In this paper, we analyze and model the dependence of house prices of Metropolitan Statistical Areas (MSAs) in the US, taking into account the dynamics of dependence. We model the dynamics in the dependence, using a regime switching model with a two-state hidden Markov chain. We use a multivariate Gaussian copula and a Canonical Vine copula to model the dependence of house price changes of MSAs, and identify a high and low dependence regime, or a symmetric and asymmetric dependence regime in the housing market. Furthermore, we use interest rates and LTV as factors aﬀecting the transition probabilities of the Markov chain to see if those variables aﬀect the change of dependence between house prices.

The main contribution of this paper is to model dependence of house price returns of MSAs which can vary across time in a ﬂexible way using multivariate copulas and a regime switching model. Using various multivariate copulas, we implement the variation of dependence across time in terms of magnitude and shape into the model. First, we use a multivariate Gaussian model with an equicorrelation for all pairs of MSAs, and estimate two diﬀerent equicorrelations which are for diﬀerent two regimes with a regime switching model. Through this estimation, we ﬁnd a high and a low dependence regime in the housing market among MSAs. Besides the magnitude of dependence, we model diﬀerent shapes of dependence for diﬀerent regimes across time using a Canonical vine copula and a multivariate Gaussian copula with a regime switching model. The former is employed for an asymmetric dependence or tail dependence regime , and the latter is used for a symmetric dependence regime.

In this paper, we verify a symmetric and an asymmetric dependence regime for diﬀerent time period. Besides, using macroeconomic variables such as the change rate of interest rate (∆ r) and the change rate of Loan to Value (∆ LTV), we see if these variables can explain diﬀerent dependence regimes across time in a better way. We ﬁnd, especially, ∆ LTV is consistently shown to be closely related to a high dependence regime. This partly shows the vicious cycle between credit supply and house prices.