Regression Analysis Using Asymmetric Losses: A Bayesian Approach

Symmetric loss functions are sometimes inappropriate in Economics prediction problems. Asymmetric loss functions can then be applied where errors of the same magnitude but with a different sign can reflect different loss levels. We develop a Bayesian framework that estimates regression models which incorporate asymmetric loss functions such as the linex loss. Given that the likelihood function is not of a known form, estimation is implemented using a Laplace-type estimator within a Markov Chain Monte Carlo framework. We illustrate this method using simulated and real estate data series. The results demonstrate significant findings with regard to the prediction of linear models that use the linex loss function.