Markov-switching models, rational expectations and the term structure of interest rates

Abstract

In order to evaluate the efficiency of the monetary transmission mechanism, we develop the formulas for testing rational expectations theory in the term structure of interest rates with VAR models of stochastically switching regimes in which all the parameters are regime dependent. These formulas are obtained for the strict version of rational expectations as well as for the case where measurement errors are assumed in the expectations relationship. They are extensible to other contexts that involve variables linked by rational-expectations behaviours. The testing procedure is implemented on interest rates of the Spanish inter-bank money market. Measurement errors must be assumed to find signs favourable to the theory.

Notes

¹Bansal and Zhou (2002) also make use of Markov-switching model but in a different approach: they introduce a two-state MS process in the Cox–Ingersoll–Ross Model for the term structure and obtain strong empirical support for their model but do not test the expectations hypothesis. Other papers using Markov-switching models in relation with the term structure of interest rates are Ang and Bekaert (2005) and Tillman (2005). These papers confirm the utility of the Markov-switching approach and its relation with the stance of monetary policy, but do not test REH.

²See for instance Prats Albentosa and Beyaert (1998)

³See for instance Campbel and Shiller(1987) and Prats-Albentosa and Beyaert (1998)

⁴The subscript n on S_t has been eliminated to simplify the notation. In what follows, it will be used only when necessary to avoid confusion.

⁵Kirikos (1996) considers a theoretical model of these characteristics, for the study of the exchange rate determination. However, at the estimation stage, he simplifies it down to a static nonautoregressive model, in which only the mean and the variance–covariance matrix is allowed to vary between states.

⁶Moreover, both options give rise to models with exactly the same total number of parameters. So there is no inferential reason to prefer one or another model, either.

⁷Prats-Albentosa and Beyaert (1998) obtain the same conclusions but with a shorter sample, which stops in 1992.

⁸The weekly rates have been converted into rates of instantaneous capitalisation, in order to allow the comparison between interest rates of different terms.

⁹See Hamilton (1996) and Beyaert and Perez-Castejón (2000) for details.

¹⁰See Prats Albentosa and Beyaert (1998).

¹¹See Prats Albentosa and Beyaert (1998).

¹²Obviously, it would be interesting to test also the restrictions on the premium; given the difficulty that testing only (A9) entails in the type of nonlinear models that we are considering, this is left for future research. Note however that a rejection of (A9) implies a rejection of the theory, whereas an acceptance of (A9) means that the data are compatible with the theory.