We present a novel specification of a dynamic multinomial ordered choice model, where the latent variable is a function of strictly stationary exogenous variables and lags of the choice variable. We prove that such a model with weakly dependent errors will have a strictly stationary solution which is L-2 near epoch dependent. We also derive consistency and asymptotic normality of the maximum likelihood estimator for a probit specification of the model. We illustrate a possible application of the model by estimating a discrete version of a robust ``difference" monetary policy rule for the period 1990:2006 at a monthly frequency.
Many papers in the housing literature treat the intertemporal evolution of the logarithm of US real house prices as a unit root process. They also study the cointegration relationship among the logarithm of real house prices and fundamental economic variables such as income and they apply an error correction specification for modeling and forecasting real house prices. This paper argues that the logarithm of US real house price is not a unit root process. Instead, the evidence from a 120-year national dataset and metro area level and state level panel data sets supports the notion that US house prices are trend stationary. One result of this conclusion is that the validity of analyses of US house prices based on cointegration and error correction models needs to be reconsidered.