SAIC for the transformed model. Since the SAIC is in the form of the minus twice log-likelihood function plus a penalty term, under the normality assumption of the error terms, minimizing the negative the log-likelihood function, is identical to minimizing the sum squares error (SSE). Therefore, the system with minimum value of SAIC can be classified to the “best” system of the model. The results of simulation can be concluded as follows. The values of estimated regression coefficients from the model before transformation, from the model which is transformed by the proposed transformation, and from the model which is transformed by the Cochrane-Orcutt transformation, are insignificant and they are also insignificantly indifferent from the fixed values. In other words, the estimated regression coefficients from the model before and after transformation are unbiased. The estimated standard errors of the model before transformation are greater than those of the transformed models, at 0.05 level of significance, whereas two transformed models have the estimated standard errors are insignificantly indifferent. The errors after transformation from the proposed transformation, and from the Cochrane-Orcutt transformation, are white noises and that before removing the autocorrelation in the errors of the model; the sample mean squared errors are greater than the ones after the autocorrelation problem has been corrected, at 0.05 level of significance. The sample mean squared errors of the transformed models by the proposed transformation, and by the Cochrane-Orcutt transformation, are insignificantly indifferent. Where sample size is small, the recovering of the two lost observations by the proposed transformation should be more advantageous than Cochrane-Orcutt transformation, because no degree of freedom is decreased. The SAIC and multivariate AIC can remove all irrelevant independent variables from the model, but under the correct specification of the model, multivariate AIC still overestimates the errors compared with SAIC, because when presenting the autocorrelation problem, the ordinary least squares (OLS) estimate of contemporaneous covariance matrix will overestimate. A further study could consider other model selection criteria, such as the Schwarz Bayesian criterion (SBC) and the Kullback information criterion (KIC). Other schema of error-generating might be considered, such as the moving average scheme instead of the autoregressive
dc.format.extentxi, 223 leaves : ill. ; 30
dc.publisherNational Institute of Development Administrationth
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
dc.subjectSimultaneous equation modelsth
dc.subject.lccQA 278.2 W197 2009th
dc.subject.otherRegression analysisth
dc.subject.otherEquations, Simultaneousth
dc.titleSelection of a system of simultaneous equations modelth
dc.typetext--thesis--doctoral thesisth
mods.physicalLocationNational Institute of Development Administration. Library and Information Centerth of Applied Statisticsth Institute of Development Administrationth of Philosophyth
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