Sometimes, invoking a single causal relationship to explain dependency between variables might not be appropriate particularly in some economic problems. Instead, two jointly related equations, where one of the explanatory variables is endogenous, can represent the actual inheritance inter-relationship among variables. Such typical models are called simultaneous equation models of which the seemingly unrelated regression (SUR) models is a special case. Substantial progress has been made regarding the statistical inference on estimating the parameters of these models in which errors follow a normal distribution. But, less research was devoted to a case that the distributions of the errors are asymmetric. In this paper, statistical inference on the parameters for the SUR models, assuming the skew-normal density for errors, is tackled. Moreover, the results of the study are compared with those of other naive methodologies. The proposed model is utilized to analyze the income and expenditure of Iranian rural households in the year 2009.
Abstract. The instrumental variable (IV) regression is a common model in econometrics and other applied disciplines. This model is one of the proper candidate in dealing with endogeneity phenomenon which occurs in analyzing the multivariate regression when the errors are correlated with some covariates. One can consider IV regression as an special case of simultaneous equation models (SEM). There are some cases in which the normality assumption might not hold for the error term in these models and so the skew-normal distribution might be a suitable candidate. The present paper tackle the Bayesian inference based on Markov Chain Monte Carlo (MCMC) using this density for the error term while some instrumental variables are considered in the corresponding regression model. The proposed model is utilized to analysis the Iranian rural households income and expenditure collected in 2009.
In recent decades, the issue of ecological footprint (EF) in the world
has become a serious anxiety between environmental stakeholders. This
anxiety is more in top tourism attracting countries. The purpose of this
research is the performance of mixed and penalized effects models in
predicting the value of the EF of tourism in the top eight countries of
tourism destinations. The World Bank and Global Footprint Network
databases have been used in this study. Penalized regression and MCMC
models have been used to estimate the EF over the past 19 years
(2000-2018). The findings of the study showed that the amount of
ecological footprint in China, France and Italy is much higher than
other countries. In addition, a slight improvement in the performance of
penalized models to linear regression was observed. The comparison of
the models shows that in the Ridge and Elastic Net models, more
indicators were selected than Lasso, but Lasso has a better predictive
performance than other models on ecological footprint. Therefore, the
use of penalized models is only slightly better than linear regression,
but they provide the selection of appropriate indices for model
parsimoniousness. The results showed that the penalized models are
powerful tools that can provide a significant performance in the
accuracy and prediction of the EF variable in tourism attracting
countries.
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