GUÍA DE OBSERVACIÓN Nº 8 SERIE “LAS CHICAS DEL CABLE”

Chang et al (2008, 2009), among others, take an initial step in this direction by building various versions of the SVAR models in order to study the interaction between the monetary policy, the real econ-omy and the asset markets. In particular, they differentiate their efforts from the previous literature by allowing “two-way causality”, ie, not only that the asset market returns be affected by the mone-tary policy and the real economy, but also that the asset returns could have an influence on the monetary policy and the real economy. This is a well-known advantage of the SVAR model.

The second innovation is to allow for the possibility of regime-switching, ie, allowing the relationship among the monetary policy, the real economy and the asset markets to vary across different time periods. Such a consideration is motivated by several strands of the literature. On the theoretical front, regime switching can occur in a general equilibrium setting. Azariadis and Smith (1988) may have built the first general equilibrium in which the market economy would permanently fluctuate between the regime with credit rationing and the regime without it. Chen and Leung (2008), among others, apply their insight in the asset market analysis. They consider a situation where the land and structure (real estate) can be used for both residential and commercial purposes. Both the households and some constrained producers are leveraged in their purchase of this real estate. Chen and Leung show that under some conditions a negative shock will initiate a “fire sale”, ie, both the household side and the producer side are trying to sell real estate, which leads to a further drop in the asset price and more liquidation (spillover effect). Perhaps more importantly, they show analytically that the correlations between the real output and the asset price are different under different “regimes”; the same amount of output decline is associated with a larger decrease in asset price in the “bad regime” (ie, when the spillover effect of the asset price occurs). In other words, a linear vector auto-regressive (VAR) model between the real economy and the asset price could deliver misleading results. This clearly calls for an econometric framework which will allow for some degree of non-linearity.

On the empirical front, it has long been suggested that economic time series may be better characterised by a Markov regime-switch-ing process, rather than a smooth autoregressive movregime-switch-ing-average (ARMA) process. For instance, Hamilton (1989) shows that the aggregate output in the US can be characterised by such a pro-cess. Regime-switching models have since been widely used in mod-elling different classes of asset prices, including stock, option, foreign exchange, interest rate, etc (see, for example, Hansen and Poulsen 2000; Maheu and McCurdy 2000).

The empirical literature on market efficiency provides an addi-tional reason to employ the regime-switching model. It has long been recognised that the change in housing price, or the housing return (we will use these two terms interchangeably throughout),

is predictable, at least in the short run (see, for example, Case and Shiller 1990; Shiller 2008). It has been cited as evidence for market efficiency. Although the logical link between predictability and mar-ket efficiency is weak,²it is still puzzling from an intuitive point of view: if the short-run house price can be predicted, then people may leverage to buy and profit from it, as much as the leverage will allow.

In other words, there is room for arbitrage for profit, which seems to contradict the notion of an “efficient market”. In fact, this intu-ition applies only for the single-regime econometric model, such as the conventional ordinary-least-squares or linear VAR models. With multiple regimes and the randomness in the occurrence of regime switching, the situation can be very different. To fix this idea, let us consider the following simple example

yt+1=

⎧⎨

⎩

a1yt+ ut+1 when yt+1is in regime 1 a^₁yt+ u^_t+1 when yt+1is in regime 2

where a1≠ a^₁, and the distributions of the error terms ut+1, u^_t+1may not be identical. (The language here is somewhat informal. More formal treatment on the regime-switching model will be provided in later sections.) And we further assume that the probability for yt+1 is in regime j, given that yt is in regime i, is pij, 0 < pij < 1, i, j= 1, 2. Now consider the case when the regime tends to be very persistent, meaning that pii, i = 1, 2, is very close to unity. For the sake of argument, assume that the system is now in regime 1. Then, in the short run, this system behaves like a simple AR(1) process

y_t+1= a1y_t+ ut+1

and hence becomes “very predictable”. On the other hand, as long as pii<1, regime switching occurs and those who bet based on a sim-ple AR(1) process will suddenly realise a capital loss. In other words, the persistence of regime can lead to short-run predictability, while the random occurrence of regime switching rules out long-run prof-itability. Short-run predictability can be compatible with long-run non-profitability in a multiple regime setting. The regime-switching model brings in not only new econometric tools, but also new eco-nomic intuition. We therefore consider that the employment of a regime-switching SVAR model is appropriate in this stage of the empirical study of the policy effect on asset returns.

Table 5.1 Statistical summary of federal funds rate, interest rate spread, housing market returns, and equity REIT returns (1975 Q2–2008 Q1)

FFR SPR HRET REIT

Mean 6.464 1.490 1.401 1.519

Median 5.618 1.581 1.345 1.852

Maximum 17.780 3.611 4.425 18.523

Minimum 0.997 ₋2.182 ₋0.406 ₋18.174

Std. Dev. 3.493 1.341 0.947 6.849

Skewness 1.040 ₋0.604 0.564 ₋0.182

Kurtosis 4.307 2.904 3.284 3.173

Observations 132.000 132.000 132.000 132.000 FFR, federal funds rate; SPR, interest rate spread; HRET, housing market returns; REIT, equity REIT returns.