REIT markets and rational speculative bubbles: an empirical investigation

Abstract

This study uses the momentum threshold autoregressive (MTAR) model and the residuals-augmented Dickey–Fuller (RADF) approach to test for the presence of Evans’ (1991) periodically collapsing bubbles in four real estate investment trusts (REIT) classifications. The RADF test shows evidence of bubbles, but the results of the MTAR test are mixed. The MTAR test shows asymmetric adjustment for each REIT market with the exception of hybrid REITs, but only mortgage REITs show evidence of bubbles, which turn out to be negative meaning the price falls substantially below the level warranted by fundamentals.

Notes

¹ In the case of REITs, Payne and Zuehlke (2005) present evidence of positive duration dependence except in the case of mortgage REIT expansions.

² Payne and Waters (2005a) restrict their analysis to testing for negative periodically collapsing bubbles and find evidence of such bubbles in the case of mortgage and hybrid REITs. As an extension to the study by Jirasakuldech et al. (2005), Payne and Waters (2005b) follow the literature by restricting their analysis in testing for positive periodically collapsing bubbles in the equity REIT market with inconclusive results.

³ The theoretical section draws heavily from Payne and Waters (2005a, b). However, unlike Payne and Waters (2005a, b), there is no restriction as to the whether a bubble can be negative or positive.

⁴ Charemza and Deadmen (1995) specify a more general model of periodically collapsing bubbles.

⁵ Skewness is equal to zero for all symmetric distributions; however, the skewness statistic is positive when the upper tail of the distribution is thicker than the lower tail and negative when the lower tail is thicker. Kurtosis is equal to three for a normal distribution; however, the kurtosis statistic will be greater than three when the tails of the distribution are thicker than the normal and less than three when the tails of the distribution are thinner than the normal (Pindyck and Rubinfeld, 1998).

⁶ This test is based on the work of Im (1996) with respect to residuals-augmented least squares estimators.

⁷ The adjustment for skewness and excess kurtosis has superior power over standard cointegration tests to correctly reject a mean-reverting error model as a bubble. Taylor and Peel (1998), Sarno and Taylor (1999, 2003), as well as Capelle-Blancard and Raymond (2004) construct critical values and analyse the power of this test against alternatives.

⁸ The covariance matrix of is estimated by where

and μ _i denotes the ith central moment of u_t . is the vector of the lagged series of centered residuals and the idempotent matrix, , is given by where I_T is the identity matrix and W is the matrix of the centered residuals of .

⁹ The MTAR model was initially used in the detection of periodically collapsing bubbles by Bohl (2003) with US stock market data.

¹⁰ Chan (1993) requires sorting the estimated residuals in ascending order, eliminating 15% of the largest and smallest values. The threshold parameter that yields the lowest sum of squared errors from the remaining 70% of the residuals is used in the MTAR model. We found similar results using 10% and 5% cutoffs.