Explosive Behavior In Australian Housing Markets: Rational Bubbles Or Not?

Philip Inyeob Ji

Dongguk University Seoul – Dongguk University Seoul

Glenn Otto

UNSW Australia Business School, School of Economics

December 15, 2015

UNSW Business School Research Paper No. 2015-27

Abstract:

Using recently developed econometric procedures (Phillips, Wu and Yu, 2011; Phillips, Shi and Yu, 2015), we find evidence of temporary episodes of explosive behaviour in price-to-rent ratios for established houses, in five of Australia’s largest cities. One interpretation of our results is that stochastic, rational bubbles were a feature of Australia’s major housing markets; particularly during the early to mid-2000s. However, further analysis of each city’s price-to-rent ratio indicates a very different pattern of behaviour in Sydney and Perth to that experienced in Brisbane, Adelaide and Canberra. For the latter three cities, we present evidence suggesting the explosive root tests are likely capturing the effects of a one-time structural break in their respective price-to-rent ratios. In any event, based on the estimated timing of the explosive episodes in Australia’s housing markets, there is little evidence that what might be identified as house price bubbles had any important negative consequences for the wider economy. Despite the ability of the econometric procedures to provide a real-time signal of explosive behaviour, results from Australian housing markets, suggest policymakers need to be cautious in responding too aggressively to a positive signal from the tests.

Explosive Behavior In Australian Housing Markets: Rational Bubbles Or Not? – Introduction

There has been a persistent debate over whether house prices in Australia are overvalued; in the sense that market prices are too high relative to some fundamental value for residential property. Advocates of the overvaluation hypothesis typically use indicators such as house price-to-income or house price-to-rent ratios as the basis for their claims (Demographia, 2015; The Economist, 2015). The case for overvaluation is often made by comparing the current value of these ratios to historical norms or by comparing the magnitude of the ratios in Australia to the values in other advanced countries. In fact standard measures of price-to-income and price-to-rent ratios for Australia have exhibited an upward trend over the last two decades and are typically at the high-end of international comparisons. However an inherent problem with this type of analysis – for drawing conclusions about overvaluation – is that price-to-rent and price-to-income ratios are themselves likely to be influenced by other economic factors and, in practice, tend to exhibit relatively persistent low-frequency fluctuations.

One potential source of overvaluation in Australian housing markets is the presence of speculative bubbles. Bubbles provide one mechanism which can lead house prices to (positively) diverge from economic fundamentals. In practice it is difficult to test for the existence of speculative bubbles (Gürkaynak, 2008). A key problem is distinguishing between the effects of economic fundamentals on an asset’s price and the possible effects of a speculative bubble. Consider a situation where the price of an asset depends on its fundamental value and on a bubble. Fluctuations in the asset’s price are driven by a combination of economic fundamentals and the bubble term, both of which are typically unobserved. So even if we observe sharp rises and falls in the asset price, how can one be really certain that these changes are caused by the bubble and are not due to changes in economic fundamentals? In principle it is possible to establish the absence of a bubble, if – subject to sampling uncertainty – 100 percent of the variation in an asset’s price can be explained by some econometric model of economic fundamentals (Cochrane, 1992). In practice it is difficult to identify good specifications for asset prices; so it is generally unclear when economic fundamentals do not fully explain the observed variation in an asset’s price, whether this is due to a speculative bubble or because the model for fundamentals is misspecified?

In recent work Phillips and co-authors have developed econometric tests which have power to detect rational speculative bubbles (Phillips, Wu and Yu, (PWY) 2011; Phillips, Shi and Yu (PSY), 2015). Present value models of asset prices allow for the presence of a rational bubble term in an asset price, which grows at an explosive rate. If there is some probability attached to a bubble bursting in any period, this gives rise to stochastic bubbles that can grow explosively for a random period of time, before collapsing. The approach used in the PWY and PSY procedures is to search a univariate time-series on asset prices for temporary periods of explosive behaviour. Subject to some minimum length requirement, a bubble is identified with the periods during which the auto-regressive root for the time-series is (statistically) explosive (greater than unity). The distribution of the test statistic is non-standard but critical values can be calculated using simulations. A potentially attractive feature of these tests – compared to conventional tests for bubbles – is that identification of a bubble episode does not require a correct model for fundamentals.

In this paper we apply the PWY and PSY tests to measures of house price-to-rent ratios in Australia’s six largest capital cities1. We find evidence of temporary periods of explosive behaviour in price-to-rent ratios in all cities except Melbourne. Taken at face-value, our results can be interpreted as providing support for the existence of speculative bubbles (or periods of overvaluation) in most of Australia’s major housing markets in the early to mid-2000s and also in the Sydney market at the beginning of 2015. However closer inspection indicates that price-to-rent ratios display different behaviour in Sydney and Perth than in Brisbane, Adelaide and Canberra. In Sydney and Perth, price-to-rent ratios reached a maximum value – around the estimated time of their 2000 bubble episodes – and subsequently declined. In the other three cities, price-to-rent ratios grew rapidly in the early to mid-2000s, but have subsequently remained at a permanently higher level. This behaviour suggests that the explosive root tests may have power against alternative hypotheses – other than a rational bubble – such as abrupt structural breaks in fundamentals or nonlinear adjustment in the price-to-rent ratio to changed fundamentals (Pavlidis, Yusupova, Paya, Peel, Martinez-Garcia, Mack and Grossman, 2015).

To investigate these possible alternatives, we estimate a fundamental equilibrium model of a city’s price-to-rent ratio for the period prior to the estimated start-date of their bubble episodes. This model is then used to forecast a path for the long-run (or steady-state) fundamental value of the price-to-rent ratio over the remainder of the sample. Since a rational bubble episode is expected to be transitory, we might expect to observe some convergence between the forecast fundamentals and the observed price-to-rent ratio after the bubble has burst. While we do find some evidence of convergence between estimated fundamentals and house price-to-rent ratios for Sydney and Perth, this is not the case for Brisbane, Adelaide and Canberra. To provide some further evidence we apply a test for parameter stability in co-integrating regressions due to Hansen (1992) to our fundamental models – estimated on the full sample – and find evidence of a break in the effect of the real interest rate on price-to-rent ratios in Brisbane and Adelaide just prior to the periods identified as bubbles by the PSY test. In

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