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Empirical Economics

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01.09.2016

Testing for a housing bubble at the national and regional level: the case of Israel

verfasst von: Itamar Caspi

Erschienen in: Empirical Economics | Ausgabe 2/2016

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Abstract

Between 2008 and 2013, home prices in Israel appreciated by roughly 50 % in real terms, with increases in nearly 60 % in some regions. This paper examines whether this phenomenon reflects the presence of a national or regional housing bubble by applying econometric tests for explosive behavior to quality-adjusted national- and regional-level data on the home price to rent ratio, while controlling for various fundamental factors, including interest rates, income and the leverage ratio. Overall, study results indicate that the national- and regional-level data are inconsistent with a housing bubble scenario. Most of the results are robust to a variety of tests and alternate specifications. The framework I provide to study the Israeli case may be applied to study other housing markets facing similar developments.

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Diba and Grossman (1988a) were among the first to argue that given a constant discount factor, identifying explosive characteristics in stock prices is equivalent to detecting a bubble.

Regional-level analysis is common in the empirical literature on housing bubbles. For examples see Himmelberg et al. (2005), Case and Shiller (2003), Smith and Smith (2006), Clark and Coggin (2011).

Some other bubble detection strategies, not discussed here, include comparing the annual cost of housing to actual rent (Himmelberg et al. 2005) and a direct derivation of the fundamental price using ex post and projected fundamentals (Smith and Smith 2006).

The “International House Price Database of the Federal Reserve Bank of Dallas” is documented in Mack and Martínez-García (2011).

Case and Shiller (2003), Smith and Smith (2006), Himmelberg et al. (2005) and McCarthy and Peach (2004) are earlier examples of this strand of literature. These papers focus on the US housing market during the pre-subprime crisis.

Housing bubble indices developed in Dovman et al. (2012) are now updated on a regular basis and used for monitoring purposes by the Bank of Israel.

For surveys on other types of bubbles see Brunnermeier (2008), Iraola and Santos (2008) and Scherbina (2013).

Proving the existence of bubbles can also serve as a tool for discriminating between models (Flood and Hodrick 1990).

For a discussion of the approximation’s accuracy, see “Appendix 1”.

For simplicity of exposition, I choose to ignore other variables that might also be included in $ v_t $, such as depreciation, maintenance, property and transaction taxes, the mortgage rate, leverage etc.

The assumption of constant expected risk premiums (or discount factors) is common in the literature on testing for rational bubbles (Gürkaynak 2008). Nonetheless, relaxing this assumption need not change the main conclusions as long as we rule out explosive risk premiums.

Campbell et al. (2009) assume a time-varying risk premium.

Campbell et al. (2009) assume in their model that no bubbles are present.

The explosiveness property of $ b_t $ comes from the fact that $1+e^{\left( \overline{r-p} \right) }>1$. Hence, when $ b_t\ne 0 $, the log bubble component grows at rate g in expectations, where $ g=e^{\left( \overline{r-p} \right) }>0 $.

Diba and Grossman (1988a) point out another implication of the model, namely, that $ b_t $ can be either zero at all times or positive at all times. To see why, note that a negative value of $ b_t $ today implies that investors expect a future price of zero. Given free disposal, a negative bubble can be ruled out. Yet, a bubble cannot emerge at some point in the future since this necessarily implies that the forecast error of the bubble component is not zero in expectations, thus violating Eq. (9).

See Flood and Hodrick (1990) for an early survey of the literature and Gürkaynak (2008) for an updated survey of econometric tests for bubbles.

Other examples for bubble test methods include the variance bounds test (LeRoy and Porter 1981; Shiller 1981), West’s two-step tests (West 1987) and the intrinsic bubbles test (Froot and Obstfeld 1992).

Phillips et al. (2015b) generalize the PWY procedure such that it is possible to test for multiple bubbles in long time series.

The asymptotic theory of mildly explosive processes is developed in Phillips and Magdalinos (2007).

Large sample properties of the bubble date-stamping procedure are developed in Phillips and Yu (2009).

Hamilton (1986) argues that the interpretation of the results of econometric tests for speculative price bubbles depends on the nature of any nonstationarity in the fundamentals.

Phillips and Magdalinos (2007) define a mildly explosive root using the following data generating process

$$\begin{aligned} y_t=\delta _n y_{t-1}+\varepsilon _t, \end{aligned}$$

where $ \delta _n=1+\frac{c}{k_n}$, and where $ (k_n)_{n\in {\mathbb {N}}} $ is a sequence increasing to $ \infty $ such that $ k_n=o(n) $ as $ n\rightarrow \infty $.

We can think of this sample as a standardized version of true sample (i.e., divided by T ).

For a detailed presentation of the date stamping procedure, see Phillips et al. (2011) and Phillips and Yu (2011).

In order to get a consistent test procedure that asymptotically eliminate type I errors there is a need to let $ \beta _{T} \rightarrow 0 $ as $ T\rightarrow 0 $. However in applied work it is convenient to use a constant $ \beta _{T}$ such as 5 % [see Phillips et al. (2015b)].

Phillips and Yu (2011) argue that the date-stamping procedure requires that the duration of the bubble to be non-negligible. In Phillips et al. (2015b) the authors define $ \log (T)/T $ as a minimal lasting time (in fractional terms of the sample) for a bubble period.

The critical values for 90, 95 and 99 % are 6.315, 12.7 and 63.66, correspondingly.

The problem of a biased estimate also holds when the true data are generated with $ \delta \le 1 $.

The latter is included in the CPI, while the former is not.

Expected inflation here is similar to the notion of the ‘TIPS Spread’ in the USA.

Alternatively, I used the yield on 1-year CPI-indexed government bonds (zero coupon bonds). Results are similar (not presented).

For recent surveys on developments in the Israeli housing market see Dovman et al. (2012) and Nagar and Segal (2010).

For further background on the Israeli stabilization program, see Ben Basat (2002) and Liviatan (2003).

For example, testing for a bubble in the stock market during the early 2000s using some general stock price index might miss the presence of a bubble, since the “dot.com” bubble was largely confined to the technology sector. The NASDAQ Composite Index would be more appropriate in this case.

Based on Monte Carlo simulations, Phillips et al. (2015b) argue that the SIC provides satisfactory sizes for the SADF test.

Adding lags is highly relevant when making use of the home prices index since it is constructed as a smoothed index which makes it serially correlated by construction. (The home prices index reported by the CBS is a 2-month moving average.)

In a more recent paper, Phillips et al. (2015a) suggest adding an asymptotically negligible drift to the data generating process of the null as means of increasing the size and power of the test. Adding this drift term does not change my main conclusions. (Not presented, available on demand.)

Though it is possible to apply tests for explosive behavior to any variable, I note that in general, one can rule out explosive behavior in fundamentals ($ \varDelta r_t $ and $ i_t $ in our case) based on theoretical grounds. This stems from the notion that no plausible economic model gives rise to an equilibrium in which fundamental factors exhibit explosive patterns.

Interestingly, the null of no-bubble in the risk-free rate is close to rejection at the 90 % level. However, closer inspection reveals that the probable cause of the rejection is the sudden drop of 200 bp in the Bank of Israel policy rate on January 2002. The SADF test is close to mistakenly identifying this period as bubble.

I estimated the indirect inference estimator using MATLAB, and I have applied the Euclidean distance metric. The m-file is available on demand.

I have also conducted the SADF test on the price to rent ratio (without log), and on the price to income ratio (with and without log) and was unable to reject the null of no-bubble at conventional levels for either of these indicators. (See “Appendix 1”.)

Recall that according to the date-stamping procedure, crossing the threshold from below signals a starting point of a bubble conditioned on the existence of such a bubble, i.e., declaring the starting point of a bubble can only be made in retrospect. However, crossing the threshold from below may be viewed as an early warning sign of a potential bubble.

The zero coupon rate is derived from an estimate of the real yield curve of Israeli government bonds.

$ {V}_t$ is bounded between $ \tilde{V}_t $ (when $ \lambda _t=0 $) and $ V^m_t $ (when $ \lambda _t=1 $). Since the natural logarithm function is a monotonic transformation, $ {v}_t$ is also bounded between $ \tilde{v}_t $ and $ i^m_t $ (where $ i^m_t\equiv \log I^m_t $).

I owe this part to a suggestion from an anonymous referee.

There is another recent study by Nagar and Segal (2010) who estimate a model of the Israeli housing market using cointegration methods and investigates departures from the long-run levels of home prices and rent. I choose not to refer to their analysis in this comparison since despite relating to the possibility of a bubble, the authors do not explicitly model or estimate it. More specifically, in the theoretical section Nagar and Segal (2010) assume that the transversality condition holds, thus they implicitly rule out rational bubbles.

A table with a sensitivity analysis for changing the minimal window size is presented in “Appendix 1”.

In order to make all statistics comparable, I set the first observation of the sample to 1999:M8, namely 1999:M1 plus the maximum number of lags plus one.

The sample issue is irrelevant to the regional analysis since data for mean rent payments only exists since the first quarter of 1998.

Clearly, a rent index based on existing rent does not properly reflect real-time conditions of the housing market but rather the ones at the time they were signed.

The GSADF procedure can be viewed as a mechanism that ’fines’ possible data mining with the SADF procedure. That is, given a specific sample, one can arbitrarily choose any starting point. Experimenting with different samples involves losing degrees of freedom, thus making the SADF critical values invalid. The GSADF procedure takes this into account by computing correct critical values for a procedure that uses the SADF test for every starting point available.

Prior to 1999 the Owner Occupied Dwellings Services Price Index was calculated indirectly using a variation of the home prices index.

In Israel, the kitchen is not counted as a room, and half a room often refers to a small room.

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Titel: Testing for a housing bubble at the national and regional level: the case of Israel
verfasst von: Itamar Caspi
Publikationsdatum: 01.09.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 2/2016
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-015-1007-y

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