Putting the present value model into practice: a comparison of two alternative approaches

Abstract

A key issue around putting the present-value model into practice is how to construct the unobserved future expectations of the fundamental variables related to an asset. One approach is to fit a vector autoregression (VAR) for the fundamental variables and deduce their future expectations from the estimated VAR. An alternative is to directly specify the future expectations as unobserved components (UC) and use the Kalman filter to extract their estimates from the realized data. This article examines whether the predictions of the present-value model are consistent across the two approaches. Constructing the VAR and UC versions of the standard present-value model, we examine how the two versions compare in identifying the main driver of the US and UK housing markets. For the UK, the two approaches consistently attribute most variations in the price-rent ratio to the expected future risk premium for housing investment. For the US, however, the two approaches deliver considerably different results: the VAR version marks the expected risk-free rate of return, whereas the UC version singles out the expected risk premium as the main driver of the ratio. We conclude that the choice between the VAR and UC approaches is not a trivial issue related to utilizing the present-value model.