Self-exciting effects of house prices on unit prices in Australian capital cities

Abstract

Chinese

This paper examines the long- and short-run relationship between Australian house and unit prices across all capital cities over the period December 1995 to June 2015. We find that house and unit prices are cointegrated and, based on the results of Granger causality and generalised impulse responses, that house prices significantly influence unit prices across all cities. However, bi-directional causality (responses) exists only for major capital cities with the exception of Brisbane. We also, for the first time, apply self-excited threshold models to explore the complex interplay between house and unit prices in Australia. We find that when the market for units is self-excited, or bullish, the positive effects of house prices on unit prices are noticeably larger than otherwise. There is a varying degree of herd mentality in the Australian property market with Sydney and Darwin being the most and least ‘excitable’ capital cities, respectively.

Keywords

Australia cointegration house prices self-exciting threshold model unit prices

Introduction

Australian housing prices have experienced strong growth since the middle of the 1990s. Unlike many countries, the upward trajectory in Australian housing prices has proven to be resilient in the aftermath of the Global Financial Crisis (GFC).¹ This strong growth has fuelled debate about the existence of a housing bubble in Australian capital cities. Former Prime Minister, Tony Abbott, and former Treasurer, Joe Hockey, have rejected the notion that Australia has a housing bubble (Aston, 2015). However, when appearing before a parliamentary inquiry into home ownership in June 2015, Treasury Secretary, John Fraser, stated that Sydney and parts of Melbourne were ‘unequivocally in a housing bubble’ (Janda, 2015). A feature of the Australian housing market is the growth in inner city units in many capital cities and much of the concern about a housing bubble has focused on oversupply of inner city units, in particular in Melbourne and Sydney (Aston, 2015).² The strong growth in housing prices, coupled with fears of a bubble, suggests that there is a need to better understand the house-unit price nexus in Australia.

In this paper, we examine the long-and-short-run relationship between house and unit prices in the eight capital cities of Australia over the period December 1995 to June 2015, employing a self-exciting threshold model (SETAR). The findings are important for several reasons. First, analysing behaviour of prices in housing submarkets in Australia is important as it is currently in an extended boom and there are fears of a housing bubble. This is in the context of the boom-bust cycle in housing prices that has been experienced in many countries around the world. One of the major causes of the subprime mortgage crisis in the United States (US) was hubris and herd mentality (Lim, 2008). This occurs when expected future capital price gains become unrealistic when extrapolated from recent history leading to excessive borrowing. Application of a SETAR allows us to examine the effect of herding in housing submarkets in Australia and, in particular, observe how the market responds when prices are on upward versus downward trajectories. We find that when unit prices are bullish, house prices exert significantly greater positive impacts on unit prices, suggesting that individuals are highly likely to follow the buying behaviour of others. Such information assists regulators to manage interactions between housing submarkets and potentially avoid the adverse consequences of the bubble that existed in US housing markets.

Second, there is much interest in Australia as to whether houses or units make the better investment. This study has important implications for portfolio decision-making, as it provides insight into the degree of substitutability and co-movement between houses and units as alternative types of investments. The results should be of particular value to those renters who also own a residential property (normally a unit) in a less desirable location. They would like to buy a residential property (normally a house) in a more desirable location at a later point but cannot afford it at the moment.

Third, better understanding of how unit and house prices are related assists urban planners to develop a more effective housing development strategy. This is particularly important in Australia given concerns about land use regulation in the outer suburban areas and the number, and size, of inner city units being built in the most populous cities of Melbourne and Sydney (Birrell and Healy, 2013).

We make the following contributions. First, we consider regional variation between submarkets for Australia, which represents an interesting contrast to the much more studied United Kingdom (UK) and US. In particular, the increased spatial dimension provides an interesting context in which to examine the relationship between house and unit prices. As Akimov et al. (2015) noted, while Australia’s population is just 36% of the UK and 7% of the US, its geographic size is similar to the latter. The Australian population is geographically diverse with a high concentration in a few major cities along the south eastern seaboard. As a consequence, it might be argued that each of the capital cities is more likely to represent separate markets in which house and unit prices in those cities are related, particularly in the more isolated capital cities.

Second, this is not only the first application of a SETAR between different types of housing markets, but it is the first to do so in the context of the Australian housing market. This allows us to explore a number of important features of time series data, which cannot adequately be captured by conventional linear models such as time-irreversibility, limit cycles, jump phenomena and occasional bursts of outlying observations. There are different approaches in the literature each having its own merit. The SETAR has several advantages over other forms of threshold autoregressive models. The estimated parameters in the SETAR exhibit a higher degree of flexibility with more certainty in relation to the prevailing regime at any point in time. The dependent variable is either in one regime or another, given the relevant value of the threshold variable. Franses and Van Dijk (2000: 772) assert that ‘the SETAR model assumes that the border between the two regimes is given by a specific value of the threshold variable’, whereas in a Markov switching model the dependent variable is in both regimes with relevant time-varying probabilities.³

The remainder of the paper is set out as follows. The next section outlines the relationship between house and unit markets. The following section contains a brief review of the literature. We then outline the method and data. The final two sections contain the results and discussion of those results.

Houses and units as submarkets

Based on the most recent census, units represent 13.7% of Australia’s housing stock, with houses the rest (ABS, 2011). The growth in inner city units in many capital cities in Australia has given rise to the emergence of distinct housing submarkets consisting of units and detached and semi-detached housing. These submarkets occur when there are alternative dwelling types that are connected by a chain of substitution (Morrison and McMurray, 1999).

The house and unit submarkets in Australia are largely delineated along geographic lines. There is a concentration of units in the inner city and in major business districts in metropolitan areas, while separate and townhouse dwellings are concentrated in the suburbs. Units in the inner city and major metropolitan business districts and detached and semi-detached suburban housing respond to heterogeneous preferences along a range of dimensions. Important first considerations are size and cost. In Melbourne, for instance, most units are small (70 square metres or less). It is not possible to construct and sell family-friendly units (90 square metres or more) for less than AUD700,000. Detached houses in the suburbs of the capital cities can be purchased for less than two bedroom units in the inner city (Birrell and Healy, 2013). For example, in the outer eastern suburbs of Melbourne, one can purchase a four bedroom detached house with its own back-and-front enclosures for AUD350,000–400,000.

A second aspect is heterogeneous preferences in terms of how close one wants to live to one’s workplace and the number of hours one spends at work. Morrison and McMurray (1999) found that an important market for inner city apartments in Wellington were high-income singles, who worked long hours in the city. In Australia there has been a gentrification of the inner city in which middle and high income white collar workers have moved in, forcing lower income individuals and families into housing estates on the city fringes (Wulff and Lobo, 2009).

A third aspect is preferences for a house and garden setting. The Great Australian Dream was always couched in terms of a detached house on a quarter acre block. While this is still undoubtedly the dream for many, perhaps reflecting longer working hours, others are shunning this idea in favour of living in the inner city or close to major business districts in smaller residences. For these people, being close to good restaurants, major sporting events and cultural events that are less readily available in the suburbs are major attractions.

House and unit submarkets in the long run

While units and detached housing are submarkets, we expect these markets to be connected in the long run because they represent substitute forms of accommodation. Property markets, by their nature, are highly co-dependent. When Granger (1986: 213) first developed the concept of cointegration, one of the examples of variables that are potentially bound together in the long run that he gave was ‘market prices of substitute commodities’. If housing markets are efficient, arbitrage should take place to eliminate price differences across submarkets.

One reason for expecting property markets to be cointegrated is that housing represents both a consumption and investment good. As an investment good, households can borrow against their equity in the home and invest in a second property. This is particularly prevalent in a home ownership society such as Australia. Negative gearing encourages individuals to borrow against the equity in their home to buy an investment property. Capital gains tax provisions, introduced in September 1999, facilitate this phenomenon. The changes to the capital gains tax provided investors with a 50% discount on capital gains tax if they hold their property for one year. Investors with self-managed superannuation funds can also borrow to finance investment in property, allowing them to take advantage of negative gearing. In 2010, 10% of Australian taxpayers owned a negatively geared investment property (Colebatch, 2010). In November 2011, investors accounted for 41.5% of mortgages taken out (excluding refinancing), but by June 2015 this figure had increased to 52% (Jericho, 2015).

From the viewpoint of the potential investor, units and detached housing represent substitutable investments. Both the housing and unit submarket are used by the buy-to-let market. In percentage terms, the split between markets for investment purposes is fairly even. According to the most recent census in 2011, 44.8% of renters lived in multi-unit buildings, while 54.5% of renters lived in detached housing (ABS, 2011). That over half of renters lived in detached housing reflects several factors (Stone et al., 2013). One factor is that detached housing gives investors more control because they do not need to purchase with a body corporate. A second factor is that many ‘mum and dad investors’, who own a negatively geared investment property, live in the suburbs and prefer to purchase in the local area with which they are familiar. A third factor has been demand for rental accommodation from lower income families with children who live in the suburbs. In 2011, 40.4% of renters were family households (ABS, 2011). A fourth factor is that many renters have been priced out of the inner city in which most units are located.

Much of the growth in Australia’s inner city unit market has been fuelled by strong investor interest from Asia and, in particular, China. Asian developers and investors have been the major participants in the inner city unit market in Melbourne and Sydney since the late 2000s (Birrell and Healy, 2013; Johanson, 2014). Affluent individuals from mainland China are increasingly looking offshore to hedge against political risk at home. The preferred cities for investing have been London, Vancouver, Melbourne and Sydney (Johanson, 2014). In 2015, it was reported that Brisbane and the Gold Coast are becoming new preferred destinations for Chinese property investors, attracted by lower prices in those locales (Ludlow, 2015). On the demand side, there has been strong demand for inner city units from international students, in particular in Melbourne and Sydney. The peak of the international student demand in Australia was 2010, prior to changes in migration rules. In 2010, for example, it was estimated that there were almost 18,000 international students residing in inner Melbourne alone, many of which were the main occupants of the cheaper, smaller unit stock in the city (Birrell and Healy, 2013).

Another reason for expecting detached housing and units to be connected in the long-run is by way of analogy to the suggestion that regional house prices might converge due to migration flows between regions (Meen, 1999). The same reasoning can be applied to the demographic-based flows between inner city units and detached housing. One major category of those occupying inner city units is single young professionals. When they get married and have children, many prefer a house and garden in the suburbs. Moving in the opposite direction, a second major category of those occupying inner city units are older empty nesters who have downsized when their children leave home (Liu and Daly, 2011). If these flows are large enough, in the long run price differences between detached housing and units will be arbitraged away.

Literature review

Most of the time series literature on housing prices has focused on whether there is regional convergence in house prices (see e.g. Blanco et al., 2015; Gupta et al., 2014). Relatively few studies have examined links between house prices and other variables. Most have focused on the relationship between house prices and market fundamentals (Oikarinen, 2014). Other studies have focused on the relationship between house and other asset prices, such as stocks (He, 2000) or house prices and macroeconomic variables (Kemme and Roy, 2012). Jones et al. (2003) apply time series methods to test the stability of spatial housing markets in Glasgow. Jones and Leishman (2006) examine the house price ripple effect at the level of local housing markets using housing data for Strathclyde. Only a limited number of recent studies have used SETAR to examine bullish or bearish behaviour of housing prices in the UK and US (Barari et al., 2014; Park and Hong, 2012; Walther, 2011). In contrast to our study, these studies apply SETAR to analyse cycles or forecast house price movements in a single house price index, rather than the relationship between housing submarkets, such as units and houses.

Among existing Australian studies, most of the literature has concentrated on determinants of house prices (Abelson et al., 2013). Some of the Australian literature mirrors that for other countries. There are studies of regional house price convergence (Ma and Liu, 2014) and the relationship between house prices and market fundamentals (Costello et al., 2011). Other studies examine issues such as common cycles in house prices (Akimov et al., 2015).

To summarise, there are no studies applying SETAR models to house prices outside the UK and US, focusing on the relationship between different submarkets. We address this issue by examining the market dynamics of Australian housing and unit prices.

Methodology

We examine time series properties of the data by using the Augmented Dickey and Fuller and additive outlier unit root tests (Vogelsang and Perron, 1998). We then apply the Johansen (1995) and Hansen (1992) tests to examine cointegration between each pair. We conduct a conventional Granger causality test between monthly returns of house and unit prices. The optimal lag length is chosen using the Schwarz information criterion (SIC). To examine future dynamic behaviour of unit prices to shocks affecting house prices, we also use generalised impulse response functions.

To address endogeneity caused by long-run covariation between the residuals and the right hand side variable, we use Fully Modified Ordinary Least Squares (FMOLS) (Phillips, 1995). With this approach the initial OLS estimates of the symmetric and one-sided long-run covariance matrix of the residuals are modified using a semi-parametric correction. The FMOLS estimators are asymptotically unbiased with fully efficient mixture normal asymptotics. Once cointegration is established, the long-run relationship between house and unit prices can be written as:

U_{t} = ϕ_{0} + ϕ_{1} T_{t} + ϕ_{2} H_{t} + e_{t}

(1)

Where:

U_t = Ln(UP_t),

H_t = Ln(HP_t),

UP_t = monthly unit prices at time t,

HP_t = monthly house prices at time t,

T_t = time trend,

e_t = random residuals at time t,

Ln = natural logarithm, and

$ϕ s$ = long-run coefficients to be estimated.

The above equation assumes that the cointegrating vector is normalised in terms of unit prices. Given the causality test results, such an assumption is reasonable. The time trend variable is kept in the regression as long as it is statistically significant. In order to avoid the loss of important information in level data, we incorporate the resulting lagged residual from the cointegrating equation as an error correction (e_t-1 = EC_t–1) mechanism into a short-run dynamic model. However, a self-exciting model can represent a number of important features of time series data, which cannot adequately be captured by conventional Gaussian linear models. The parameters of self-exciting models enjoy a higher degree of flexibility through regime switching behaviour. We adopt a two-regime self-exciting threshold model of order k with the threshold parameter γ:

\begin{array}{l} Δ U_{t} = (α_{1} + \sum_{i = 0}^{k} β_{1 i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{1 i} Δ U_{t - i} + μ_{1} E C_{t - 1}) (Δ U_{t - d} < γ) + \\ (α_{2} + \sum_{i = 0}^{k} β_{2 i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{2 i} Δ U_{t - i} + μ_{2} E C_{t - 1}) 1 (Δ U_{t - d} \geq γ) + ε_{t} \end{array}

(2)

Where 1(·) is the indicator function, which equals one if the condition in the parentheses is met and zero otherwise, d is the length of the delay and $ε_{t}$ is the stochastic residual series distributed independently and identically with zero mean and finite non-zero variance σ². Unlike a conventional short-run dynamic model, at any point in time the intercept, the slope and error correction coefficients can all switch from regime 1 ( $α_{1}$ , $β_{1 i}$ , $λ_{1 i}$ and $μ_{1}$ ) to regime 2 ( $α_{2}$ , $β_{2 i}$ , $λ_{2 i}$ and $μ_{2}$ ) depending on the value taken by the ‘threshold variable’ or $Δ U_{t - d}$ . Equation (2) can also be written in a compact form:

Δ U_{t} = \sum_{j = 1}^{2} 1_{j} (Δ U_{t - d}, γ) \cdot [α_{j} + \sum_{i = 0}^{k} β_{j i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{j i} Δ U_{t - i} + μ_{j} E C_{t - 1}] + ε_{t}

(3)

If the threshold variable was a variable other than the lagged dependent variable, we would have a conventional threshold model. Moreover, if all $β_{ji}$ coefficients were set equal to zero, equation 3 would be reduced to a SETAR model. In order to estimate the ‘nuisance parameters’ (γ, d), it is a standard practice to conduct a two-dimensional grid search for γ and d. For each pair (γ, d) in the grid, the indicator function is first defined and equation (2) is estimated. Then, based on a given trimming region, a lower bound γ^l and an upper bound γ^u are defined for the threshold parameter. We assume the trimming percentage to be 15. Within the specified range for γ, the aim is to minimise the residual sum of squares (RSS) with respect to the four sets of parameters:

S (β_{j i}, λ_{j i}, μ_{j}, γ) = \sum_{t = 1}^{T} {Δ U_{t - d} - \sum_{j = 1}^{2} 1_{j} (Δ U_{t - d}, γ) \cdot [α_{j} + \sum_{i = 0}^{k} β_{j i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{j i} Δ U_{t - i} + μ_{j} E C_{t - 1}]}^{2}

(4)

We add a small increment such as 0.0001 to the lower bound (i.e. γ^l+ 0.0001) and re-estimate RSS. In the next iteration we consider γ^l+ 0.0002 and record RSS. This iterative process continues until we reach the upper bound γ^u. We then select an optimum value of the threshold, which yields the lowest residual sum of squares:

\begin{matrix} \hat{γ} = arg min RSS (γ) \\ γ \in [γ^{l}, γ^{u}] \end{matrix}

(5)

Knowing d a priori does not affect the asymptotic properties of the estimators (Chan, 1993). After determining (γ, d), the sample is divided into two sub-samples and a conventional estimation method can then be applied to each sub-sample. The threshold model (equation 3) is tested against a standard non-threshold linear model using the Bai and Perron (2003) test. The number of regimes can be decided based on theory or preliminary examination of the data.

Data

Monthly house and unit prices from December 1995 to June 2015 for Australia’s eight capital cities (Adelaide, Brisbane, Canberra, Darwin, Hobart, Melbourne, Perth and Sydney) are sourced from CoreLogic RP Data.⁴ The series are compiled based on the hedonic imputation methodology, which is recognised as being robust at varying levels of disaggregation both across time and space (Goh et al., 2012). This method utilises information from transacting properties and their attributes for the general stock of housing at any given location and time interval to impute a value for properties having a certain set of characteristics. The sample may include both sold and unsold properties. By considering a wide range of property attributes, this approach reduces bias that exists in other house price indicators for Australia such as median or repeat sale indices. Moreover, unlike the ABS or Real Estate Institute of Australia (REIA) price indices, which are only available at quarterly frequency with a much shorter sample period, CoreLogic RP Data are available monthly, enabling us to estimate the SETAR models with sufficient sample size.

Results

Preliminary statistics

Summary statistics of house and unit prices are shown in Table 1. The highest average house and unit prices are observed in Sydney (AUD539,000, AUD403,000) and the lowest in Hobart (AUD246,000, AUD214,000) with Perth displaying the greatest volatility for both house (AUD188,000 = standard deviation) and unit (AUD141,000) prices. All 16 house and unit price series resemble a platykurtic distribution as Kurtosis is less than three. Except house prices in Melbourne, all other price series are negatively skewed, suggesting that the median is greater than the mean. The Jarque-Bera normality hypothesis is rejected for all series at the 1% level of significance, except for prices in Sydney, which are rejected at 10%.

Table 1.

Summary statistics of the monthly data (1995M12–2015M06).

City	No. obs.	Mean($ 000)	Max.($ 000)	Min.($ 000)	Std. Dev.$ 000	Skewness	Kurtosis	Jarque-Bera χ²
Adelaide
Houses	235	307	472	125	126	−0.216	1.421	26.24^*
Units	235	244	369	114	94	−0.166	1.392	26.40^*
Brisbane
Houses	235	340	521	140	144	−0.238	1.380	27.90^*
Units	235	283	418	151	97	−0.089	1.314	28.15^*
Canberra
Houses	235	414	642	159	172	−0.276	1.524	24.33^*
Units	235	301	444	135	110	−0.354	1.521	26.31^*
Darwin
Houses	195	366	578	183	144	−0.017	1.352	22.08^*
Units	195	298	473	141	111	−0.097	1.394	21.26^*
Hobart
Houses	235	246	371	105	104	−0.340	1.306	32.65^*
Units	214	214	318	73	83	−0.526	1.636	26.48^*
Melbourne
Houses	235	422	760	147	185	0.064	1.688	17.02^*
Units	235	319	510	129	122	−0.059	1.700	16.68^*
Perth
Houses	235	394	644	152	188	−0.068	1.226	31.00^*
Units	235	319	510	140	141	−0.060	1.246	30.26^*
Sydney
Houses	235	539	972	221	180	−0.079	2.338	4.54
Units	235	403	651	198	113	−0.052	2.245	5.69

Note: ^*Significant at 5% or better.

Figure 1 presents the individual time series plots of house and unit prices for each city separately. House and unit prices exhibit a strong degree of co-movement without any sign of collapsing over time. House and unit prices tend to deviate from each other quite often; however, as can be seen by the green dotted lines in Figure 1, every now and then the inflated gap is narrowed (adjusted). In all cities, except for Canberra, the narrowing takes place after a sustained period of widening. This suggests that most homebuyers may eventually consider houses and units to be close substitutes, even if they initially regard them differently.

Figure 1.

Monthly house and unit prices in Australian capital cities.

Unit root and cointegration test results

The ADF test results indicated that most prices are I(1) and all 16 monthly growth series become I(0) when we apply the additive outlier test with one breakpoint in the trend function.⁵Table 2 shows the results of the Johansen (1995) and Hansen (1992) tests suggesting that H_t and U_t are cointegrated and the long-run relationship is not subject to significant instability.

Table 2.

Johansen and Hansen cointegration tests.

No. ofvectors	Johansen test					Hansen test
	Eigenvalue	Max-eigenstatistic	5% criticalvalue	Tracestatistic	5% criticalvalue	Lc statistic	p-value
Adelaide
None	0.14	36.47^*	15.89	40.41^*	20.26
At most 1	0.02	3.93	9.16	3.93	9.16	0.038	> 0.20
Brisbane
None	0.08	18.28^*	14.26	20.82^*	15.49
At most 1	0.01	2.55	3.84	2.55	3.84	0.075	> 0.20
Canberra
None	0.06	14.24^*	11.22	14.32^*	12.32
At most 1	0.00	0.08	4.13	0.08	4.13	0.103	> 0.20
Darwin
None	0.09	18.13^*	15.89	25.89^*	20.26
At most 1	0.04	7.75	9.16	7.75	9.16	0.086	> 0.20
Hobart
None	0.07	16.11^*	15.89	23.07^*	20.26
At most 1	0.03	6.96	9.16	6.96	9.16	0.113	> 0.20
Melbourne
None	0.13	32.14^*	15.89	34.14^*	20.26
At most 1	0.01	2.00	9.16	2.00	9.16	0.083	> 0.20
Perth
None	0.06	15.19	15.89	22.45^*	20.26
At most 1	0.03	7.25	9.16	7.25	9.16	0.109	> 0.20
Sydney
None	0.14	35.45^*	15.89	38.87^*	20.26
At most 1	0.01	3.42	9.16	3.42	9.16	0.343	0.19

Note: ^*Significant at 5% or better.

Causality and generalised impulse responses

The causality test results between ΔU_t = ΔLn(UP_t) and ΔH_t = ΔLn(HP_t) are presented in Table 3. The VAR version of the Granger causality test reveals that short-run changes in house prices can influence unit prices in all capital cities. However, unit price changes affect house prices only in Adelaide, Melbourne, Perth and Sydney. Therefore, with the exception of Brisbane, bi-directional causality exists only for the larger cities. In the smaller capital cities (Canberra, Darwin and Hobart) house prices can influence unit prices, but not the other way around.

Table 3.

Granger causality test between house and unit prices.

City	Null hypothesis				Optimal lag length	SIC
	ΔU_t does not cause ΔH_t		ΔH_t does not cause ΔU_t
	F statistic	p-value	F statistic	p-value
Adelaide	8.53	< 0.01	6.36	< 0.01	3	−12.27
Brisbane	1.31	0.27	11.34	< 0.01	3	−12.79
Canberra	1.26	0.29	24.41	< 0.01	2	−12.20
Darwin	0.76	0.38	10.04	< 0.01	1	−9.73
Hobart	0.26	0.61	4.57	0.03	1	−9.35
Melbourne	21.27	< 0.01	8.36	< 0.01	1	−12.77
Perth	2.90	0.04	22.27	< 0.01	3	−12.53
Sydney	5.56	0.02	19.04	< 0.01	1	−13.43

Figure 2 shows the generalised impulse responses of ΔU_t to a one standard deviation shock imposed on the corresponding innovations of ΔH_t using the estimated VAR model. The results for the impulse responses are fairly consistent with the Granger causality test results in that unit prices react to changes in house prices in almost all cities, particularly in Adelaide, Canberra, Darwin, Hobart, Melbourne and Sydney. In Darwin, Hobart, Melbourne and Sydney the dynamic responses die off after approximately five months, whereas in the other capital cities these responses are smaller albeit more persistent.

Figure 2.

Generalised impulse responses of ΔU_t to ΔH_t to 10 months ahead.

Estimated self-exciting threshold models

The estimated SETARs for all eight cities are shown in Table 4. For comparative purposes, if ${\hat{β}}_{1 i}$ or ${\hat{λ}}_{1 i}$ in regime 1 are statistically significant, the corresponding coefficients for regime 2 (i.e. ${\hat{β}}_{2 i}$ or ${\hat{λ}}_{2 i}$ ) are also reported irrespective of whether they are significant or not. Out of 16 error correction coefficients ( $μ_{1 i}$ and $μ_{2 i}$ ), nine are statistically significant at the 10% level or better with the expected negative sign. Table 4 reveals that the estimated error correction coefficients in all capital cities (except Adelaide, Canberra and Darwin) are smaller (in absolute values) when the market is self-excited. This makes intuitive sense because when the market is bullish, it typically takes longer to eliminate the resulting disequilibrium. Despite the fact that the dependent variable is in logarithmic differences, the eight estimated equations presented in Table 4 perform well in terms of goodness-of-fit statistics, particularly for Sydney ( ${\bar{R}}^{2}$ = 0.554), Melbourne ( ${\bar{R}}^{2}$ = 0.508) and Perth ( ${\bar{R}}^{2}$ = 0.411). The residual-based diagnostic tests in Table 4 also indicate that there is no sign of serial correlation. The coefficient sum of the lagged dependent variables in both regimes, i.e. $\sum λ_{1 i}$ and $\sum λ_{2 i}$ , are well below unity.

Table 4.

Estimated self-exciting threshold models. $Δ U_{t} = (α_{1} + \sum_{i = 0}^{k} β_{1 i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{1 i} Δ U_{t - i} + μ_{1} E C_{t - 1}) 1 (Δ U_{t - 1} < γ) + (α_{2} + \sum_{i = 0}^{k} β_{2 i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{2 i} Δ U_{t - i} + μ_{2} E C_{t - 1}) 1 (Δ U_{t - 1} \geq γ) + ε_{t}$ .

Variable	Adelaide		Brisbane		Canberra		Darwin
	ΔU_t–1 < 0.0154 (n = 183)		ΔU_t–1 < 0.0047 (n = 109)		ΔU_t–1 < 0.0062 (n = 119)		ΔU_t–1 < 0.0240 (n = 157)
	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value
Intercept	0.001	0.249	0.003	0.043	0.000	0.80	0.003	0.16
ΔH_t	0.488	0.000	0.275	0.046	0.257	0.04	0.069	0.42
ΔH_t–1	0.127	0.216			0.316	0.01	0.167	0.07
ΔH_t–3	−0.058	0.565
Sum	0.557		0.275		0.573		0.236
ΔU_t–1	−0.198	0.020	−0.235	0.032	−0.191	0.02	0.091	0.33
ΔU_t–2							−0.028	0.69
ΔU_t–3	−0.277	0.000	−0.068	0.433			0.212	0.00
ΔU_t–4							0.100	0.15
ΔU_t–5							−0.119	0.09
ΔU_t–6							0.222	0.00
EC_t–1	−0.065	0.013	−0.077	0.012	−0.098	0.03	−0.073	0.00
	ΔU_t–1≥ 0.0154 (n = 47)		ΔU_t–1≥ 0.0047 (n = 121)		ΔU_t–1≥ 0.0062 (n = 111)		ΔU_t–1≥ 0.0240 (n = 30)
Intercept	−0.003	0.637	0.006	0.007	0.002	0.15	0.010	0.35
ΔH_t	0.980	0.000	0.443	0.000	0.515	0.00	0.592	0.00
ΔH_t–1	0.425	0.004			0.369	0.00	0.329	0.09
ΔH_t–3	0.488	0.002
Sum	1.894		0.443		0.884		0.921
ΔU_t–1	−0.254	0.239	−0.473	0.001	−0.079	0.37	−0.764	0.00
ΔU_t–2							−0.503	0.01
ΔU_t–3	−0.321	0.009	0.353	0.000			−0.098	0.53
ΔU_t–4							0.969	0.00
ΔU_t–5							0.836	0.00
ΔU_t–6							0.076	0.71
EC_t–1	−0.103	0.137	−0.037	0.091	−0.177	0.00	−0.056	0.43
Adjusted R²	0.386		0.308		0.383		0.328
Overall F test	12.08		12.32		16.79		5.78
DW	1.97		2.02		1.96		2.03
SIC	−5.871		−6.129		−5.997		−4.735
BGSC^(a) LM test	F(2214) = 0.227	0.80	F(2218) = 0.365	0.69	F(2218) = 1.308	0.27	F(2165) = 1.922	0.15
Scaled F test^(b)	40.52	0.00	19.84	0.00	39.55	0.00	51.05	0.00
Variable	Hobart		Melbourne		Perth		Sydney
	ΔU_t–1 < –0.0211 (n = 37)		ΔU_t–1 < 0.0107 (n = 155)		ΔU_t–1 < 0.0010 (n = 67)		ΔU_t–1 < 0.0000 (n = 61)
	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value
Intercept	−0.026	0.03	0.001	0.27	0.001	0.71	−0.002	0.03
ΔH_t	0.187	0.69	0.669	0.00	0.465	0.00	0.405	0.00
ΔH_t–1	0.593	0.04	0.245	0.00	−0.185	0.17	0.055	0.60
ΔH_t–2			−0.072	0.25			−0.344	0.00
ΔH_t–3	−0.170	0.67			0.288	0.04	0.302	0.00
Sum	0.609		0.841		0.567		0.419
ΔU_t–1	−0.694	0.01	−0.312	0.00	−0.287	0.02
ΔU_t–2	0.518	0.00			−0.270	0.01	−0.579	0.00
ΔU_t–3			−0.019	0.79			0.518	0.00
ΔU_t–4					0.229	0.02
EC_t–1	−0.139	0.02	−0.029	0.22	−0.161	0.00	−0.036	0.44
	ΔU_t–1≥–0.0211 (n = 173)		ΔU_t–1≥ 0.0107 (n = 75)		ΔU_t–1≥ 0.00101 (n = 162)		ΔU_t–1≥ 0.0000 (n = 169)
Intercept	0.001	0.62	−0.003	0.32	−0.001	0.31	0.002	0.00
ΔH_t	0.520	0.00	0.665	0.00	−0.028	0.79	0.365	0.00
ΔH_t–1	0.036	0.84	−0.043	0.72	0.504	0.00	0.175	0.00
ΔH_t–2			0.356	0.00			−0.033	0.55
ΔH_t–3	0.294	0.05			0.254	0.06	0.033	0.58
Sum	0.849		0.978		0.730		0.540
ΔU_t–1	−0.012	0.91	0.072	0.66	−0.032	0.76
ΔU_t–2	−0.034	0.66			0.190	0.02	−0.077	0.31
ΔU_t–3			−0.052	0.52			−0.014	0.86
ΔU_t–4					0.005	0.95
EC_t–1	−0.056	0.04	−0.002	0.94	−0.033	0.30	0.006	0.81
Adjusted R²	0.193		0.508		0.411		0.554
Overall F test	4.85		19.15		11.59		19.97
DW	1.99		1.95		2.00		2.01
SIC	−3.930		−6.565		−6.028		−7.210
BGSC^(a) LM test	F(2194) = 1.520	0.22	F(2214) = 0.161	0.85	F(2211) = 1.778	0.17	F(2212) = 0.239	0.79
Scaled F test^(b)	25.41	0.05	23.58	0.05	39.72	0.00	52.07	0.00

Notes: (a) BGSC = Breusch-Godfrey Serial Correlation. (b) The Bai-Perron test (2003) for zero versus one threshold. (c) The results in the upper part of the table are related to $α_{1} + \sum_{i = 0}^{k} β_{1 i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{1 i} Δ U_{t - i} + μ_{1} E C_{t - 1}$ when $Δ U_{t - 1} < γ$ . The lower part shows the results corresponding to $α_{2} + \sum_{i = 0}^{k} β_{2 i} Δ H_{t - i} + \sum_{i = 1}^{k} λ_{2 i} Δ U_{t - i} + μ_{2} E C_{t - 1}$ when $Δ U_{t - 1} \geq γ$ .

Using a conventional 15% trimming region, the estimated threshold parameter ( $\hat{γ}$ ) is positive for seven out of eight cities: Adelaide (0.0154), Brisbane (0.0047), Canberra (0.0062), Darwin (0.0240), Hobart (–0.0211), Melbourne (0.0107), Perth (0.0010) and Sydney (0.0000). To illustrate what the monthly growth figures in parenthesis imply, consider Adelaide as an example. In Adelaide when unit prices are on an upward trajectory [regime 2 with a return exceeding 1.54% in the previous month or ΔLn(UP_t-1)≥ 0.0154], a 1% increase in house prices has a total effect ( $\sum {\hat{β}}_{2 i}$ ) of 1.89% on unit prices. However, when the market is not ‘excited’ and the previous month’s growth rate is below 1.54%, the above total effect ( $\sum {\hat{β}}_{1 i}$ = 0.56%) in regime 1 is less than one-third of that of regime 2. Therefore, rising house prices has a three-fold greater positive influence on unit prices when the Adelaide property market for units is ‘excited’ (i.e. experiencing monthly growth in excess of 1.54%).

With a threshold of zero ( $\hat{γ}$ = 0.00) the Sydney market for units is the most ‘excitable’ city (see Table 4). When unit prices experience negative growth, a 1% rise in house prices boosts unit prices by 0.418%, but when unit prices experience positive monthly growth (however small), this same rise leads to a 0.54% increase. While $\sum {\hat{β}}_{1 i}$ = 0.54 for Sydney, which is lower than most other cities (e.g. Adelaide, Darwin and Melbourne), it has enjoyed a bullish property market for a longer period (n = 169 in the second regime) – see the corresponding n in Table 4. The threshold parameter (1.07%) for Melbourne is more than that of Sydney (0.00%), suggesting that Melbourne requires greater growth in unit prices to get excited. However, both $\sum {\hat{β}}_{1 i}$ = 0.842 and $\sum {\hat{β}}_{2 i}$ = 0.978 for Melbourne are greater than those of Sydney.

Hobart is the only city for which the threshold parameter is negative (–0.0211). This implies that 82% of times during the adjusted sample period (173 out of 210 months), unit prices respond to house prices according to the short-run responses in regime 2. Under these circumstances, within the first three months a 1% increase in Hobart house prices pushes unit prices up by $\sum {\hat{β}}_{2 i}$ = 0.85%. This effect is limited to 0.61% when the previous monthly return is below −2.1%. In a sense one may argue that unit prices in Hobart are easily excitable by a higher chance of switching to regime 2. Having said that, both house and unit prices have been quite stagnant since the 2008 GFC, making Hobart very different from Sydney in terms of the likelihood of market excitability. Unlike all other capital cities, Hobart is the only city where the threshold parameter is negative and the gap between house and unit prices has not been rising since the 2008 GFC. In fact, in October 2010 the two prices were almost equal.

With the highest threshold parameter (0.0240), Darwin is the least excitable city. When the lagged monthly growth rate of unit prices is below 2.4%, a 1% increase in house prices results in a meagre rise (0.234%) in unit prices. Only when unit prices in Darwin enjoy extremely buoyant market conditions do house prices exert a greater degree of influence (regime 2 in lieu of regime 1 with $\sum {\hat{β}}_{2 i}$ = 0.921). This only occurred 16% of the time (30 out of 187 months). Hobart is the only capital city in which the gap between unit and house prices is not widening.

Both Darwin and Hobart are anomalies. Unlike all other capital cities for which house and unit prices are available from 1995 onwards, Darwin and Hobart have smaller sample periods (see also Table 1). Both house and unit prices in Darwin are available after April 1999 and Hobart unit prices after September 1997. As we have a smaller number of observations than for the other capital cities, the results in Table 4 for Darwin and Hobart are not fully comparable and should be viewed with caution. Both cities also have some unique features that may partly account for the results. Darwin has a relatively small and transient population with a lot on ‘fly in, fly out’ workers engaged in mining. Hence, there is relatively less interest in the investor market. Hobart also has a small population, but much more land compared with the large cities.

The results of the Bai-Perron (2003) test, which compares zero threshold (one-regime model) with one threshold (two-regime model), are at the bottom of Table 4. Since the null hypothesis is rejected at the 5% level for all eight cities, the varying threshold effects are statistically justifiable.⁶

Discussion and conclusion

We have examined the dynamic interaction between house prices and unit prices in Australian capital cities. We find that house and unit prices are cointegrated. There are at least three reasons for this finding. First, from the perspective of the potential investor, houses and units are substitutable investments. Second, negative gearing and capital gains provisions encourage individuals to borrow against the equity in their home to buy an investment property, which is often a unit. When the price of the family home rises, this increases demand for units, pushing up their price as well. Third, the long run relationship between house and unit prices is reinforced by demographic-based flows between those purchasing houses and units as owner-occupiers.

Based on the results of Granger causality and generalised impulse responses, house prices significantly influence unit prices across all cities. However, there is bi-directional causality between unit and house prices only in four of the major cities; namely, Adelaide, Melbourne, Perth and Sydney. Based on the SETAR we conclude that when the market for units is self-excited, or bullish, the positive effects of house prices on unit prices are markedly larger than would otherwise be the case. We find evidence of varying degrees of herd mentality in the Australian property market with Sydney and Darwin being the most and least ‘excitable’ cities.

In the introduction we suggested that the findings were important for three reasons – i.e. that they could assist regulators to avoid the subprime crisis that occurred in housing markets in the US; they could assist with urban planning; and they provide investors with useful information. In conclusion, we return to what can be learned from our results for each of these three areas.

We begin with implications of our results for Australia avoiding a housing crisis similar to what occurred in the US. One of the major causes of the subprime crisis in the US was a herding mentality. A widely publicised report by global fund managers PIMCO suggests that low interest rates and rising house prices in Australia are driving a herd mentality (Ryan L, 2015). The SETAR has allowed us to examine whether there is formal evidence of a herd mentality in Australian metropolitan property markets. We find that when unit prices are on the rise (i.e. the market is self-excited or bullish) house prices exert significantly greater positive impacts on unit prices, suggesting that investors exhibit herding behaviour. This is consistent with there being unrealistic expectations about future capital price gains based on recent experience, leading to excessive borrowings that, in turn, further drive unit prices higher.

Our findings for Sydney, in particular, are consistent with a commonly accepted view, evident in the PIMCO report (Ryan L, 2015) that Sydney property prices exhibit irrational exuberance. We show that the herding mentality is manifested in the interplay between submarkets. This result is consistent with the view expressed by 2002 Nobel Prize winner in Economics, Vernon Smith, who, on a visit to Australia in July 2015, expressed the view that Sydney house prices have grown too fast and that the housing bubble centred on Sydney is threatening to burst (Ryan P, 2015). There are various ways in which the hubris might be addressed, including raising interest rates, changing the provisions around negative gearing and reforms to self-managed superannuation. Some of these changes have been introduced. In 2015, the Australian Prudential Regulation Authority placed a cap on growth in lending for property investment, forcing banks to apply stricter lending criteria to investors. The Reserve Bank of Australia has advocated a review of negative gearing tax breaks (Greber, 2015), although radical measures such as this need to be carefully assessed given that they may inadvertently cause a major downturn in housing markets.

Next, we turn to the implications of our results for investors deciding between investing in the housing and unit submarkets. Our results are useful given widespread interest in whether it is better to invest in houses or units. We find that in those cities which are excitable, such as Sydney, investors can profit by investing in units because the positive effects of rising house prices in those cities on unit prices are considerably larger than would otherwise be the case.

Finally, we consider the implications of our results for urban planning. An important reason for the growth in units close to the Central Business District in Melbourne and Sydney is land use regulation at the state and local level, which has greatly reduced affordable land for building (Birrell and Healy, 2013; Liu and Daly, 2011). The building approval process in Melbourne and Sydney has been described as ‘slow and cumbersome’ (Weller and Van Hulten, 2012), impeding suburban development. It is estimated that, on average, it takes from 6.3 to 14.5 years to convert urban fringe land into new houses (Liu and Daly, 2011). Our results suggest that in these major cities growth in unit prices is being driven by growth in house prices. By increasing the availability of affordable land in the urban fringes, urban planners could ease the upward pressure on housing prices and, indirectly, unit prices. A flow through effect would be to make inner city unit living more affordable for lower income households. This, in turn, would assist to address the burgeoning oversupply of inner city units in Melbourne and Sydney (Aston, 2015).

Footnotes

Acknowledgements

We thank the Editor of Urban Studies and four anonymous referees, whose feedback improved earlier versions of this paper. The usual caveat applies.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Notes

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