A Non-Parametric Bayesian Approach To Estimate Linear Model With Omitted Variables Problem

Omitted variables problem is always an outstanding thorny one for linear model. We develop a Bayesian non-parametric approach to deal with it based on Bayesian frame. A random term is added to an ordinary linear regression equation which can be considered as a omitted variable or a mixture of some omitted variables. We specify a dirichlet process prior to the random term and our nonparametric method for its distributions can be interpreted as a type of mixture model. MCMC method is used to estimate the parameters. The procedures are coded in R.Two simulations are designed to test the accuracy and flexibility of our approach. The results show both the estimated coefficient vector and omitted variable sequence are very close to the true values and the results are better than classical Bayesian method's. An empirical study is done with the data from CHNS.