Simultaneous Equations in the Markov-Switching Model

In this paper, Hamilton’s (1989) Markov-switching model is extended to the simultaneous equations model. Using a framework for an instrumental variable interpretation of full information maximum likelihood (FIML) by Hausman (1975), we can deal with the problem of simultaneous equations based on the Hamilton filter. When we compared the proposed FIML Markov-switching model to LIML Markovswitching models such as Kim (2004a), Spagnolo, F., Psaradakis, Z., and Sola, M.(2005), we found that LIML Markov-switching models are a special case of the proposed FIML Markov-switching model where all but the first equation are just identified. Moreover, the proposed FIML Markov-switching model is a general form in the simultaneous equations and covers a broad class of models that could not be handled before. As we applied the proposed model to Campbell and Mankiw’s (1989) consumption function, by allowing for possibilities of structural breaks in the sensitivity of consumption growth to income growth, we can assume a marginal propensity to consumption β constant because the difference between 0 β and 1 β is very small. JEL classification: C13; C32 Keyword: full information maximum likelihood estimation, FIML, LIML, instrumental variable, simultaneous equation, Markov switching, Hamilton filter, consumption 1 POSCO Research Institute, POSRI, 147, Samsung-dong, Gangnam-gu, Seoul 135-878, Korea Phone: +82-2-3457-8228; fax: +82-2-3457-8040. E-mail: [email protected]