Dealing with Markov-switching parameters in quantile regression models

Quantile regression has become a standard modern econometric method because of its capability to investigate the relationship between economic variables at various quantiles. The econometric method of Markov-switching regression is also considered important because it can deal with structural models or time-varying parameter models flexibly. A combination of these two methods, known as "Markov-switching quantile regression (MSQR)," has recently been proposed. Liu and, Liu and Luger propose MSQR models using the Bayesian approach whereas Ye et al.'s proposal for MSQR models is based on the classical approach. In our study, we extend the results of Ye et al. First, we propose an efficient estimation method based on the expectation-maximization algorithm. In our second extension, we adopt the quasi-maximum likelihood approach to estimate the proposed MSQR models unlike the maximum likelihood approach that Ye et al. use. Our simulation results confirm that the proposed expectation-maximization (EM) estimation method for MSQR models works quite well.